(a) Only two conservative forces are discussed in this

A 75.0-kg firefighter climbs a flight of stairs 28.0 m high. How much work does he do?

The head of a hammer with a mass of 1.2 kg is allowed to fall onto a nail from a height of 0.50 m. What is the maximum amount of work it could do on the nail? Why do people not just let it fall but add their own force to the hammer as it falls?

How much work did the movers do (horizontally) pushing a 46.0-kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0.50?

How much work did the movers do (horizontally) pushing a 46.0-kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0.50?

What is the minimum work needed to push a 950-kg car 710 m up along a 9.0 incline? Ignore friction

Estimate the work you do to mow a lawn 10 m by 20 m with a 50-cm-wide mower. Assume you push with a force of about 15 N.

Estimate the work you do to mow a lawn 10 m by 20 m with a 50-cm-wide mower. Assume you push with a force of about 15 N.

(II) A lever such as that shown in Fig. 6–35 can be used to lift objects we might not otherwise be able to lift. Show that the ratio of output force, \(F_O\), to input force, \(F_I\), is related to the lengths \(\ell_I\) and \(\ell_O\) from the pivot by \(F_O / F_I = \ell_I / \ell_O\). Ignore friction and the mass of the lever, and assume the work output equals the work input.

A box of mass 4.0 kg is accelerated from rest by a force across a floor at a rate of for 7.0 s. Find the net work done on the box.

(II) A 380-kg piano slides 2.9 m down a \(25^{\circ}\) incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 6–36). Determine: (a) the force exerted by the man, (b) the work done on the piano by the man, (c) the work done on the piano by the force of gravity, and (d) the net work done on the piano. Ignore friction.

(II) Recall from Chapter 4, Example 4–14, that you can use a pulley and ropes to decrease the force needed to raise a heavy load (see Fig. 6–37). But for every meter the load is raised, how much rope must be pulled up? Account for this, using energy concepts.

A grocery cart with mass of 16 kg is being pushed at constant speed up a 12 ramp by a force which acts at an angle of 17 below the horizontal. Find the work done by each of the forces on the cart if the ramp is 7.5 m long.

The force on a particle, acting along the x axis, varies as shown in Fig. 638. Determine the work done by this force to move the particle along the x axis: (a) from to x = 10.0 m; (b) from to x = 0.0 x = 15.0 m.

A 17,000-kg jet takes off from an aircraft carrier via a catapult (Fig. 639a). The gases thrust out from the jets engines exert a constant force of 130 kN on the jet; the force exerted on the jet by the catapult is plotted in Fig. 639b. Determine the work done on the jet: (a) by the gases expelled by its engines during launch of the jet; and (b) by the catapult during launch of the jet.

At room temperature, an oxygen molecule, with mass of typically has a kinetic energy of about How fast is it moving?

If the kinetic energy of a particle is tripled, by what factor has its speed increased? (b) If the speed of a particle is halved, by what factor does its kinetic energy change?

(I) How much work is required to stop an electron \((m = 9.11 \times 10^{-31}\ kg)\) which is moving with a speed of \(1.10 \times 10^6\ m/s\)?

(I) How much work must be done to stop a 925-kg car traveling at 95 km/h?

Two bullets are fired at the same time with the same kinetic energy. If one bullet has twice the mass of the other, which has the greater speed and by what factor? Which can do the most work?

A baseball traveling moves a fielders glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?

An 85-g arrow is fired from a bow whose string exerts an average force of 105 N on the arrow over a distance of 75 cm. What is the speed of the arrow as it leaves the bow?

If the speed of a car is increased by 50%, by what factor will its minimum braking distance be increased, assuming all else is the same? Ignore the drivers reaction time.

At an accident scene on a level road, investigators measure a cars skid mark to be 78 m long. It was a rainy day and the coefficient of friction was estimated to be 0.30. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. (Why does the cars mass not matter?)

At an accident scene on a level road, investigators measure a cars skid mark to be 78 m long. It was a rainy day and the coefficient of friction was estimated to be 0.30. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. (Why does the cars mass not matter?)

A 265-kg load is lifted 18.0 m vertically with an acceleration by a single cable. Determine (a) the tension in the cable; (b) the net work done on the load; (c) the work done by the cable on the load; (d) the work done by gravity on the load; (e) the final speed of the load assuming it started from rest.

A 265-kg load is lifted 18.0 m vertically with an acceleration by a single cable. Determine (a) the tension in the cable; (b) the net work done on the load; (c) the work done by the cable on the load; (d) the work done by gravity on the load; (e) the final speed of the load assuming it started from rest.

A spring has a spring constant k of How much must this spring be compressed to store 45.0 J of potential energy?

If it requires 6.0 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additional 4.0 cm?

A 66.5-kg hiker starts at an elevation of 1270 m and climbs to the top of a peak 2660 m high. (a) What is the hikers change in potential energy? (b) What is the minimum work required of the hiker? (c) Can the actual work done be greater than this? Explain.

A 1.60-m-tall person lifts a 1.65-kg book off the ground so it is 2.20 m above the ground. What is the potential energy of the book relative to (a) the ground, and (b) the top of the persons head? (c) How is the work done by the person related to the answers in parts (a) and (b)?

A novice skier, starting from rest, slides down an icy frictionless 8.0 incline whose vertical height is 105 m. How fast is she going when she reaches the bottom?

(I) Jane, looking for Tarzan, is running at top speed (5.0 m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upward? Does the length of the vine affect your answer?

A sled is initially given a shove up a frictionless 23.0 incline. It reaches a maximum vertical height 1.22 m higher than where it started at the bottom. What was its initial speed?

In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground in order to lift his center of mass 2.10 m and cross the bar with a speed of

A spring with hangs vertically next to a ruler. The end of the spring is next to the 15-cm mark on the ruler. If a 2.5-kg mass is now attached to the end of the spring, and the mass is allowed to fall, where will the end of the spring line up with the ruler marks when the mass is at its lowest position?

A 0.48-kg ball is thrown with a speed of at an upward angle of 36. (a) What is its speed at its highest point, and (b) how high does it go? (Use conservation of energy.)

A 1200-kg car moving on a horizontal surface has speed when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?

A 62-kg trampoline artist jumps upward from the top of a platform with a vertical speed of (a) How fast is he going as he lands on the trampoline, 2.0 m below (Fig.640)? (b) If the trampoline behaves like a spring of spring constant how far down does he depress it? 5.8 * 104 Nm,

A vertical spring (ignore its mass), whose spring constant is is attached to a table and is compressed down by 0.160 m. (a) What upward speed can it give to a 0.380-kg ball when released? (b) How high above its original position (spring compressed) will the ball fly?

A roller-coaster car shown in Fig. 641 is pulled up to point 1 where it is released from rest. Assuming no friction, calculate the speed at points 2, 3, and 4.

Chris jumps off a bridge with a bungee cord (a heavy stretchable cord) tied around his ankle, Fig. 642. He falls for 15 m before the bungee cord begins to stretch. Chriss mass is 75 kg and we assume the cord obeys Hookes law, with If we neglect air resistance, estimate what distance d below the bridge Chriss foot will be before coming to a stop. Ignore the mass of the cord (not realistic, however) and treat Chris as a particle.

What should be the spring constant k of a spring designed to bring a 1200-kg car to rest from a speed of so that the occupants undergo a maximum acceleration of 4.0 g?

An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable breaks when the elevator is at a height h above the top of the spring, calculate the value that the spring constant k should have so that passengers undergo an acceleration of no more than 5.0 g when brought to rest. Let M be the total mass of the elevator and passengers.

A block of mass m is attached to the end of a spring (spring stiffness constant k), Fig. 643. The mass is given an initial displacement from equilibrium, and an initial speed Ignoring friction and the mass of the spring, use energy methods to find (a) its maximum speed, and (b) its maximum stretch from equilibrium, in terms of the given quantities.

A cyclist intends to cycle up a 7.50 hill whose vertical height is 125 m. The pedals turn in a circle of diameter 36.0 cm. Assuming the mass of bicycle plus person is 75.0 kg, (a) calculate how much work must be done against gravity. (b) If each complete revolution of the pedals moves the bike 5.10 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses.

Two railroad cars, each of mass 66,000 kg, are traveling toward each other. They collide head-on and come to rest. How much thermal energy is produced in this collision?

Two railroad cars, each of mass 66,000 kg, are traveling toward each other. They collide head-on and come to rest. How much thermal energy is produced in this collision?

A ski starts from rest and slides down a 28 incline 85 m long. (a) If the coefficient of friction is 0.090, what is the skis speed at the base of the incline? (b) If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level? Use energy methods

A 145-g baseball is dropped from a tree 12.0 m above the ground. (a) With what speed would it hit the ground if air resistance could be ignored? (b) If it actually hits the ground with a speed of what is the average force of air resistance exerted on it?

Suppose the roller-coaster car in Fig. 641 passes point 1 with a speed of If the average force of friction is equal to 0.23 of its weight, with what speed will it reach point 2? The distance traveled is 45.0 m

A skier traveling reaches the foot of a steady upward 19 incline and glides 15 m up along this slope before coming to rest. What was the average coefficient of friction?

A skier traveling reaches the foot of a steady upward 19 incline and glides 15 m up along this slope before coming to rest. What was the average coefficient of friction?

A 66-kg skier starts from rest at the top of a 1200-mlong trail which drops a total of 230 m from top to bottom. At the bottom, the skier is moving How much energy was dissipated by friction?

A projectile is fired at an upward angle of 38.0 from the top of a 135-m-high cliff with a speed of What will be its speed when it strikes the ground below? (Use conservation of energy.)

(II) The Lunar Module could make a safe landing if its vertical velocity at impact is 3.0 m/s or less. Suppose that you want to determine the greatest height h at which the pilot could shut off the engine if the velocity of the lander relative to the surface at that moment is (a) zero; (b) 2.0 m/s downward; (c) 2.0 m/s upward. Use conservation of energy to determine h in each case. The acceleration due to gravity at the surface of the Moon is \(1.62 m/s^2\).

Early test flights for the space shuttle used a glider (mass of 980 kg including pilot). After a horizontal launch at at a height of 3500 m, the glider eventually landed at a speed of (a) What would its landing speed have been in the absence of air resistance? (b) What was the average force of air resistance exerted on it if it came in at a constant glide angle of 12 to the Earths surface?

(I) How long will it take a 2750-W motor to lift a 385-kg piano to a sixth-story window 16.0 m above?

(I) (a) Show that one British horsepower \((550\ ft \cdot lb/s)\) is equal to 746 W. (b) What is the horsepower rating of a 75-W lightbulb?

An 85-kg football player traveling is stopped in 1.0 s by a tackler. (a) What is the original kinetic energy of the player? (b) What average power is required to stop him?

If a car generates 18 hp when traveling at a steady what must be the average force exerted on the car due to friction and air resistance?

An outboard motor for a boat is rated at 35 hp. If it can move a particular boat at a steady speed of what is the total force resisting the motion of the boat?

A shot-putter accelerates a 7.3-kg shot from rest to in 1.5 s. What average power was developed?

A driver notices that her 1080-kg car, when in neutral, slows down from to in about 7.0 s on a flat horizontal road. Approximately what power (watts and hp) is needed to keep the car traveling at a constant 80 kmh?

How much work can a 2.0-hp motor do in 1.0 h?

A 975-kg sports car accelerates from rest to in 6.4 s. What is the average power delivered by the engine?

During a workout, football players ran up the stadium stairs in 75 s. The distance along the stairs is 83 m and they are inclined at a 33 angle. If a player has a mass of 82 kg, estimate his average power output on the way up. Ignore friction and air resistance

A pump lifts 27.0 kg of water per minute through a height of 3.50 m. What minimum output rating (watts) must the pump motor have?

A ski area claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the maximum total power needed.

A 65-kg skier grips a moving rope that is powered by an engine and is pulled at constant speed to the top of a 23 hill. The skier is pulled a distance along the incline and it takes 2.0 min to reach the top of the hill. If the coefficient of kinetic friction between the snow and skis is what horsepower engine is required if 30 such skiers (max) are on the rope at one time?

What minimum horsepower must a motor have to be able to drag a 370-kg box along a level floor at a speed of if the coefficient of friction is 0.45?

A bicyclist coasts down a 6.0 hill at a steady speed of Assuming a total mass of 75 kg (bicycle plus rider), what must be the cyclists power output to climb the same hill at the same speed?

Spiderman uses his spider webs to save a runaway train moving about Fig. 644. His web stretches a few city blocks (500 m) before the train comes to a stop. Assuming the web acts like a spring, estimate the effective spring constant.

A 36.0-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 225 N. For the first 11.0 m the floor is frictionless, and for the next 10.0 m the coefficient of friction is 0.20. What is the final speed of the crate after being pulled these 21.0 m?

. How high will a 1.85-kg rock go from the point of release if thrown straight up by someone who does 80.0 J of work on it? Neglect air resistance.

A mass m is attached to a spring which is held stretched a distance x by a force F, Fig. 645, and then released. The spring pulls the mass to the left, towards its natural equilibrium length. Assuming there is no friction, determine the speed of the mass m when the spring returns: (a) to its normal length (b) to half its original extension (x2).

An elevator cable breaks when a 925-kg elevator is 28.5 m above the top of a huge spring at the bottom of the shaft. Calculate (a) the work done by gravity on the elevator before it hits the spring; (b) the speed of the elevator just before striking the spring; (c) the amount the spring compresses (note that here work is done by both the spring and gravity

(a) A 3.0-g locust reaches a speed of during its jump. What is its kinetic energy at this speed? (b) If the locust transforms energy with 35% efficiency, how much energy is required for the jump

In a common test for cardiac function (the stress test), the patient walks on an inclined treadmill (Fig. 646). Estimate the power required from a 75-kg patient when the treadmill is sloping at an angle of 12 and the velocity is (How does this power compare to the power rating of a lightbulb?)

An airplane pilot fell 370 m after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the pilots mass was 88 kg and his speed at impact was estimate: (a) the work done by the snow in bringing him to rest; (b) the average force exerted on him by the snow to stop him; and (c) the work done on him by air resistance as he fell. Model him as a particle

Many cars have bumpersthat are designed to compress and rebound elastically without any physical damage at speeds below If the material of the bumpers permanently deforms after a compression of 1.5 cm, but remains like an elastic spring up to that point, what must be the effective spring constant of the bumper material, assuming the car has a mass of 1050 kg and is tested by ramming into a solid wall?

In climbing up a rope, a 62-kg athlete climbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used to accomplish this feat?

If a 1300-kg car can accelerate from to in 3.8 s, how long will it take to accelerate from to Assume the power stays the same, and neglect frictional losses

A cyclist starts from rest and coasts down a 4.0 hill. The mass of the cyclist plus bicycle is 85 kg. After the cyclist has traveled 180 m, (a) what was the net work done by gravity on the cyclist? (b) How fast is the cyclist going? Ignore air resistance and friction.

A film of Jesse Owens’s famous long jump (Fig. 6–47) in the 1936 Olympics shows that his center of mass rose 1.1 m from launch point to the top of the arc. What minimum speed did he need at launch if he was traveling at 6.5 m/s at the top of the arc?

Water flows over a dam at the rate of and falls vertically 88 m before striking the turbine blades. Calculate (a) the speed of the water just before striking the turbine blades (neglect air resistance), and (b) the rate at which mechanical energy is transferred to the turbine blades, assuming 55% efficiency

A 55-kg skier starts from rest at the top of a ski jump, point A in Fig. 648, and travels down the ramp. If friction and air resistance can be neglected, (a) determine her speed when she reaches the horizontal end of the ramp at B. (b) Determine the distance s to where she strikes the ground at C

Electric energy units are often expressed in kilowatt-hours. (a) Show that one kilowatt-hour (kWh) is equal to (b) If a typical family of four uses electric energy at an average rate of 580 W, how many kWh would their electric bill show for one month, and (c) how many joules would this be? (d) At a cost of $0.12 per kWh, what would their monthly bill be in dollars? Does the monthly bill depend on the rate at which they use the electric energy?

. If you stand on a bathroom scale, the spring inside the scale compresses 0.60 mm, and it tells you your weight is 760 N. Now if you jump on the scale from a height of 1.0 m, what does the scale read at its peak?

A 65-kg hiker climbs to the top of a mountain 4200 m high. The climb is made in 4.6 h starting at an elevation of 2800 m. Calculate (a) the work done by the hiker against gravity, (b) the average power output in watts and in horsepower, and (c) assuming the body is 15% efficient, what rate of energy input was required

A ball is attached to a horizontal cord of length whose other end is fixed, Fig. 649. (a) If the ball is released, what will be its speed at the lowest point of its path? (b)A peg is located a distance h directly below the point of attachment of the cord. If what will be the speed of the ball when it reaches the top of its circular path about the peg? h = 0.80l, l 3.6 * 106 J. h l Peg F

An 18-kg sled starts up a \(28^\circ\) incline with a speed of 2.3 m/s. The coefficient of kinetic friction is \(\mu_\mathrm {k}=0.25\). (a) How far up the incline does the sled travel? (b) What condition must you put on the coefficient of static friction if the sled is not to get stuck at the point determined in part (a)? (c) If the sled slides back down, what is its speed when it returns to its starting point?

A 56-kg student runs at grabs a hanging 10.0-m-long rope, and swings out over a lake (Fig. 650). He releases the rope when his velocity is zero. (a) What is the angle when he releases the rope? (b) What is the tension in the rope just before he releases it? (c) What is the maximum tension in the rope during the swing?

Some electric power companies use water to store energy. Water is pumped from a low reservoir to a high reservoir. To store the energy produced in 1.0 hour by a 180-MW electric power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Assume the upper reservoir is an average of 380 m above the lower one. Water has a mass of for every 10m3?

A softball having a mass of 0.25 kg is pitched horizontally at 129 km/h. By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch. The distance between the plate and the pitcher is about 15 m.

Problem 1COQ A skier starts at the top of a hill. On which run does her gravitational potential energy change the most: (a), (b), (c), or (d); or are they (e) all the same? On which run would her speed at the bottom be the fastest if the runs are icy and we assume no friction or air resistance? Recognizing that there is always some friction, answer the above two questions again. List your four answers now.

You push very hard on a heavy desk, trying to move it. You do work on the desk: (a) whether or not it moves, as long as you are exerting a force. (b) only if it starts moving. (c) only if it doesn’t move. (d) never—it does work on you. (e) None of the above.

Problem 1P (I) A 75.0-kg firefighter climbs a flight of stairs 28.0 m high. How much work does he do?

Problem 1Q In what ways is the word “work” as used in everyday language the same as it is defined in physics? In what ways is it different? Give examples of both.

Problem 1SL In what ways is the word “work” as used in everyday language the same as it is defined in physics? In what ways is it different? Give examples of both.

Problem 2MCQ A satellite in circular orbit around the Earth moves at constant speed. This orbit is maintained by the force of gravity between the Earth and the satellite, yet no work is done on the satellite. How is this possible? (a) No work is done if there is no contact between objects. (b) No work is done because there is no gravity in space. (c) No work is done if the direction of motion is perpendicular to the force. (d) No work is done if objects move in a circle.

Problem 2P (I) The head of a hammer with a mass of 1.2 kg is allowed to fall onto a nail from a height of 0.50 m. What is the maximum amount of work it could do on the nail? Why do people not just “let it fall” but add their own force to the hammer as it falls?

Problem 2Q Can a centripetal force ever do work on an object? Explain.

Problem 2SL The brakes on a truck can overheat and catch on fire if the truck goes down a long steep hill without shifting into a lower gear. (a) Explain why this happens in terms of energy and power. (b) Would it matter if the same elevation change was made going down a steep hill or a gradual hill? Explain your reasoning. [Hint: Read Sections 6–4, 6–9, and 6–10 carefully.] (c) Why does shifting into a lower gear help? [Hint: Use your own experience, downshifting in a car.] (d) Calculate the thermal energy dissipated from the brakes in an 8000-kg truck that descends a 12° hill. The truck begins braking when its speed is 95 km/h and slows to a speed of 35 km/h in a distance of 0.36 km measured along the road.

When the speed of your car is doubled, by what factor does its kinetic energy increase? () \(\sqrt{2}\) (b) 2. (c) 4. (d) 8. ________________ Equation Transcription: Text Transcription: sqrt 2

Problem 3P (II) How much work did the movers do (horizontally) pushing a 46.0-kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0.50?

Why is it tiring to push hard against a solid wall even though you are doing no work?

Problem 3SL (a) Only two conservative forces are discussed in this Chapter. What are they, and how are they accounted for when you are dealing with conservation of energy? (b) Not mentioned is the force of water on a swimmer. Is it conservative or nonconservative?

A car traveling at a velocity v can stop in a minimum distance d. What would be the car’s minimum stopping distance if it were traveling at a velocity of 2? () d. (b) \(\sqrt{2} d\). (c) 2d. (d) 4d. (e) 8d. ________________ Equation Transcription: Text Transcription: sqrt{2}d

Problem 4P (II) A 1200-N crate rests on the floor. How much work is required to move it at constant speed (a) 5.0 m along the floor against a friction force of 230 N, and (b) 5.0 m vertically?

Problem 4Q Can the normal force on an object ever do work? Explain.

Problem 4SL Give at least two examples of friction doing positive work. Reread parts of Chapters 4 and 6.

Problem 5MCQ A bowling ball is dropped from a height h onto the center of a trampoline, which launches the ball back up into the air. How high will the ball rise? (a) Significantly less than h. (b) More than h. The exact amount depends on the mass of the ball and the springiness of the trampoline. (c) No more than h—probably a little less. (d) Cannot tell without knowing the characteristics of the trampoline.

Problem 5P (II) What is the minimum work needed to push a 950-kg car 710 m up along a 9.0° incline? Ignore friction.

You have two springs that are identical except that spring 1 is stiffer than spring \(2\left(k_{1}>k_{2}\right)\). On which spring is more work done: (a) if they are stretched using the same force; (b) if they are stretched the same distance? Equation Transcription: Text Transcription: 2 (k_1 > k_2)

Show that on a roller coaster with a circular vertical loop (Fig. 6–51), the difference in your apparent weight at the top of the loop and the bottom of the loop is 6.0 times your weight. Ignore friction. Show also that as long as your speed is above the minimum needed (so the car holds the track), this answer doesn’t depend on the size of the loop or how fast you go through it. [Reread Sections 6–6, 5–2, and 4–6.]

A box is dragged a distance d across a floor by a force \(\vec{F}_{P}\) which makes an angle \(\theta\) with the horizontal as in Fig. 6–1 or 6–3. If the magnitude of \(\vec{F}_{P}\) is held constant but the angle \(\theta\) is increased, the work done by \(\vec{F}_{P}\) () remains the same; (b) increases; (c) decreases; (d) first increases, then decreases. ________________ Equation Transcription: Text Transcription: vector F_P theta vector F_P theta vector F_P

(a) Make a guess: will the work needed to accelerate the car in Example 6–4 from rest to (\(20\mathrm{\ m}/\mathrm{s}\) be more than, less than, or equal to the work already calculated to accelerate it from to (\(20\mathrm{\ m}/\mathrm{s}\) to (\(30\mathrm{\ m}/\mathrm{s}\)? b) Make the calculation. ________________ Equation Transcription: Text Transcription: 20 m/s 20 m/s 30 m/s v1=60 km/h v2=0 F d(d=20 m) v1=1200 km/h v2=0 F d(d=?) 60 km/h 120 km/h

Problem 6EC Can kinetic energy ever be negative?

Problem 6ED (a) If the kinetic energy of a baseball is doubled, by what factor has its speed increased? (b) If its speed is doubled, by what factor does its kinetic energy increase?

An object acted on by a constant force F moves from point 1 to point 2 and back again. The work done by the force F in this round trip is 60 J. Can you determine from this information if F is a conservative or nonconservative force?

Problem 6EF Return to the Chapter-Opening Question, page 138, and answer it again now. Try to explain why you may have answered differently the first time. CHAPTER-OPENING QUESTION A skier starts at the top of a hill. On which run does her gravitational potential energy change the most: (a), (b), (c), or (d); or are they (e) all the same? On which run would her speed at the bottom be the fastest if the runs are icy and we assume no friction or air resistance? Recognizing that there is always some friction, answer the above two questions again. List your four answers now.

Problem 6MCQ A ball is thrown straight up. At what point does the ball have the most energy? Ignore air resistance. (a) At the highest point of its path. (b)When it is first thrown. (c) Just before it hits the ground. (d)When the ball is halfway to the highest point of its path. (e) Everywhere; the energy of the ball is the same at all of these points.

Problem 6P (II) Estimate the work you do to mow a lawn 10 m by 20 m with a 50-cm-wide mower. Assume you push with a force of about 15 N.

Problem 6Q If the speed of a particle triples, by what factor does its kinetic energy increase?

Problem 6SL Suppose that the track in Fig. 6–51 is not frictionless and the values of h and R are given. (See Sections 6–9 and 6–1.) (a) If you measure the velocity of the roller coaster at the top of the hill (of height h) and at the top of the circle (of height 2R), can you determine the work done by friction during the time the roller coaster moves between those two points? Why or why not? (b) Can you determine the average force of friction between those two points? Why or why not? If not, what additional information do you need?

Problem 7MCQ A car accelerates from rest to 30 km/h. Later, on a highway it accelerates from 30km/h to 60 km/h. Which takes more energy, going from 0 to 30, or from 30 to 60? (a) 0 to 30km/h. (b) 30 to 60 km/h (c) Both are the same.

Problem 7P (II) In a certain library the first shelf is 15.0 cm off the ground, and the remaining four shelves are each spaced 38.0 cm above the previous one. If the average book has a mass of 1.40 kg with a height of 22.0 cm, and an average shelf holds 28 books (standing vertically), how much work is required to fill all the shelves, assuming the books are all laying flat on the floor to start?

Problem 7Q List some everyday forces that are not conservative, and explain why they aren’t.

Problem 8MCQ Engines, including car engines, are rated in horsepower. What is horsepower? (a) The force needed to start the engine. (b) The force needed to keep the engine running at a steady rate. (c) The energy the engine needs to obtain from gasoline or some other source. (d) The rate at which the engine can do work. (e) The amount of work the engine can perform.

(II) A lever such as that shown in Fig. 6- 35 can be used to lift objects we might not otherwise be able to lift. Show that the ratio of output force, \(F_{O}\), to input force, \(F_{I}\), is related to the lengths \(\ell_{I}\) and \(\ell_{O}\) from the pivot by \(F_{O} / F_{I}=\ell_{I} / \ell_{O}\). Ignore friction and the mass of the lever, and assume the work output equals the work input. ________________ Equation Transcription: ?I ?O ?I/?O ?I ?O Text Transcription: F_O F_I ell_I ell_O F_O/F_I=ell_I/ell_O

A hand exerts a constant horizontal force on a block that is free to slide on a frictionless surface (Fig. 6–30). The block starts from rest at point A, and by the time it has traveled a distance d to point B it is traveling with speed \(v_{B}\).When the block has traveled another distance d to point C, will its speed be greater than, less than, or equal to \(2 v_{B}\)? Explain your reasoning. ________________ Equation Transcription: Text Transcription: v_B 2v_B

Problem 9MCQ Two balls are thrown off a building with the same speed, one straight up and one at a 45° angle. Which statement is true if air resistance can be ignored? (a) Both hit the ground at the same time. (b) Both hit the ground with the same speed. (c) The one thrown at an angle hits the ground with a lower speed. (d) The one thrown at an angle hits the ground with a higher speed. (e) Both (a) and (b).

Problem 9P (II) A box of mass 4.0 kg is accelerated from rest by a force across a floor at a rate of 2.0 m/s2 for 7.0 s. Find the net work done on the box.

Problem 9Q You lift a heavy book from a table to a high shelf. List the forces on the book during this process, and state whether each is conservative or nonconservative.

A skier starts from rest at the top of each of the hills shown in Fig. 6–34. On which hill will the skier have the highest speed at the bottom if we ignore friction: (a), (b), (c), (d), or (e) c and d equally?

(II) A 380-kg piano slides 2.9 m down a \(25^{\circ}\) incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 6–36). Determine: () the force exerted by the man, (b) the work done on the piano by the man, (c) the work done on the piano by the force of gravity, and (d) the net work done on the piano. Ignore friction. ________________ Equation Transcription: Text Transcription: 25^o

A hill has a height \(h\). A child on a sled (total mass \(m\)) slides down starting from rest at the top. Does the speed at the bottom depend on the angle of the hill if (a) it is icy and there is no friction, and (b) there is friction (deep snow)? Explain your answers. Equation Transcription: Text Transcrition: h m

Answer MisConceptual Question 10 assuming a small amount of friction. A skier starts from rest at the top of each of the hills shown in Fig. 6–34. On which hill will the skier have the highest speed at the bottom if we ignore friction: (), (b), (c), (d), or (????) c and d equally?

(II) Recall from Chapter 4, Example 4–14, that you can use a pulley and ropes to decrease the force needed to raise a heavy load (see Fig. 6–37). But for every meter the load is raised, how much rope must be pulled up? Account for this, using energy concepts. ________________ Equation Transcription: Text Transcription: vector F_T vector F_T vector F_T m vector g

Analyze the motion of a simple swinging pendulum in terms of energy, (a) ignoring friction, and (b) taking friction into account. Explain why a grandfather clock has to be wound up.

A man pushes a block up an incline at a constant speed. As the block moves up the incline, (a) its kinetic energy and potential energy both increase. (b) its kinetic energy increases and its potential energy remains the same. (c) its potential energy increases and its kinetic energy remains the same. (d) its potential energy increases and its kinetic energy decreases by the same amount.

(III) A grocery cart with mass of 16 kg is being pushed at constant speed up a \(12^{\circ}\) ramp by a force \(F_{P}\) which acts at an angle of \(17^{\circ}\) below the horizontal. Find the work done by each of the forces \(\left(m\vec{g},\ \vec{F}_N,\ \vec{F}_P\right)\)) on the cart if the ramp is 7.5 m long. ________________ Equation Transcription: Text Transcription: 12^o F_P 17^o (m vector g, vector F_N, vector F_P)

In Fig. 6–31, water balloons are tossed from the roof of a building, all with the same speed but with different launch angles. Which one has the highest speed when it hits the ground? Ignore air resistance. Explain your answer.

Problem 13MCQ You push a heavy crate down a ramp at a constant velocity. Only four forces act on the crate. Which force does the greatest magnitude of work on the crate? (a) The force of friction. (b) The force of gravity. (c) The normal force. (d) The force of you pushing. (e) The net force.

(II) The force on a particle, acting along the x axis, varies as shown in Fig. 6–38. Determine the work done by this force to move the particle along the x axis: () from \(x=0.0\) to \(x=10.0 \mathrm{\ m}\); (b) from to \(x=0.0\) to \(x=15.0 \mathrm{\ m}\). ________________ Equation Transcription: Text Transcription: x=0.0 x=10.0 m x=0.0 x=15.0 m F_{x}(N) x(m)

Problem 13Q What happens to the gravitational potential energy when water at the top of a waterfall falls to the pool below?

Problem 14MCQ A ball is thrown straight up. Neglecting air resistance, which statement is not true regarding the energy of the ball? (a) The potential energy decreases while the ball is going up. (b) The kinetic energy decreases while the ball is going up. (c) The sum of the kinetic energy and potential energy is constant. (d) The potential energy decreases when the ball is coming down. (e) The kinetic energy increases when the ball is coming down.

(III) A 17,000-kg jet takes off from an aircraft carrier via a catapult (Fig. 6–39a). The gases thrust out from the jet’s engines exert a constant force of 130 kN on the jet; the force exerted on the jet by the catapult is plotted in Fig. 6–39b. Determine the work done on the jet: () by the gases expelled by its engines during launch of the jet; and (b) by the catapult during launch of the jet. ________________ Equation Transcription: Text Transcription: F(kN) x(m)

Problem 14Q Experienced hikers prefer to step over a fallen log in their path rather than stepping on top and stepping down on the other side. Explain.

Problem 15P (I) At room temperature, an oxygen molecule, with mass of 5.31 X 10–26 kg typically has a kinetic energy of about 6.21 X 10-26 kg, How fast is it moving?

Problem 15Q The energy transformations in pole vaulting and archery are discussed in this Chapter. In a similar fashion, discuss the energy transformations related to: (a) hitting a golf ball; (b) serving a tennis ball; and (c) shooting a basket in basketball.

Problem 16P (I) (a) If the kinetic energy of a particle is tripled, by what factor has its speed increased? (b) If the speed of a particle is halved, by what factor does its kinetic energy change?

Describe precisely what is “wrong” physically in the famous Escher drawing shown in Fig. 6–32.

Problem 17P (I) How much work is required to stop an electron (m = 9.11 X 10-31) which is moving with a speed of 1.10 X 106 m/s?

Problem 17Q Two identical arrows, one with twice the speed of the other, are fired into a bale of hay. Assuming the hay exerts a constant “frictional” force on the arrows, the faster arrow will penetrate how much farther than the slower arrow? Explain.

Problem 18P (I) How much work must be done to stop a 925-kg car traveling at 95 km/h?

A heavy ball is hung from the ceiling by a steel wire. The instructor pulls the ball back and stands against the wall with the ball against his chin. To avoid injury the instructor is supposed to release the ball without pushing it (Fig. 6–33). Why?

Problem 19P (II) Two bullets are fired at the same time with the same kinetic energy. If one bullet has twice the mass of the other, which has the greater speed and by what factor? Which can do the most work?

Problem 19Q Describe the energy transformations when a child hops around on a pogo stick (there is a spring inside).

(II) A baseball (m = 145 g) traveling 32 m/s moves a fielder’s glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?

Problem 20Q Describe the energy transformations that take place when a skier starts skiing down a hill, but after a time is brought to rest by striking a snowdrift.

Problem 21P (II) An 85-g arrow is fired from a bow whose string exerts an average force of 105 N on the arrow over a distance of 75 cm. What is the speed of the arrow as it leaves the bow?

Problem 21Q Suppose you lift a suitcase from the floor to a table. The work you do on the suitcase depends on which of the following: (a) whether you lift it straight up or along a more complicated path, (b) the time the lifting takes, (c) the height of the table, and (d) the weight of the suitcase?

Problem 22P (II) If the speed of a car is increased by 50%, by what factor will its minimum braking distance be increased, assuming all else is the same? Ignore the driver’s reaction time.

Repeat Question 21 for the power needed instead of the work.

Problem 23P (II) At an accident scene on a level road, investigators measure a car’s skid mark to be 78 m long. It was a rainy day and the coefficient of friction was estimated to be 0.30. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. (Why does the car’s mass not matter?)

Problem 23Q Why is it easier to climb a mountain via a zigzag trail rather than to climb straight up?

Problem 24P (III) One car has twice the mass of a second car, but only half as much kinetic energy. When both cars increase their speed by 8.0 m/s, they then have the same kinetic energy. What were the original speeds of the two cars?

(III) A 265-kg load is lifted 18.0 m vertically with an acceleration a = 0.160 g by a single cable. Determine (a) the tension in the cable; (b) the net work done on the load; (c) the work done by the cable on the load; (d) the work done by gravity on the load; (e) the final speed of the load assuming it started from rest.

(I) By how much does the gravitational potential energy of a 54-kg pole vaulter change if her center of mass rises about 4.0 m during the jump?

(I) A spring has a spring constant k of 88.0 N/m. How much must this spring be compressed to store 45.0 J of potential energy?

Problem 28P (II) If it requires 6.0 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additional 4.0 cm?

Problem 29P (II) A 66.5-kg hiker starts at an elevation of 1270 m and climbs to the top of a peak 2660 m high. (a) What is the hiker’s change in potential energy? (b) What is the minimum work required of the hiker? (c) Can the actual work done be greater than this? Explain.

Problem 30P (II) A 1.60-m-tall person lifts a 1.65-kg book off the ground so it is 2.20 m above the ground. What is the potential energy of the book relative to (a) the ground, and (b) the top of the person’s head? (c) How is the work done by the person related to the answers in parts (a) and (b)?

Problem 31P (I) A novice skier, starting from rest, slides down an icy frictionless 8.0° incline whose vertical height is 105 m. How fast is she going when she reaches the bottom?

Problem 32P (I) Jane, looking for Tarzan, is running at top speed (5.0 m/s) and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upward? Does the length of the vine affect your answer?

Problem 33P (II) A sled is initially given a shove up a frictionless 23.0° incline. It reaches a maximum vertical height 1.22 m higher than where it started at the bottom. What was its initial speed?

Problem 34P (II) In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground in order to lift his center of mass 2.10 m and cross the bar with a speed of 0.50 m/s?q

Problem 35P (II) A spring with K=83 n/M hangs vertically next to a ruler. The end of the spring is next to the 15-cm mark on the ruler. If a 2.5-kg mass is now attached to the end of the spring, and the mass is allowed to fall, where will the end of the spring line up with the ruler marks when the mass is at its lowest position?

Problem 36P (II) A 0.48-kg ball is thrown with a speed of 8.8 m/s at an upward angle of 36°. (a) What is its speed at its highest point, and (b) how high does it go? (Use conservation of energy.)

(II) A 1200-kg car moving on a horizontal surface has speed \(v=85\ km/h\) when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?

(II) A 62-kg trampoline artist jumps upward from the top of a platform with a vertical speed of \(4.5 \mathrm{\ m} / \mathrm{s}\). () How fast is he going as he lands on the trampoline, 2.0 m below (Fig.6–40)? (b) If the trampoline behaves like a spring of spring constant \(5.8 \times 10^{4} \mathrm{\ N} / \mathrm{m}\), how far down does he depress it? ________________ Equation Transcription: Text Transcription: 4.5 m/s 5.8x10^4 N/m

Problem 39P (II) A vertical spring (ignore its mass), whose spring constant Is 875 N/m, is attached to a table and is compressed down by 0.160 m. (a) What upward speed can it give to a 0.380-kg ball when released? (b) How high above its original position (spring compressed) will the ball fly?

(II) A roller-coaster car shown in Fig. is pulled up to point 1 where it is released from rest. Assuming no friction, calculate the speed at points 2,3, and FIGURE 6-41 Problems 40 and 50

(II) Chris jumps off a bridge with a bungee cord (a heavy stretchable cord) tied around his ankle, Fig. He falls for before the bungee cord begins to stretch. Chris's mass is and we assume the cord obeys Hooke's law, \(F=-k x\), with \(k=55\mathrm{\ N}/\mathrm{m}\). If we neglect air resistance, estimate what distance below the bridge Chris's foot will be before coming to a stop. Ignore the mass of the cord (not realistic, however) and treat Chris as a particle. FIGURE 6–42 Problem 41. (a) Bungee jumper about to jump. (b) Bungee cord at its unstretched length. (c) Maximum stretch of cord. ________________ Equation Transcription: Text Transcription: F=-kx k=55 N/m Delta y=? y=0

Problem 42P (II) What should be the spring constant k of a spring designed to bring a 1200-kg car to rest from a speed of 95 km/h so that the occupants undergo a maximum acceleration of 4.0 g?

Problem 43P (III) An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable breaks when the elevator is at a height h above the top of the spring, calculate the value that the spring constant k should have so that passengers undergo an acceleration of no more than 5.0 g when brought to rest. Let M be the total mass of the elevator and passengers.

(III) A block of mass m is attached to the end of a spring (spring stiffness constant k), Fig. 6–43. The mass is given an initial displacement \(x_0\) from equilibrium, and an initial speed \(v_0\). Ignoring friction and the mass of the spring, use energy methods to find (a) its maximum speed, and (b) its maximum stretch from equilibrium, in terms of the given quantities.

Problem 45P (III) A cyclist intends to cycle up a 7.50° hill whose vertical height is 125 m. The pedals turn in a circle of diameter 36.0 cm. Assuming the mass of bicycle plus person is 75.0 kg, (a) calculate how much work must be done against gravity. (b) If each complete revolution of the pedals moves the bike 5.10 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses.

Problem 46P (I) Two railroad cars, each of mass 66,000 kg, are traveling 85 km/h toward each other. They collide head-on and come to rest. How much thermal energy is produced in this collision?

Problem 47P (I) A 16.0-kg child descends a slide 2.20 m high and, starting from rest, reaches the bottom with a speed of 1.25 m/s. How much thermal energy due to friction was generated in this process?

(II) A ski starts from rest and slides down a \(28^{\circ}\) incline 85 m long. (a) If the coefficient of friction is 0.090, what is the ski’s speed at the base of the incline? (b) If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level? Use energy methods.

Problem 49P (II) A 145-g baseball is dropped from a tree 12.0 m above the ground. (a) With what speed would it hit the ground if air resistance could be ignored? (b) If it actually hits the ground with a speed of 8.00 m/s, what is the average force of air resistance exerted on it?

(II) Suppose the roller-coaster car in Fig. 6–41 passes point 1 with a speed of 1.30 m/s If the average force of friction is equal to 0.23 of its weight, with what speed will it reach point 2? The distance traveled is 45.0 m.

Problem 51P (II) A skier traveling 11.0 m/s reaches the foot of a steady upward 19° incline and glides 15 m up along this slope before coming to rest. What was the average coefficient of friction?

Problem 52P (II) You drop a ball from a height of 2.0 m, and it bounces back to a height of 1.6 m. a) What fraction of its initial energy is lost during the bounce? (b) What is the ball’s speed just before and just after the bounce? (c) Where did the energy go?

Problem 53P (II) A 66-kg skier starts from rest at the top of a 1200-mlong trail which drops a total of 230 m from top to bottom. At the bottom, the skier is moving 11.0 m/s. How much energy was dissipated by friction?

Problem 54P (II) A projectile is fired at an upward angle of 38.0° from the top of a 135-m-high cliff with a speed of 165 m/s, What will be its speed when it strikes the ground below? (Use conservation of energy.)

(II) The Lunar Module could make a safe landing if its vertical velocity at impact is 3.0 m/s or less. Suppose that you want to determine the greatest height h at which the pilot could shut off the engine if the velocity of the lander relative to the surface at that moment is (a) zero; (b) 2.0 m/s downward; (c) 2.0 m/s upward. Use conservation of energy to determine h in each case. The acceleration due to gravity at the surface of the Moon is \(1.62 m/s^2\).

Problem 56P (III) Early test flights for the space shuttle used a “glider” (mass of 980 kg including pilot). After a horizontal launch At 480 km/h at a height of 3500 m, the glider eventually landed at a speed of 210 km/h. (a) What would its landing speed have been in the absence of air resistance? (b)What was the average force of air resistance exerted on it if it came in at a constant glide angle of 12° to the Earth’s surface?

(I) (a) Show that one British horsepower (\(550\ ft \cdot lb/s\)) is equal to 746 W. (b) What is the horsepower rating of a 75-W lightbulb?

Problem 57P (I) How long will it take a 2750-W motor to lift a 385-kg piano to a sixth-story window 16.0 m above?

Problem 59P (I) An 85-kg football player traveling 5.0 m/s is stopped in 1.0 s by a tackler. (a) What is the original kinetic energy of the player? (b) What average power is required to stop him?

Problem 60P (II) If a car generates 18 hp when traveling at a steady 95 km/h what must be the average force exerted on the car due to friction and air resistance?

Problem 61P (II) An outboard motor for a boat is rated at 35 hp. If it can move a particular boat at a steady speed of 35 km/h what is the total force resisting the motion of the boat?

Problem 62P (II) A shot-putter accelerates a 7.3-kg shot from rest to 14 m/s in 1.5 s. What average power was developed?

Problem 63P (II) A driver notices that her 1080-kg car, when in neutral, slows down from 95 km/h to 65 km/h in about 7.0 s on a flat horizontal road. Approximately what power (watts and hp) is needed to keep the car traveling at a constant 80 km/h?

Problem 64P (II) How much work can a 2.0-hp motor do in 1.0 h?

Problem 65P (II) A 975-kg sports car accelerates from rest to 95 km/h in 6.4 s. What is the average power delivered by the engine?

Problem 66P (II) During a workout, football players ran up the stadium stairs in 75 s. The distance along the stairs is 83 m and they are inclined at a 33° angle. If a player has a mass of 82 kg, estimate his average power output on the way up. Ignore friction and air resistance.

Problem 67P (II) A pump lifts 27.0 kg of water per minute through a height of 3.50 m. What minimum output rating (watts) must the pump motor have?

(II) A ski area claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the maximum total power needed.

Problem 69P (II) A 65-kg skier grips a moving rope that is powered by an engine and is pulled at constant speed to the top of a 23° hill. The skier is pulled a distance x =320 m along the incline and it takes 2.0 min to reach the top of the hill. If the coefficient of kinetic friction between the snow and skis is µk =0.10, what horsepower engine is required if 30 such skiers (max) are on the rope at one time?

(II) What minimum horsepower must a motor have to be able to drag a 370-kg box along a level floor at a speed of 1.20 m/s if the coefficient of friction is 0.45?

Problem 71P (III) A bicyclist coasts down a 6.0° hill at a steady speed Of 4.0 m/s. Assuming a total mass of 75 kg (bicycle plus rider), what must be the cyclist’s power output to climb the same hill at the same speed?

Spiderman uses his spider webs to save a runaway tain moving about \(60 \mathrm{\ km} / \mathrm{h}\), Fig. . His web stretches a few city blocks before the \(10^{4}\)-kg train comes to a stop. Assuming the web acts like a spring, estimate the effective spring constant. FIGURE 6–44 Problem 72. ________________ Equation Transcription: Text Transcription: 60 km/h 104

Problem 73GP A 36.0-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 225 N. For the first 11.0 m the floor is frictionless, and for the next 10.0 m the coefficient of friction is 0.20. What is the final speed of the crate after being pulled these 21.0 m?

Problem 74GP How high will a 1.85-kg rock go from the point of release if thrown straight up by someone who does 80.0 J of work on it? Neglect air resistance.

A mass m is attached to a spring which is held stretched a distance x by a force F, Fig. 6–45, and then released. The spring pulls the mass to the left, towards its natural equilibrium length. Assuming there is no friction, determine the speed of the mass m when the spring returns: (a) to its normal length (x = 0); (b) to half its original extension (x/2).

Problem 76GP An elevator cable breaks when a 925-kg elevator is 28.5 m above the top of a huge spring (k = 8.00 x 104 N/m) at the bottom of the shaft. Calculate (a) the work done by gravity on the elevator before it hits the spring; (b) the speed of the elevator just before striking the spring; (c) the amount the spring compresses (note that here work is done by both the spring and gravity).

Problem 77GP (a) A 3.0-g locust reaches a speed of 3.0 m/s during its jump. What is its kinetic energy at this speed? (b) If the locust transforms energy with 35% efficiency, how much energy is required for the jump?

In a common test for cardiac function (the "stress test"), the patient walks on an inclined treadmill (Fig. 6-46). Estimate the power required from a 75-kg patient when the treadmill is sloping at an angle of \(12^{\circ}\) and the velocity is \(3.1 \mathrm{\ km} / \mathrm{h}\). (How does this power compare to the power rating of a lightbulb?) FIGURE 6–46 Problem 78. ________________ Equation Transcription: Text Transcription: 120^o 3.1 km/h

Problem 79GP An airplane pilot fell 370 m after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the pilot’s mass was 88 kg and his speed at impact was 45 m/s, estimate: (a) the work done by the snow in bringing him to rest; (b) the average force exerted on him by the snow to stop him; and (c) the work done on him by air resistance as he fell. Model him as a particle.

Problem 80GP Many cars have “5 mi/h (8 km/h) bumpers”that are designed to compress and rebound elastically without any physical damage at speeds below 8 km/h. If the material of the bumpers permanently deforms after a compression of 1.5 cm, but remains like an elastic spring up to that point, what must be the effective spring constant of the bumper material, assuming the car has a mass of 1050 kg and is tested by ramming into a solid wall?

Problem 81GP In climbing up a rope, a 62-kg athlete climbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used to accomplish this feat?

Problem 82GP If a 1300-kg car can accelerate from 35km/h to 65km/h in 3.8 s, how long will it take to accelerate from 55km/h to 95km/h? Assume the power stays the same, and neglect frictional losses.

Problem 83GP A cyclist starts from rest and coasts down a 4.0° hill. The mass of the cyclist plus bicycle is 85 kg. After the cyclist has traveled 180 m, (a) what was the net work done by gravity on the cyclist? (b) How fast is the cyclist going? Ignore air resistance and friction.

A film of Jesse Owens's famous long jump (Fig. 6-47) in the 1936 Olympics shows that his center of mass rose from launch point to the top of the arc. What did he need at traveling at \(6.5 \mathrm{\ m} / \mathrm{s}\) of the arc? FIGURE 6–47 Problem 84. ________________ Equation Transcription: Text Transcription: 6.5 m/s

Problem 85GP Water flows over a dam at the rate of 680 kg/s and falls vertically 88 m before striking the turbine blades. Calculate (a) the speed of the water just before striking the turbine blades (neglect air resistance), and (b) the rate at which mechanical energy is transferred to the turbine blades, assuming 55% efficiency.

A skier starts from rest at the top of a ski jump, point in Fig. , and travels down the ramp. If friction and air resistance can be neglected, determine her speed \(v_{B}\) when she reaches the horizontal end of the ramp at B. (b) Determine the distance to where she strikes the ground at . FIGURE 6–48 Problem 86. ________________ Equation Transcription: Text Transcription: v_B vector B 30.0^o

Problem 87GP Electric energy units are often expressed in “kilowatt-hours.” (a) Show that one kilowatt-hour (kWh) is equal to 3.6 x 106 J. (b) If a typical family of four uses electric energy at an average rate of 580 W, how many kWh would their electric bill show for one month, and (c) how many joules would this be? (d) At a cost of $0.12 per kWh, what would their monthly bill be in dollars? Does the monthly bill depend on the rate at which they use the electric energy?

Problem 88GP If you stand on a bathroom scale, the spring inside the scale compresses 0.60 mm, and it tells you your weight is 760 N. Now if you jump on the scale from a height of 1.0 m, what does the scale read at its peak?

Problem 89GP A 65-kg hiker climbs to the top of a mountain 4200 m high. The climb is made in 4.6 h starting at an elevation of 2800 m. Calculate (a) the work done by the hiker against gravity, (b) the average power output in watts and in horsepower, and (c) assuming the body is 15% efficient, what rate of energy input was required.

A ball is attached to a horizontal cord of length whose other end is fixed, Fig. If the ball is released, what will be its speed at the lowest point of its path? (b) A peg is located a distance directly below attachment of the cord. If \(h=0.80 \ell\), what will be the speed of the ball when it reaches the top of its circular path about the peg? FIGURE 6–49 Problem 90. ________________ Equation Transcription: ? Text Transcription: h=0.80 ell

An sled starts up a \(28^{\circ}\) incline with a speed of \(2.3 \mathrm{~m} / \mathrm{s}\). The coefficient of kinetic friction is \(\mu_{k}=0.25\). (a) How far up the incline does the sled travel? (b) What condition must you put on the coefficient of static friction if the sled is not to get stuck at the point determined in part If the sled slides back down, what is its speed when it returns to its starting point? ________________ Equation Transcription: Text Transcription: 28^o 2.3 m/s mu_k=0.25

A student runs at \(6.0 \mathrm{\ m} / \mathrm{s}\), grabs a hanging -m-long rope, and swings out over a lake (Fig. 6-50). He releases the rope when his velocity is zero. ( ) What is the angle \(\theta\) when he releases the rope? (b) What is the tension in the rope just before he releases it? (c) What is the maximum tension in the rope during the swing? FIGURE 6–50 Problem 92. ________________ Equation Transcription: Text Transcription: 6.0 m/s theta

Problem 93GP Some electric power companies use water to store energy. Water is pumped from a low reservoir to a high reservoir. To store the energy produced in 1.0 hour by a 180-MW electric power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Assume the upper reservoir is an average of 380 m above the lower one. Water has a mass of 1.00 x 103 for every 1.0 m3.

Problem 94GP A softball having a mass of 0.25 kg is pitched horizontally at 120 km/h. By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch. The distance between the plate and the pitcher is about 15 m.

A 75.0-kg firefighter climbs a flight of stairs 28.0 m high. How much work does he do?

The head of a hammer with a mass of 1.2 kg is allowed to fall onto a nail from a height of 0.50 m. What is the maximum amount of work it could do on the nail? Why do people not just let it fall but add their own force to the hammer as it falls?

How much work did the movers do (horizontally) pushing a 46.0-kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0.50?

How much work did the movers do (horizontally) pushing a 46.0-kg crate 10.3 m across a rough floor without acceleration, if the effective coefficient of friction was 0.50?

What is the minimum work needed to push a 950-kg car 710 m up along a 9.0 incline? Ignore friction

Estimate the work you do to mow a lawn 10 m by 20 m with a 50-cm-wide mower. Assume you push with a force of about 15 N.

Estimate the work you do to mow a lawn 10 m by 20 m with a 50-cm-wide mower. Assume you push with a force of about 15 N.

A lever such as that shown in Fig. 6–35 can be used to lift objects we might not otherwise be able to lift. Show that the ratio of output force, \(F_\mathrm O\), to input force, \(F_\mathrm I\), is related to the lengths \(\ell_\mathrm I\) and \(\ell_\mathrm O\) from the pivot by \(F_\mathrm O / F_\mathrm I = \ell_ \mathrm I / \ell_ \mathrm O\). Ignore friction and the mass of the lever, and assume the work output equals the work input.

A box of mass 4.0 kg is accelerated from rest by a force across a floor at a rate of for 7.0 s. Find the net work done on the box.

A 380-kg piano slides 2.9 m down a 25 incline and is kept from accelerating by a man who is pushing back on it parallel to the incline (Fig. 636). Determine: (a) the force exerted by the man, (b) the work done on the piano by the man, (c) the work done on the piano by the force of gravity, and (d) the net work done on the piano. Ignore friction

Recall from Chapter 4, Example 414, that you can use a pulley and ropes to decrease the force needed to raise a heavy load (see Fig. 637). But for every meter the load is raised, how much rope must be pulled up? Account for this, using energy concepts.

A grocery cart with mass of 16 kg is being pushed at constant speed up a 12 ramp by a force which acts at an angle of 17 below the horizontal. Find the work done by each of the forces on the cart if the ramp is 7.5 m long.

The force on a particle, acting along the x axis, varies as shown in Fig. 638. Determine the work done by this force to move the particle along the x axis: (a) from to x = 10.0 m; (b) from to x = 0.0 x = 15.0 m.

A 17,000-kg jet takes off from an aircraft carrier via a catapult (Fig. 639a). The gases thrust out from the jets engines exert a constant force of 130 kN on the jet; the force exerted on the jet by the catapult is plotted in Fig. 639b. Determine the work done on the jet: (a) by the gases expelled by its engines during launch of the jet; and (b) by the catapult during launch of the jet.

At room temperature, an oxygen molecule, with mass of typically has a kinetic energy of about How fast is it moving?

If the kinetic energy of a particle is tripled, by what factor has its speed increased? (b) If the speed of a particle is halved, by what factor does its kinetic energy change?

How much work is required to stop an electron which is moving with a speed of

How much work must be done to stop a 925-kg car traveling at

Two bullets are fired at the same time with the same kinetic energy. If one bullet has twice the mass of the other, which has the greater speed and by what factor? Which can do the most work?

A baseball traveling moves a fielders glove backward 25 cm when the ball is caught. What was the average force exerted by the ball on the glove?

(II) An 85-g arrow is fired from a bow whose string exerts an average force of 105 N on the arrow over a distance of 75 cm. What is the speed of the arrow as it leaves the bow?

(II) If the speed of a car is increased by 50%, by what factor will its minimum braking distance be increased, assuming all else is the same? Ignore the driver’s reaction time.

At an accident scene on a level road, investigators measure a cars skid mark to be 78 m long. It was a rainy day and the coefficient of friction was estimated to be 0.30. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. (Why does the cars mass not matter?)

At an accident scene on a level road, investigators measure a cars skid mark to be 78 m long. It was a rainy day and the coefficient of friction was estimated to be 0.30. Use these data to determine the speed of the car when the driver slammed on (and locked) the brakes. (Why does the cars mass not matter?)

A 265-kg load is lifted 18.0 m vertically with an acceleration by a single cable. Determine (a) the tension in the cable; (b) the net work done on the load; (c) the work done by the cable on the load; (d) the work done by gravity on the load; (e) the final speed of the load assuming it started from rest.

A 265-kg load is lifted 18.0 m vertically with an acceleration by a single cable. Determine (a) the tension in the cable; (b) the net work done on the load; (c) the work done by the cable on the load; (d) the work done by gravity on the load; (e) the final speed of the load assuming it started from rest.

A spring has a spring constant k of How much must this spring be compressed to store 45.0 J of potential energy?

If it requires 6.0 J of work to stretch a particular spring by 2.0 cm from its equilibrium length, how much more work will be required to stretch it an additional 4.0 cm?

A 66.5-kg hiker starts at an elevation of 1270 m and climbs to the top of a peak 2660 m high. (a) What is the hikers change in potential energy? (b) What is the minimum work required of the hiker? (c) Can the actual work done be greater than this? Explain.

A 1.60-m-tall person lifts a 1.65-kg book off the ground so it is 2.20 m above the ground. What is the potential energy of the book relative to (a) the ground, and (b) the top of the persons head? (c) How is the work done by the person related to the answers in parts (a) and (b)?

A novice skier, starting from rest, slides down an icy frictionless 8.0 incline whose vertical height is 105 m. How fast is she going when she reaches the bottom?

Jane, looking for Tarzan, is running at top speed and grabs a vine hanging vertically from a tall tree in the jungle. How high can she swing upward? Does the length of the vine affect your answer?

A sled is initially given a shove up a frictionless 23.0 incline. It reaches a maximum vertical height 1.22 m higher than where it started at the bottom. What was its initial speed?

(II) In the high jump, the kinetic energy of an athlete is transformed into gravitational potential energy without the aid of a pole. With what minimum speed must the athlete leave the ground in order to lift his center of mass 2.10 m and cross the bar with a speed of 0.50 m/s?

A spring with hangs vertically next to a ruler. The end of the spring is next to the 15-cm mark on the ruler. If a 2.5-kg mass is now attached to the end of the spring, and the mass is allowed to fall, where will the end of the spring line up with the ruler marks when the mass is at its lowest position?

A 0.48-kg ball is thrown with a speed of at an upward angle of 36. (a) What is its speed at its highest point, and (b) how high does it go? (Use conservation of energy.)

A 1200-kg car moving on a horizontal surface has speed when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?

A 62-kg trampoline artist jumps upward from the top of a platform with a vertical speed of (a) How fast is he going as he lands on the trampoline, 2.0 m below (Fig.640)? (b) If the trampoline behaves like a spring of spring constant how far down does he depress it? 5.8 * 104 Nm,

A vertical spring (ignore its mass), whose spring constant is is attached to a table and is compressed down by 0.160 m. (a) What upward speed can it give to a 0.380-kg ball when released? (b) How high above its original position (spring compressed) will the ball fly?

A roller-coaster car shown in Fig. 641 is pulled up to point 1 where it is released from rest. Assuming no friction, calculate the speed at points 2, 3, and 4.

Chris jumps off a bridge with a bungee cord (a heavy stretchable cord) tied around his ankle, Fig. 642. He falls for 15 m before the bungee cord begins to stretch. Chriss mass is 75 kg and we assume the cord obeys Hookes law, with If we neglect air resistance, estimate what distance d below the bridge Chriss foot will be before coming to a stop. Ignore the mass of the cord (not realistic, however) and treat Chris as a particle.

(II) What should be the spring constant k of a spring designed to bring a 1200-kg car to rest from a speed of 95 km/h so that the occupants undergo a maximum acceleration of 4.0 g?

An engineer is designing a spring to be placed at the bottom of an elevator shaft. If the elevator cable breaks when the elevator is at a height h above the top of the spring, calculate the value that the spring constant k should have so that passengers undergo an acceleration of no more than 5.0 g when brought to rest. Let M be the total mass of the elevator and passengers.

A block of mass m is attached to the end of a spring (spring stiffness constant k), Fig. 643. The mass is given an initial displacement from equilibrium, and an initial speed Ignoring friction and the mass of the spring, use energy methods to find (a) its maximum speed, and (b) its maximum stretch from equilibrium, in terms of the given quantities.

A cyclist intends to cycle up a 7.50 hill whose vertical height is 125 m. The pedals turn in a circle of diameter 36.0 cm. Assuming the mass of bicycle plus person is 75.0 kg, (a) calculate how much work must be done against gravity. (b) If each complete revolution of the pedals moves the bike 5.10 m along its path, calculate the average force that must be exerted on the pedals tangent to their circular path. Neglect work done by friction and other losses.

Two railroad cars, each of mass 66,000 kg, are traveling toward each other. They collide head-on and come to rest. How much thermal energy is produced in this collision?

Two railroad cars, each of mass 66,000 kg, are traveling toward each other. They collide head-on and come to rest. How much thermal energy is produced in this collision?

A ski starts from rest and slides down a 28 incline 85 m long. (a) If the coefficient of friction is 0.090, what is the skis speed at the base of the incline? (b) If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level? Use energy methods

A 145-g baseball is dropped from a tree 12.0 m above the ground. (a) With what speed would it hit the ground if air resistance could be ignored? (b) If it actually hits the ground with a speed of what is the average force of air resistance exerted on it?

Suppose the roller-coaster car in Fig. 641 passes point 1 with a speed of If the average force of friction is equal to 0.23 of its weight, with what speed will it reach point 2? The distance traveled is 45.0 m

A skier traveling reaches the foot of a steady upward 19 incline and glides 15 m up along this slope before coming to rest. What was the average coefficient of friction?

A skier traveling reaches the foot of a steady upward 19 incline and glides 15 m up along this slope before coming to rest. What was the average coefficient of friction?

A 66-kg skier starts from rest at the top of a 1200-mlong trail which drops a total of 230 m from top to bottom. At the bottom, the skier is moving How much energy was dissipated by friction?

A projectile is fired at an upward angle of 38.0 from the top of a 135-m-high cliff with a speed of What will be its speed when it strikes the ground below? (Use conservation of energy.)

The Lunar Module could make a safe landing if its vertical velocity at impact is or less. Suppose that you want to determine the greatest height h at which the pilot could shut off the engine if the velocity of the lander relative to the surface at that moment is (a) zero; (b) downward; (c) upward. Use conservation of energy to determine h in each case. The acceleration due to gravity at the surface of the Moon is 1.62 ms 2 .

Early test flights for the space shuttle used a glider (mass of 980 kg including pilot). After a horizontal launch at at a height of 3500 m, the glider eventually landed at a speed of (a) What would its landing speed have been in the absence of air resistance? (b) What was the average force of air resistance exerted on it if it came in at a constant glide angle of 12 to the Earths surface?

How long will it take a 2750-W motor to lift a 385-kg piano to a sixth-story window 16.0 m above?

(a) Show that one British horsepower is equal to 746 W. (b) What is the horsepower rating of a 75-W lightbulb?

An 85-kg football player traveling is stopped in 1.0 s by a tackler. (a) What is the original kinetic energy of the player? (b) What average power is required to stop him?

If a car generates 18 hp when traveling at a steady what must be the average force exerted on the car due to friction and air resistance?

An outboard motor for a boat is rated at 35 hp. If it can move a particular boat at a steady speed of what is the total force resisting the motion of the boat?

A shot-putter accelerates a 7.3-kg shot from rest to in 1.5 s. What average power was developed?

A driver notices that her 1080-kg car, when in neutral, slows down from to in about 7.0 s on a flat horizontal road. Approximately what power (watts and hp) is needed to keep the car traveling at a constant 80 kmh?

How much work can a 2.0-hp motor do in 1.0 h?

A 975-kg sports car accelerates from rest to in 6.4 s. What is the average power delivered by the engine?

(II) During a workout, football players ran up the stadium stairs in 75 s. The distance along the stairs is 83 m and they are inclined at a \(33^\circ\) angle. If a player has a mass of 82 kg, estimate his average power output on the way up. Ignore friction and air resistance.

A pump lifts 27.0 kg of water per minute through a height of 3.50 m. What minimum output rating (watts) must the pump motor have?

A ski area claims that its lifts can move 47,000 people per hour. If the average lift carries people about 200 m (vertically) higher, estimate the maximum total power needed.

A 65-kg skier grips a moving rope that is powered by an engine and is pulled at constant speed to the top of a 23 hill. The skier is pulled a distance along the incline and it takes 2.0 min to reach the top of the hill. If the coefficient of kinetic friction between the snow and skis is what horsepower engine is required if 30 such skiers (max) are on the rope at one time?

What minimum horsepower must a motor have to be able to drag a 370-kg box along a level floor at a speed of if the coefficient of friction is 0.45?

A bicyclist coasts down a 6.0 hill at a steady speed of Assuming a total mass of 75 kg (bicycle plus rider), what must be the cyclists power output to climb the same hill at the same speed?

Spiderman uses his spider webs to save a runaway train moving about 60 km/h. Fig. 6-44. His web stretches a few city blocks (500 m) before the \(10^4-kg\) comes to a stop. Assuming the web acts like a spring, estimate the effective spring constant.

A 36.0-kg crate, starting from rest, is pulled across a floor with a constant horizontal force of 225 N. For the first 11.0 m the floor is frictionless, and for the next 10.0 m the coefficient of friction is 0.20. What is the final speed of the crate after being pulled these 21.0 m?

. How high will a 1.85-kg rock go from the point of release if thrown straight up by someone who does 80.0 J of work on it? Neglect air resistance.

A mass m is attached to a spring which is held stretched a distance x by a force F, Fig. 645, and then released. The spring pulls the mass to the left, towards its natural equilibrium length. Assuming there is no friction, determine the speed of the mass m when the spring returns: (a) to its normal length (b) to half its original extension (x2).

An elevator cable breaks when a 925-kg elevator is 28.5 m above the top of a huge spring at the bottom of the shaft. Calculate (a) the work done by gravity on the elevator before it hits the spring; (b) the speed of the elevator just before striking the spring; (c) the amount the spring compresses (note that here work is done by both the spring and gravity

(a) A 3.0-g locust reaches a speed of during its jump. What is its kinetic energy at this speed? (b) If the locust transforms energy with 35% efficiency, how much energy is required for the jump

In a common test for cardiac function (the stress test), the patient walks on an inclined treadmill (Fig. 646). Estimate the power required from a 75-kg patient when the treadmill is sloping at an angle of 12 and the velocity is (How does this power compare to the power rating of a lightbulb?)

An airplane pilot fell 370 m after jumping from an aircraft without his parachute opening. He landed in a snowbank, creating a crater 1.1 m deep, but survived with only minor injuries. Assuming the pilots mass was 88 kg and his speed at impact was estimate: (a) the work done by the snow in bringing him to rest; (b) the average force exerted on him by the snow to stop him; and (c) the work done on him by air resistance as he fell. Model him as a particle

Many cars have bumpersthat are designed to compress and rebound elastically without any physical damage at speeds below If the material of the bumpers permanently deforms after a compression of 1.5 cm, but remains like an elastic spring up to that point, what must be the effective spring constant of the bumper material, assuming the car has a mass of 1050 kg and is tested by ramming into a solid wall?

In climbing up a rope, a 62-kg athlete climbs a vertical distance of 5.0 m in 9.0 s. What minimum power output was used to accomplish this feat?

If a 1300-kg car can accelerate from to in 3.8 s, how long will it take to accelerate from to Assume the power stays the same, and neglect frictional losses

A cyclist starts from rest and coasts down a 4.0 hill. The mass of the cyclist plus bicycle is 85 kg. After the cyclist has traveled 180 m, (a) what was the net work done by gravity on the cyclist? (b) How fast is the cyclist going? Ignore air resistance and friction.

A film of Jesse Owenss famous long jump (Fig. 647) in the 1936 Olympics shows that his center of mass rose 1.1 m from launch point to the top of the arc. What minimum speed did he need at launch if he was traveling at at the top of the arc?

Water flows over a dam at the rate of and falls vertically 88 m before striking the turbine blades. Calculate (a) the speed of the water just before striking the turbine blades (neglect air resistance), and (b) the rate at which mechanical energy is transferred to the turbine blades, assuming 55% efficiency

A 55-kg skier starts from rest at the top of a ski jump, point A in Fig. 648, and travels down the ramp. If friction and air resistance can be neglected, (a) determine her speed when she reaches the horizontal end of the ramp at B. (b) Determine the distance s to where she strikes the ground at C

Electric energy units are often expressed in kilowatt-hours. (a) Show that one kilowatt-hour (kWh) is equal to (b) If a typical family of four uses electric energy at an average rate of 580 W, how many kWh would their electric bill show for one month, and (c) how many joules would this be? (d) At a cost of $0.12 per kWh, what would their monthly bill be in dollars? Does the monthly bill depend on the rate at which they use the electric energy?

If you stand on a bathroom scale, the spring inside the scale compresses 0.60 mm, and it tells you your weight is 760 N. Now if you jump on the scale from a height of 1.0 m, what does the scale read at its peak?

A 65-kg hiker climbs to the top of a mountain 4200 m high. The climb is made in 4.6 h starting at an elevation of 2800 m. Calculate (a) the work done by the hiker against gravity, (b) the average power output in watts and in horsepower, and (c) assuming the body is 15% efficient, what rate of energy input was required

A ball is attached to a horizontal cord of length whose other end is fixed, Fig. 649. (a) If the ball is released, what will be its speed at the lowest point of its path? (b)A peg is located a distance h directly below the point of attachment of the cord. If what will be the speed of the ball when it reaches the top of its circular path about the peg? h = 0.80l, l 3.6 * 106 J. h l Peg F

An 18-kg sled starts up a 28 incline with a speed of The coefficient of kinetic friction is (a) How far up the incline does the sled travel? (b) What condition must you put on the coefficient of static friction if the sled is not to get stuck at the point determined in part (a)? (c) If the sled slides back down, what is its speed when it returns to its starting point?

A 56-kg student runs at grabs a hanging 10.0-m-long rope, and swings out over a lake (Fig. 650). He releases the rope when his velocity is zero. (a) What is the angle when he releases the rope? (b) What is the tension in the rope just before he releases it? (c) What is the maximum tension in the rope during the swing?

Some electric power companies use water to store energy. Water is pumped from a low reservoir to a high reservoir. To store the energy produced in 1.0 hour by a 180-MW electric power plant, how many cubic meters of water will have to be pumped from the lower to the upper reservoir? Assume the upper reservoir is an average of 380 m above the lower one. Water has a mass of for every 10m3?

A softball having a mass of 0.25 kg is pitched horizontally at By the time it reaches the plate, it may have slowed by 10%. Neglecting gravity, estimate the average force of air resistance during a pitch. The distance between the plate and the pitcher is about 15 m.