In 1887 in Bridgeport, Connecticut, C. J. Belknap built

A weight lifter lifts a 350-N set of weights from ground level to a position over his head, a vertical distance of 2.00 m. How much work does the weight lifter do, assuming he moves the weights at constant speed?

If a man lifts a 20.0-kg bucket from a well and does 6.00 kJ of work, how deep is the well? Assume that the speed of the bucket remains constant as it is lifted.

A tugboat exerts a constant force of 5.00  103 N on a ship moving at constant speed through a harbor. How much work does the tugboat do on the ship if each moves a distance of 3.00 km?

A shopper in a supermarket pushes a cart with a force of 35 N directed at an angle of 25 downward from the horizontal. Find the work done by the shopper as she moves down a 50-m length of aisle.

Starting from rest, a 5.00-kg block slides 2.50 m down a rough 30.0 incline. The coefcient of kinetic friction between the block and the incline is k  0.436. Determine (a) the work done by the force of gravity, (b) the work done by the friction force between block and incline, and (c) the work done by the normal force.

A horizontal force of 150 N is used to push a 40.0-kg packing crate a distance of 6.00 m on a rough horizontal surface. If the crate moves at constant speed, nd (a) the work done by the 150-N force and (b) the coefcient of kinetic friction between the crate and surface.

A sledge loaded with bricks has a total mass of 18.0 kg and is pulled at constant speed by a rope inclined at 20.0 above the horizontal. The sledge moves a distance of 20.0 m on a horizontal surface. The coefcient of kinetic friction between the sledge and surface is 0.500. (a) What is the tension in the rope? (b) How much work is done by the rope on the sledge? (c) What is the mechanical energy lost due to friction?

A block of mass 2.50kg is pushed 2.20m along a frictionless horizontal table by a constant 16.0-N force directed 25.0 below the horizontal. Determine the work done by (a) the applied force, (b) the normal force exerted by the table, (c) the force of gravity, and (d) the net force on the block.

A mechanic pushes a 2.50  103-kg car from rest to a speed of v, doing 5 000 J of work in the process. During this time, the car moves 25.0 m. Neglecting friction between car and road, nd (a) v and (b) the horizontal force exerted on the car.

A 7.00-kg bowling ball moves at 3.00 m/s. How fast must a 2.45-g Ping-Pong ball move so that the two balls have the same kinetic energy?

A person doing a chin-up weighs 700 N, exclusive of the arms. During the rst 25.0 cm of the lift, each arm exerts an upward force of 355 N on the torso. If the upward movement starts from rest, what is the persons velocity at that point?

The pulling force is 100 N parallel to the incline, which makes an angle of 20.0 with the horizontal. The coefcient of kinetic friction is 0.400, and the crate is pulled 5.00 m. (a) How much work is done by gravity? (b) How much mechanical energy is lost due to friction? (c) How much work is done by the 100-N force? (d) What is the change in kinetic energy of the crate? (e) What is the speed of the crate after being pulled 5.00 m?

A 70-kg base runner begins his slide into second base when he is moving at a speed of 4.0 m/s. The coefcient of friction between his clothes and Earth is 0.70. He slides so that his speed is zero just as he reaches the base. (a) How much mechanical energy is lost due to friction acting on the runner? (b) How far does he slide?

An outelder throws a 0.150-kg baseball at a speed of 40.0 m/s and an initial angle of 30.0. What is the kinetic energy of the ball at the highest point of its motion?

A 2.0-g bullet leaves the barrel of a gun at a speed of 300 m/s. (a) Find its kinetic energy. (b) Find the average force exerted by the expanding gases on the bullet as it moves the length of the 50-cm-long barrel.

A 0.60-kg particle has a speed of 2.0 m/s at point A and a kinetic energy of 7.5 J at point B. What is (a) its kinetic energy at A? (b) its speed at point B? (c) the total work done on the particle as it moves from A to B?

A 2 000-kg car moves down a level highway under the actions of two forces: a 1 000-N forward force exerted on the drive wheels by the road and a 950-N resistive force. Use the workenergy theorem to nd the speed of the car after it has moved a distance of 20 m, assuming that it starts from rest.

On a frozen pond, a 10-kg sled is given a kick that imparts to it an initial speed of v0  2.0 m/s. The coefcient of kinetic friction between sled and ice is k  0.10. Use the workenergy theorem to nd the distance the sled moves before coming to rest.

Find the height from which you would have to drop a ball so that it would have a speed of 9.0 m/s just before it hits the ground.

A ea is able to jump about 0.5 m. It has been said that if a ea were as big as a human, it would be able to jump over a 100-story building! When an animal jumps, it converts work done in contracting muscles into gravitational potential energy (with some steps in between). The maximum force exerted by a muscle is proportional to its cross-sectional area, and the work done by the muscle is this force times the length of contraction. If we magnied a ea by a factor of 1 000, the cross section of its muscle would increase by 1 0002 and the length of contraction would increase by 1 000. How high would this superea be able to jump? (Dont forget that the mass of the superea increases as well.)

An athlete on a trampoline leaps straight up into the air with an initial speed of 9.0 m/s. Find (a) the maximum height reached by the athlete relative to the trampoline and (b) the speed of the athlete when she is halfway up to her maximum height.

Truck suspensions often have helper springs that engage at high loads. One such arrangement is a leaf spring with a helper coil spring mounted on the axle, as shown in Figure P5.22. When the main leaf spring is compressed by distance y0, the helper spring engages and then helps to support any additional load. Suppose the leaf spring constant is 5.25  105 N/m, the helper spring constant is 3.60  105 N/m, and y0  0.500 m. (a) What is the compression of the leaf spring for a load of 5.00  105 N? (b) How much work is done in compressing the springs?

A daredevil on a motorcycle leaves the end of a ramp with a speed of 35.0m/s as in Figure P5.23. If his speed is 33.0m/s when he reaches the peak of the path, what is the maximum height that he reaches? Ignore friction and air resistance.

A softball pitcher rotates a 0.250-kg ball around a vertical circular path of radius 0.600m before releasing it. The pitcher exerts a 30.0-N force directed parallel to the motion of the ball around the complete circular path. The speed of the ball at the top of the circle is 15.0m/s. If the ball is released at the bottom of the circle, what is its speed upon release?

The chin-up is one exercise that can be used to strengthen the biceps muscle. This muscle can exert a force of approximately 800N as it contracts a distance of 7.5cm in a 75-kg male3. How much work can the biceps muscles (one in each arm) perform in a single contraction? Compare this amount of work with the energy required to lift a 75-kg person 40cm in performing a chin-up. Do you think the biceps muscle is the only muscle involved in performing a chin-up?

A 50-kg pole vaulter running at 10 m/s vaults over the bar. Her speed when she is above the bar is 1.0 m/s. Neglect air resistance, as well as any energy absorbed by the pole, and determine her altitude as she crosses the bar.

A child and a sled with a combined mass of 50.0 kg slide down a frictionless slope. If the sled starts from rest and has a speed of 3.00 m/s at the bottom, what is the height of the hill?

A 0.400-kg bead slides on a curved wire, starting from rest at point
in Figure P5.28. If the wire is frictionless, nd the speed of the bead (a) at  and (b) at .

A 5.00-kg steel ball is dropped onto a copper plate from a height of 10.0 m. If the ball leaves a dent 3.20 mm deep in the plate, what is the average force exerted by the plate on the ball during the impact?

A bead of mass m  5.00 kg is released from point
and slides on the frictionless track shown in Figure P5.30. Determine (a) the beads speed at points  and  and (b) the net work done by the force of gravity in moving the bead from
to .

Tarzan swings on a 30.0-m-long vine initially inclined at an angle of 37.0 with the vertical. What is his speed at the bottom of the swing (a) if he starts from rest? (b) if he pushes off with a speed of 4.00 m/s?

Three objects with masses m1  5.0 kg, m2  10 kg, and m3  15 kg, respectively, are attached by strings over frictionless pulleys, as indicated in Figure P5.32. The horizontal surface is frictionless and the system is released from rest. Using energy concepts, nd the speed of m3 after it moves down a distance of 4.0 m.

The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in Figure P5.33a. If the spring is compressed a distance of 0.120 m and the gun red vertically as shown, the gun can launch a 20.0-g projectile from rest to a maximum height of 20.0 m above the starting point of the projectile. Neglecting all resistive forces, determine (a) the spring constant and (b) the speed of the projectile as it moves through the equilibrium position of the spring (where x  0), as shown in Figure P5.33b.

A projectile is launched with a speed of 40 m/s at an angle of 60 above the horizontal. Use conservation of energy to nd the maximum height reached by the projectile during its ight.

A 0.250-kg block is placed on a light vertical spring (k  5.00  103 N/m) and pushed downwards, compressing the spring 0.100 m. After the block is released, it leaves the spring and continues to travel upwards. What height above the point of release will the block reach if air resistance is negligible?

The wire in Problem 28 (Fig. P5.28) is frictionless between points
and  and rough between  and . The 0.400-kg bead starts from rest at
. (a) Find its speed at . (b) If the bead comes to rest at , nd the loss in mechanical energy as it goes from  to .

(a) A child slides down a water slide at an amusement park from an initial height h. The slide can be considered frictionless because of the water owing down it. Can the equation for conservation of mechanical energy be used on the child? (b) Is the mass of the child a factor in determining his speed at the bottom of the slide? (c) The child drops straight down rather than following the curved ramp of the slide. In which case will he be traveling faster at ground level? (d) If friction is present, how would the conservation-of-energy equation be modied? (e) Find the maximum speed of the child when the slide is frictionless if the initial height of the slide is 12.0 m.

(a) A block with a mass m is pulled along a horizontal surface for a distance x by a constant force at an angle  with respect to the horizontal. The coefcient of kinetic friction between block and table is k. Is the force exerted by friction equal to kmg? If not, what is the force exerted by friction? (b) How much work is done by the friction force and by ? (Dont forget the signs.) (c) Identify all the forces that do no work on the block. (d) Let m  2.00 kg, x  4.00 m,   37.0, F  15.0 N, and k  0.400, and nd the answers to parts (a) and (b).

A 70-kg diver steps off a 10-m tower and drops from rest straight down into the water. If he comes to rest 5.0 m beneath the surface, determine the average resistive force exerted on him by the water.

An airplane of mass 1.5  104 kg is moving at 60 m/s. The pilot then revs up the engine so that the forward thrust by the air around the propeller becomes 7.5  104 N. If the force exerted by air resistance on the body of the airplane has a magnitude of 4.0  104 N, nd the speed of the airplane after it has traveled 500 m. Assume that the airplane is in level ight throughout this motion.

A 2.1  103-kg car starts from rest at the top of a 5.0-mlong driveway that is inclined at 20 with the horizontal. If an average friction force of 4.0  103 N impedes the motion, nd the speed of the car at the bottom of the driveway.

A 25.0-kg child on a 2.00-m-long swing is released from rest when the ropes of the swing make an angle of 30.0 with the vertical. (a) Neglecting friction, nd the childs speed at the lowest position. (b) If the actual speed of the child at the lowest position is 2.00 m/s, what is the mechanical energy lost due to friction?

Starting from rest, a 10.0-kg block slides 3.00 m down to the bottom of a frictionless ramp inclined 30.0 from the oor. The block then slides an additional 5.00 m along the oor before coming to a stop. Determine (a) the speed of the block at the bottom of the ramp, (b) the coefcient of kinetic friction between block and oor, and (c) the mechanical energy lost due to friction.

A child slides without friction from a height h along a curved water slide (Fig. P5.44). She is launched from a height h/5 into the pool. Determine her maximum airborne height y in terms of h and the launch angle .

A skier starts from rest at the top of a hill that is inclined 10.5 with respect to the horizontal. The hillside is 200 m long, and the coefcient of friction between snow and skis is 0.075 0. At the bottom of the hill, the snow is level and the coefcient of friction is unchanged. How far does the skier glide along the horizontal portion of the snow before coming to rest?

In a circus performance, a monkey is strapped to a sled and both are given an initial speed of 4.0m/s up a 20 inclined track. The combined mass of monkey and sled is 20kg, and the coefcient of kinetic friction between sled and incline is 0.20. How far up the incline do the monkey and sled move?

An 80.0-kg skydiver jumps out of a balloon at an altitude of 1 000 m and opens the parachute at an altitude of 200.0 m. (a) Assuming that the total retarding force on the diver is constant at 50.0 N with the parachute closed and constant at 3 600 N with the parachute open, what is the speed of the diver when he lands on the ground? (b) Do you think the skydiver will get hurt? Explain. (c) At what height should the parachute be opened so that the nal speed of the skydiver when he hits the ground is 5.00 m/s? (d) How realistic is the assumption that the total retarding force is constant? Explain.

A skier of mass 70 kg is pulled up a slope by a motordriven cable. (a) How much work is required to pull him 60 m up a 30 slope (assumed frictionless) at a constant speed of 2.0 m/s? (b) What power must a motor have to perform this task?

Columnist Dave Barry poked fun at the name The Grand Cities, adopted by Grand Forks, North Dakota, and East Grand Forks, Minnesota. Residents of the prairie towns then named a sewage pumping station for him. At the Dave Barry Lift Station No. 16, untreated sewage is raised vertically by 5.49 m in the amount of 1 890 000 liters each day. With a density of 1 050kg/m3, the waste enters and leaves the pump at atmospheric pressure through pipes of equal diameter. (a) Find the output power of the lift station. (b) Assume that a continuously operating electric motor with average power 5.90kW runs the pump. Find its efciency. In January 2002, Barry attended the outdoor dedication of the lift station and a festive potluck supper to which the residents of the different Grand Forks sewer districts brought casseroles, Jell-O salads, and bars (desserts).

While running, a person dissipates about 0.60J of mechanical energy per step per kilogram of body mass. If a 60-kg person develops a power of 70W during a race, how fast is the person running? (Assume a running step is 1.5 m long.)

The electric motor of a model train accelerates the train from rest to 0.620 m/s in 21.0 ms. The total mass of the train is 875 g. Find the average power delivered to the train during its acceleration.

An electric scooter has a battery capable of supplying 120 Wh of energy. [Note that an energy of 1 Wh  (1 J/s)(3600 s)  3600 J] If frictional forces and other losses account for 60.0% of the energy usage, what change in altitude can a rider achieve when driving in hilly terrain if the rider and scooter have a combined weight of 890 N?

A 1.50  103-kg car starts from rest and accelerates uniformly to 18.0 m/s in 12.0 s. Assume that air resistance remains constant at 400 N during this time. Find (a) the average power developed by the engine and (b) the instantaneous power output of the engine at t  12.0 s, just before the car stops accelerating.

A 650-kg elevator starts from rest and moves upwards for 3.00 s with constant acceleration until it reaches its cruising speed, 1.75 m/s. (a) What is the average power of the elevator motor during this period? (b) How does this amount of power compare with its power during an upward trip with constant speed?

The force acting on a particle varies as in Figure P5.55. Find the work done by the force as the particle moves (a) from x  0 to x  8.00 m, (b) from x  8.00 m to x  10.0 m, and (c) from x  0 to x  10.0 m.

An object is subject to a force Fx that varies with position as in Figure P5.56. Find the work done by the force on the object as it moves (a) from x  0 to x  5.00 m, (b) from x  5.00 m to x  10.0 m, and (c) from x  10.0 m to x  15.0 m. (d) What is the total work done by the force over the distance x  0 to x  15.0 m?

The force acting on an object is given by Fx  (8x  16) N, where x is in meters. (a) Make a plot of this force versus x from x  0 to x  3.00 m. (b) From your graph, nd the net work done by the force as the object moves from x  0 to x  3.00 m.

A 2.0-m-long pendulum is released from rest when the support string is at an angle of 25 with the vertical. What is the speed of the bob at the bottom of the swing?

An archer pulls her bowstring back 0.400m by exerting a force that increases uniformly from zero to 230N. (a) What is the equivalent spring constant of the bow? (b) How much work does the archer do in pulling the bow?

A block of mass 12.0 kg slides from rest down a frictionless 35.0 incline and is stopped by a strong spring with k  3.00  104 N/m. The block slides 3.00 m from the point of release to the point where it comes to rest against the spring. When the block comes to rest, how far has the spring been compressed?

(a) A 75-kg man steps out a window and falls (from rest) 1.0 m to a sidewalk. What is his speed just before his feet strike the pavement? (b) If the man falls with his knees and ankles locked, the only cushion for his fall is an approximately 0.50-cm give in the pads of his feet. Calculate the average force exerted on him by the ground in this situation. This average force is sufcient to cause damage to cartilage in the joints or to break bones.

A toy gun uses a spring to project a 5.3-g soft rubber sphere horizontally. The spring constant is 8.0 N/m, the barrel of the gun is 15 cm long, and a constant frictional force of 0.032 N exists between barrel and projectile. With what speed does the projectile leave the barrel if the spring was compressed 5.0 cm for this launch?

Two objects are connected by a light string passing over a light, frictionless pulley as in Figure P5.63. The 5.00-kg object is released from rest at a point 4.00 m above the oor. (a) Determine the speed of each object when the two pass each other. (b) Determine the speed of each object at the moment the 5.00-kg object hits the oor. (c) How much higher does the 3.00-kg object travel after the 5.00-kg object hits the oor?

Two blocks, A and B (with mass 50 kg and 100 kg, respectively), are connected by a string, as shown in Figure P5.64. The pulley is frictionless and of negligible mass. The coefcient of kinetic friction between block A and the incline is k  0.25. Determine the change in the kinetic energy of block A as it moves from  to , a distance of 20 m up the incline if the system starts from rest.

A 200-g particle is released from rest at point A on the inside of a smooth hemispherical bowl of radius R  30.0 cm (Fig. P5.65). Calculate (a) its gravitational potential energy at A relative to B, (b) its kinetic energy at B, (c) its speed at B, (d) its potential energy at C relative to B, and (e) its kinetic energy at C.

Energy is conventionally measured in Calories as well as in joules. One Calorie in nutrition is 1 kilocalorie, which we dene in Chapter 11 as 1 kcal  4 186 J. Metabolizing 1 gram of fat can release 9.00 kcal. A student decides to try to lose weight by exercising. She plans to run up and down the stairs in a football stadium as fast as she can and as many times as necessary. Is this in itself a practical way to lose weight? To evaluate the program, suppose she runs up a ight of 80 steps, each 0.150 m high, in 65.0 s. For simplicity, ignore the energy she uses in coming down (which is small). Assume that a typical efciency for human muscles is 20.0%. This means that when your body converts 100 J from metabolizing fat, 20 J goes into doing mechanical work (here, climbing stairs). The remainder goes into internal energy. Assume the students mass is 50.0 kg. (a) How many times must she run the ight of stairs to lose 1 pound of fat? (b) What is her average power output, in watts and in horsepower, as she is running up the stairs?

In terms of saving energy, bicycling and walking are far more efcient means of transportation than is travel by automobile. For example, when riding at 10.0 mi/h, a cyclist uses food energy at a rate of about 400 kcal/h above what he would use if he were merely sitting still. (In exercise physiology, power is often measured in kcal/h rather than in watts. Here, 1 kcal  1 nutritionists Calorie  4 186 J.) Walking at 3.00 mi/h requires about 220 kcal/h. It is interesting to compare these values with the energy consumption required for travel by car. Gasoline yields about 1.30  108 J/gal. Find the fuel economy in equivalent miles per gallon for a person (a) walking and (b) bicycling.

An 80.0-N box is pulled 20.0 m up a 30 incline by an applied force of 100 N that points upwards, parallel to the incline. If the coefcient of kinetic friction between box and incline is 0.220, calculate the change in the kinetic energy of the box.

A ski jumper starts from rest 50.0 m above the ground on a frictionless track and ies off the track at an angle of 45.0 above the horizontal and at a height of 10.0 m above the level ground. Neglect air resistance. (a) What is her speed when she leaves the track? (b) What is the maximum altitude she attains after leaving the track? (c) Where does she land relative to the end of the track?

A 5.0-kg block is pushed 3.0 m up a vertical wall with constant speed by a constant force of magnitude F applied at an angle of   30 with the horizontal, as shown in Figure P5.70. If the coefcient of kinetic friction between block and wall is 0.30, determine the work done by (a) , (b) the force of gravity, and (c) the normal force between block and wall. (d) By how much does the gravitational potential energy increase during the blocks motion?

The ball launcher in a pinball machine has a spring with a force constant of 1.20 N/cm (Fig. P5.71). The surface on which the ball moves is inclined 10.0 with respect to the horizontal. If the spring is initially compressed 5.00 cm, nd the launching speed of a 0.100-kg ball when the plunger is released. Friction and the mass of the plunger are negligible.

The masses of the javelin, discus, and shot are 0.80 kg, 2.0 kg, and 7.2 kg, respectively, and record throws in the corresponding track events are about 98 m, 74 m, and 23 m, respectively. Neglecting air resistance, (a) calculate the minimum initial kinetic energies that would produce these throws, and (b) estimate the average force exerted on each object during the throw, assuming the force acts over a distance of 2.0 m. (c) Do your results suggest that air resistance is an important factor?

Jane, whose mass is 50.0 kg, needs to swing across a river lled with crocodiles in order to rescue Tarzan, whose mass is 80.0 kg. However, she must swing into a constant horizontal wind force on a vine that is initially at an angle of  with the vertical. (See Fig. P5.73.) In the gure, D  50.0 m, F  110 N, L  40.0 m, and   50.0. (a) With what minimum speed must Jane begin her swing in order to just make it to the other side? (Hint: First determine the potential energy that can be associated with the wind force. Because the wind force is constant, use an analogy with the constant gravitational force.) (b) Once the rescue is complete, Tarzan and Jane must swing back across the river. With what minimum speed must they begin their swing?

A hummingbird is able to hover because, as the wings move downwards, they exert a downward force on the air. Newtons third law tells us that the air exerts an equal and opposite force (upwards) on the wings. The average of this force must be equal to the weight of the bird when it hovers. If the wings move through a distance of 3.5 cm with each stroke, and the wings beat 80 times per second, determine the work performed by the wings on the air in 1 minute if the mass of the hummingbird is 3.0 grams.

A childs pogo stick (Fig. P5.75) stores energy in a spring (k  2.50  104 N/m). At position
(x1  0.100 m), the spring compression is a maximum and the child is momentarily at rest. At position  (x  0), the spring is relaxed and the child is moving upwards. At position , the child is again momentarily at rest at the top of the jump. Assuming that the combined mass of child and pogo stick is 25.0 kg, (a) calculate the total energy of the system if both potential energies are zero at x  0, (b) determine x2, (c) calculate the speed of the child at x  0, (d) determine the value of x for which the kinetic energy of the system is a maximum, and (e) obtain the childs maximum upward speed.

A 2.00-kg block situated on a rough incline is connected to a spring of negligible mass having a spring constant of 100 N/m (Fig. P5.76). The block is released from rest when the spring is unstretched, and the pulley is frictionless. The block moves 20.0 cm down the incline before coming to rest. Find the coefcient of kinetic friction between block and incline.

In the dangerous sport of bungee jumping, a daring student jumps from a hot-air balloon with a specially designed elastic cord attached to his waist, as shown in Figure P5.77. The unstretched length of the cord is 25.0 m, the student weighs 700 N, and the balloon is 36.0 m above the surface of a river below. Calculate the required force constant of the cord if the student is to stop safely 4.00 m above the river.

An object of mass m is suspended from the top of a cart by a string of length L as in Figure P5.78a. The cart and object are initially moving to the right at a constant speed v0. The cart comes to rest after colliding and sticking to a bumper, as in Figure P5.78b, and the suspended object swings through an angle  . (a) Show that the initial speed is . (b) If L  1.20 m and   35.0, nd the initial speed of the cart. (Hint: The force exerted by the string on the object does no work on the object.)

A truck travels uphill with constant velocity on a highway with a 7.0 slope. A 50-kg package sits on the oor of the back of the truck and does not slide, due to a static frictional force. During an interval in which the truck travels 340 m, what is the net work done on the package? What is the work done on the package by the force of gravity, the normal force, and the friction force?

As part of a curriculum unit on earthquakes, suppose that 375 000 British schoolchildren stand on their chairs and simultaneously jump down to the oor. Seismographers around the country see whether they can detect the resulting ground tremor. (This experiment was actually based on a suggestion by the children themselves.) (a) Find the energy released in the experiment. Model the children as having average mass 36.0 kg and as stepping from chair seats 38.0 cm above the oor. (b) Most of the energy is converted very rapidly into internal energy within the bodies of the children and the oors of the school buildings. Assume that 1% of the energy is carried away by a seismic wave. The magnitude of an earthquake on the Richter scale is given by where E is the seismic wave energy in joules. According to this model, what is the magnitude of the demonstration quake?

A loaded ore car has a mass of 950 kg and rolls on rails with negligible friction. It starts from rest and is pulled up a mine shaft by a cable connected to a winch. The shaft is inclined at 30.0 above the horizontal. The car accelerates uniformly to a speed of 2.20 m/s in 12.0 s and then continues at constant speed. (a) What power must the winch motor provide when the car is moving at constant speed? (b) What maximum power must the motor provide? (c) What total energy transfers out of the motor by work by the time the car moves off the end of the track, which is of length 1 250 m?

A daredevil wishes to bungee-jump from a hot-air balloon 65.0 m above a carnival midway (Fig. P5.77). He will use a piece of uniform elastic cord tied to a harness around his body to stop his fall at a point 10.0 m above the ground. Model his body as a particle and the cord as having negligible mass and a tension force described by Hookes force law. In a preliminary test, hanging at rest from a 5.00-m length of the cord, the jumper nds that his body weight stretches it by 1.50 m. He will drop from rest at the point where the top end of a longer section of the cord is attached to the stationary balloon. (a) What length of cord should he use? (b) What maximum acceleration will he experience?

The system shown in Figure P5.83 consists of a light, inextensible cord, light frictionless pulleys, and blocks of equal mass. Initially, the blocks are at rest the same height above the ground. The blocks are then released. Find the speed of block A at the moment when the vertical separation of the blocks is h.

A cafeteria tray dispenser supports a stack of trays on a shelf that hangs from four identical spiral springs under tension, one near each corner of the shelf. Each tray has a mass of 580 g and is rectangular, 45.3 cm by 35.6 cm, and 0.450 cm thick. (a) Show that the top tray in the stack can always be at the same height above the oor, however many trays are in the dispenser. (b) Find the spring constant each spring should have in order for the dispenser to function in this convenient way. Is any piece of data unnecessary for this determination?

In bicycling for aerobic exercise, a woman wants her heart rate to be between 136 and 166 beats per minute. Assume that her heart rate is directly proportional to her mechanical power output. Ignore all forces on the woman-plusbicycle system, except for static friction forward on the drive wheel of the bicycle and an air resistance force proportional to the square of the bicyclers speed. When her speed is 22.0 km/h, her heart rate is 90.0 beats per minute. In what range should her speed be so that her heart rate will be in the range she wants?

In a needle biopsy, a narrow strip of tissue is extracted from a patient with a hollow needle. Rather than being pushed by hand, to ensure a clean cut the needle can be red into the patients body by a spring. Assume the needle has mass 5.60 g, the light spring has force constant 375 N/m, and the spring is originally compressed 8.10 cm to project the needle horizontally without friction. The tip of the needle then moves through 2.40 cm of skin and soft tissue, which exerts a resistive force of 7.60 N on it. Next, the needle cuts 3.50 cm into an organ, which exerts a backward force of 9.20 N on it. Find (a) the maximum speed of the needle and (b) the speed at which a ange on the back end of the needle runs into a stop, set to limit the penetration to 5.90 cm.

The power of sunlight reaching each square meter of the Earths surface on a clear day in the tropics is close to 1 000 W. On a winter day in Manitoba, the power concentration of sunlight can be 100 W/m2. Many human activities are described by a power-per-footprint-area on the order of 102 W/m2 or less. (a) Consider, for example, a family of four paying $80 to the electric company every 30 days for 600 kWh of energy carried by electric transmission to their house, with oor area 13.0 m by 9.50 m. Compute the power-per-area measure of this energy use. (b) Consider a car 2.10 m wide and 4.90 m long traveling at 55.0 mi/h using gasoline having a heat of combustion of 44.0 MJ/kg with fuel economy 25.0 mi/gallon. One gallon of gasoline has a mass of 2.54 kg. Find the power-perarea measure of the cars energy use. It can be similar to that of a steel mill where rocks are melted in blast furnaces. (c) Explain why the direct use of solar energy is not practical for a conventional automobile.

In 1887 in Bridgeport, Connecticut, C. J. Belknap built the water slide shown in Figure P5.88. A rider on a small sled, of total mass 80.0 kg, pushed off to start at the top of the slide (point
) with a speed of 2.50 m/s. The chute was 9.76 m high at the top, 54.3 m long, and 0.51 m wide. Along its length, 725 wheels made friction negligible. Upon leaving the chute horizontally at its bottom end (point ), the rider skimmed across the water of Long Island Sound for as much as 50 m, skipping along like a at pebble, before at last coming to rest and swimming ashore, pulling his sled after him. (a) Find the speed of the sled and rider at point . (b) Model the force of water friction as a constant retarding force acting on a particle. Find the work done by water friction in stopping the sled and rider. (c) Find the magnitude of the force the water exerts on the sled. (d) Find the magnitude of the force the chute exerts on the sled at point .

Three objects with masses m1  5.0 kg, m2  10 kg, and m3  15 kg, respectively, are attached by strings over frictionless pulleys as indicated in Figure P5.32. The horizontal surface exerts a force of friction of 30 N on m2. If the system is released from rest, use energy concepts to nd the speed of m3 after it moves down 4.0 m.

Suspend a rubber band from a support and borrow some weights from your instructor to measure the rubber bands spring constant for small extensions. Calculate how much elastic potential energy is stored in the rubber band for a given extension. Use conservation of energy to predict how high a paper wad will go into the air when released from a given extension of the band. Try it to test your prediction.

Wrap a rubber band tightly around a tennis ball. Now fasten one end of a string through the rubber band and the other end to the top of a doorframe to construct a pendulum. Pull the pendulum to the side at a variety of angles to observe that the energy of the pendulumEarth system is always conserved as the pendulum swings (almost) to the same height of its arc as the height from which it was released. (The word almost in the last sentence applies because some energy is lost to friction at the point of support and to air resistance. You can observe this slight loss of energy by pulling the ball to the side and letting it go from a point about half an inch from your chin. Let it gobut dont push it!and test your belief in conservation of energy by seeing if you can avoid inching when the ball swings back toward your chin.)

While you have your pendulum from the last activity set up, predict what will happen in the following situation and then test your guess: When a pendulum is released from a given height, it swings to the same height at the other end of its arc as you noted above. However, suppose you place a meterstick across the door opening such that the pendulum string strikes the stick about halfway up the string when it moves through the opening. How high will the ball swing in this case? Will it return to the same height as that at which it started, swing to a lower height, or swing to a greater height? Explain your answer.

Measure your pulse rate while at rest. Now slowly walk up a ight of stairs and measure your pulse rate at the top of the stairs. Repeat this activity, starting with about the same rest pulse rate at the bottom of the stairs. This time, run up the stairs. Based on your pulse rate readings, what can you conclude about the amount of work and power expended in each case? Repeat this experiment with a series of 10 push-ups.

Many tness centers have stepper machines that enable a person to climb continuously without actually moving, because the steps move downwards as the person climbs. The work that the climber performs on the step is determined by the force exerted on the step times the distance the step moves. Since the net force on the climber is zero, the force exerted on the step must equal the climbers weight. A reasonably strenuous workout on this machine is 90 steps per minute, with each step being 8 inches (15.2 cm) high. What is the rate (in watts) at which a 130-lb (60 kg) climber does work on the stair steps? The energy actually expended by the climber is approximately ve times the work done. (You may notice that a lot of heat is generated!) The machines usually report this rate in Calories/hour (1 Calorie  1 kcal  4186 J). Determine the rate, in Cal/h, at which energy is expended by the 130-lb climber. Activity: If you have access to a stepper, nd the ratio used by the manufacturer to determine the energy expended from the work performed. In some cases, this ratio may vary as the step speed changes. If so, generate a graph of the ratio as a function of step speed.