Measuring coeffi cients of friction A coin is placed near

What other forces act on the airboat? Describe them.

True or False: In general, the net acceleration is always directed toward the horse that exerts the greater magnitude force.

Mars is about one and a half times as far from the Sun as Earth. To one signifi cant digit, what is the gravitational force of the Sun on a 70.0 kg man standing on Mars? (Hint: Use the result of part (a) and the inverse square nature of the force.)

Suppose one world is made of ice whereas another world with the same radius is made of rock. If g is the acceleration of gravity on the surface of the ice world, what is the approximate acceleration of gravity on the rock world? (Hint: Estimate the mass of a rock in terms of the mass of an ice cube having the same size.)

How would the answers change if a second traffi c light were attached beneath the fi rst?

Consider the same scenario on a hill with a steeper slope. Would the magnitude of the tension in the rope get larger, smaller, or remain the same as before? How would the normal force be affected?

What effect does doubling the weight have on the acceleration and the displacement?

If the car is parked on a more gentle slope, how will the time required for it to slide to the bottom of the hill be affected? Explain.

Starting from rest, an elevator accelerates upward, reaching and maintaining a constant velocity thereafter until it reaches the desired fl oor, when it begins to slow down. Describe the scale reading during this time.

How could this simple machine be used to raise objects too heavy for a person to lift?

How would a larger static friction coeffi cient affect the maximum angle?

How would the answer be affected if the puck were struck by an astronaut on a patch of ice on Mars, where the acceleration of gravity is 0.35g, with all other given quantities remaining the same?

If mass m2 is increased, does the acceleration of the system increase, decrease, or remain the same? Does the tension increase, decrease, or remain the same?

What would happen if the tension force exceeded 51.5 N?

A horizontal force of 95.0 N is applied to a 60.0-kg crate on a rough, level surface. If the crate accelerates at 1.20 m/s2, what is the magnitude of the force of kinetic friction acting on the crate? (a) 23.0 N (b) 45.0 N (c) 16.0 N (d) 33.0 N (e) 8.80 N

A 70.0-kg man stands on a pedestal of mass 27.0 kg, which rests on a level surface. What is the normal force exerted by the ground on the pedestal? (a) 265 N (b) 368 N (c) 478 N (d) 624 N (e) 951 N

Two monkeys of equal mass are holding onto a single vine of negligible mass that hangs vertically from a tree, with one monkey a few meters higher than the other. What is the ratio of the tension in the vine above the upper monkey to the tension in the vine between the two monkeys? (a) 1 2 (b) 1 (c) 1.5 (d) 2 (e) More information is required.

A force of 70.0 N is exerted at an angle of 30.0 below the horizontal on a block of mass 8.00 kg that is resting on a table. What is the magnitude of the normal force acting on the block? (a) 43.4 N (b) 78.4 N (c) 113 N (d) 126 N (e) 92.4 N

If Earths mass and radius both suddenly doubled, what would the new value of the acceleration of gravity near Earths surface? (a) 9.80 m/s2 (b) 4.90 m/s2 (c) 2.45 m/s2 (d) 19.6 m/s2 (e) 12.6 m/s2

A crate remains stationary after it has been placed on a ramp inclined at an angle with the horizontal. Which of the following statements must be true about the magnitude of the frictional force that acts on the crate? (a) It is larger than the weight of the crate. (b) It is at least equal to the weight of the crate. (c) It is equal to ms n. (d) It is greater than the component of the gravitational force acting down the ramp. (e) It is equal to the component of the gravitational force acting down the ramp.

A thrown rock hits a window, breaking the glass, and ends up on the fl oor inside the room. Which of the following statements are true? (a) The force of the rock on the glass was bigger than the force of the glass on the rock. (b) The force of the rock on the glass had the same magnitude as the force of the glass on the rock. (c) The force of the rock on the glass was less than the force of the glass on the rock. (d) The rock didnt slow down as it broke the glass. (e) None of these statements is true.

A manager of a restaurant pushes horizontally with a force of magnitude 150 N on a box of melons. The box moves across the fl oor with a constant acceleration in the same direction as the applied force. Which statement is most accurate concerning the magnitude of the force of kinetic friction acting on the box? (a) It is greater than 150 N. (b) It is less than 150 N. (c) It is equal to 150 N. (d) The kinetic friction force is steadily decreasing. (e) The kinetic friction force must be zero.

Four forces act on an object, given by A S 40 N east, aB S 50 N north, C S 70 N west, and D = 90 N south. What is the magnitude of the net force on the object? (a) 50 N (b) 70 N (c) 131 N (d) 170 N (e) 250 N

If an object of mass m moves with constant velocity v, the net force on the object is (a) mg (b) mv (c) ma (d) 0 (e) None of these answers is correct.

If an object is in equilibrium, which of the following statements is not true? (a) The speed of the object remains constant. (b) The acceleration of the object is zero. (c) The net force acting on the object is zero. (d) The object must be at rest. (e) The velocity is constant.

A truck loaded with sand accelerates along a highway. The driving force on the truck remains constant. What happens to the acceleration of the truck as its trailer leaks sand at a constant rate through a hole in its bottom? (a) It decreases at a steady rate. (b) It increases at a steady rate. (c) It increases and then decreases. (d) It decreases and then increases. (e) It remains constant.

A large crate of mass m is placed on the back of a truck but not tied down. As the truck accelerates forward with an acceleration a, the crate remains at rest relative to the truck. What force causes the crate to accelerate forward? (a) the normal force (b) the force of gravity (c) the force of friction between the crate and the fl oor of the truck (d) the ma force (e) none of these

Which of the following statements are true? (a) An astronauts weight is the same on the Moon as on Earth. (b) An astronauts mass is the same on the International Space Station as it is on Earth. (c) Earths gravity has no effect on astronauts inside the International Space Station. (d) An astronauts mass is greater on Earth than on the Moon. (e) None of these statements are true.

Two objects are connected by a string that passes over a frictionless pulley as in Active Figure 4.18, where m1 m2 and a1 and a2 are the respective magnitudes of the accelerations. Which mathematical statement is true concerning the magnitude of the acceleration a2 of mass m2? (a) a2 g (b) a2 g (c) a2 g (d) a2 a1 (e) a2 a1

An object of mass m undergoes an acceleration a S down a rough incline. Which of the following forces should not appear in the free-body diagram for the object? Choose all correct answers. (a) the force of gravity (b) m a S (c) the normal force of the incline on the object (d) the force of friction down the incline (e) the force of friction up the incline (f) the force of the object on the incline

A ball is held in a persons hand. (a) Identify all the external forces acting on the ball and the reaction to each. (b) If the ball is dropped, what force is exerted on it while it is falling? Identify the reaction force in this case. (Neglect air resistance.)

If gold were sold by weight, would you rather buy it in Denver or in Death Valley? If it were sold by mass, in which of the two locations would you prefer to buy it? Why?

If you push on a heavy box that is at rest, you must exert some force to start its motion. However, once the box is sliding, you can apply a smaller force to maintain its motion. Why?

A space explorer is moving through space far from any planet or star. He notices a large rock, taken as a specimen from an alien planet, fl oating around the cabin of the ship. Should he push it gently or should he kick it toward the storage compartment? Why?

A passenger sitting in the rear of a bus claims that she was injured as the driver slammed on the brakes, causing a suitcase to come fl ying toward her from the front of the bus. If you were the judge in this case, what disposition would you make? Why?

A weight lifter stands on a bathroom scale. She pumps a barbell up and down. What happens to the reading on the scale? Suppose she is strong enough to actually throw the barbell upward. How does the reading on the scale vary now?

What force causes an automobile to move? A propellerdriven airplane? A rowboat?

Analyze the motion of a rock dropped in water in terms of its speed and acceleration as it falls. Assume a re sistive force is acting on the rock that increases as the velocity of the rock increases.

In the motion picture It Happened One Night (Columbia Pictures, 1934), Clark Gable is standing inside a stationary bus in front of Claudette Colbert, who is seated. The bus suddenly starts moving forward and Clark falls into Claudettes lap. Why did this happen?

As a rocket is fi red from a launching pad, its speed and acceleration increase with time as its engines continue to operate. Explain why this occurs even though the thrust of the engines remains constant.

In a tug-of-war between two athletes, each pulls on the rope with a force of 200 N. What is the tension in the rope? If the rope doesnt move, what horizontal force does each athlete exert against the ground?

Draw a free-body diagram for each of the following objects: (a) a projectile in motion in the presence of air resistance, (b) a rocket leaving the launch pad with its engines operating, (c) an athlete running along a horizontal track.

Identify the actionreaction pairs in the following situations: (a) a man takes a step, (b) a snowball hits a girl in the back, (c) a baseball player catches a ball, (d) a gust of wind strikes a window.

Suppose you are driving a car at a high speed. Why should you avoid slamming on your brakes when you want to stop in the shortest possible distance? (Newer cars have antilock brakes that avoid this problem.)

The heaviest invertebrate is the giant squid, which is estimated to have a weight of about 2 tons spread out over its length of 70 feet. What is its weight in newtons?

A football punter accelerates a football from rest to a speed of 10 m/s during the time in which his toe is in contact with the ball (about 0.20 s). If the football has a mass of 0.50 kg, what average force does the punter exert on the ball?

A 6.0-kg object undergoes an acceleration of 2.0 m/s2. (a) What is the magnitude of the resultant force acting on it? (b) If this same force is applied to a 4.0-kg object, what acceleration is produced?

One or more external forces are exerted on each object enclosed in a dashed box shown in Figure 4.2. Identify the reaction to each of these forces.

A bag of sugar weighs 5.00 lb on Earth. What would it weigh in newtons on the Moon, where the free-fall acceleration is one-sixth that on Earth? Repeat for Jupiter, where g is 2.64 times that on Earth. Find the mass of the bag of sugar in kilograms at each of the three locations.

A freight train has a mass of 1.5  107 kg. If the locomotive can exert a constant pull of 7.5  105 N, how long does it take to increase the speed of the train from rest to 80 km/h?

The air exerts a forward force of 10 N on the propeller of a 0.20-kg model airplane. If the plane accelerates forward at 2.0 m/s2, what is the magnitude of the resistive force exerted by the air on the airplane?

Consider a solid metal sphere (S) a few centimeters in diameter and a feather (F). For each quantity in the list that follows, indicate whether the quantity is the same, greater, or lesser in the case of S or in that of F. Explain in each case why you gave the answer you did. Here is the list: (a) the gravitational force, (b) the time it will take to fall a given distance in air, (c) the time it will take to fall a given distance in vacuum, (d) the total force on the object when falling in vacuum.

A chinook salmon has a maximum underwater speed of 3.0 m/s, and can jump out of the water vertically with a speed of 6.0 m/s. A record salmon has a length of 1.5 m and a mass of 61 kg. When swimming upward at constant speed, and neglecting buoyancy, the fi sh experiences three forces: an upward force F exerted by the tail fi n, the downward drag force of the water, and the downward force of gravity. As the fi sh leaves the surface of the water, however, it experiences a net upward force causing it to accelerate from 3.0 m/s to 6.0 m/s. Assuming the drag force disappears as soon as the head of the fi sh breaks the surface and F is exerted until two-thirds of the fi shs length has left the water, determine the magnitude of F.

A 5.0-g bullet leaves the muzzle of a rifl e with a speed of 320 m/s. What force (assumed constant) is exerted on the bullet while it is traveling down the 0.82-m-long barrel of the rifl e?

A boat moves through the water with two forces acting on it. One is a 2 000-N forward push by the water on the propeller, and the other is a 1 800-N resistive force due to the water around the bow. (a) What is the acceleration of the 1 000-kg boat? (b) If it starts from rest, how far will the boat move in 10.0 s? (c) What will its velocity be at the end of that time?

Two forces are applied to a car in an effort to move it, as shown in Figure P4.12. (a) What is the resultant of these two forces? (b) If the car has a mass of 3 000 kg, what acceleration does it have? Ignore friction.

A 65.0-kg skydiver reaches a terminal speed of 55.0 m/s with her parachute undeployed. Suppose the drag force acting on her is proportional to the speed squared, or Fdrag kv 2. (a) What is the constant of proportionality k? (Assume the gravitational acceleration is 9.80 m/s2.) (b) What was the magnitude of her acceleration when she was falling at half terminal speed?

An object of mass m is dropped from the roof of a building of height h. While the object is falling, a wind blowing parallel to the face of the building exerts a constant horizontal force F on the object. (a) How long does it take the object to strike the ground? Express the time t in terms of g and h. (b) Find an expression in terms of m and F for the acceleration ax of the object in the horizontal direction (taken as the positive x-direction). (c) How far is the object displaced horizontally before hitting the ground? Answer in terms of m, g, F, and h. (d) Find the magnitude of the objects acceleration while it is falling, using the variables F, m, and g.

After falling from rest from a height of 30 m, a 0.50-kg ball rebounds upward, reaching a height of 20 m. If the contact between ball and ground lasted 2.0 ms, what average force was exerted on the ball?

The force exerted by the wind on the sails of a sailboat is 390 N north. The water exerts a force of 180 N east. If the boat (including its crew) has a mass of 270 kg, what are the magnitude and direction of its acceleration?

(a) Find the tension in each cable supporting the 600-N cat burglar in Figure P4.17. (b) Suppose the horizontal cable were reattached higher up on the wall. Would the tension in the other cable increase, decrease, or stay the same? Why?

A certain orthodontist uses a wire brace to align a patients crooked tooth as in Figure P4.18. The tension in the wire is adjusted to have a magnitude of 18.0 N. Find the magnitude of the net force exerted by the wire on the crooked tooth.

A 150-N bird feeder is supported by three cables as shown in Figure P4.19. Find the tension in each cable.

The leg and cast in Figure P4.20 weigh 220 N (w1). Determine the weight w2 and the angle a needed so that no force is exerted on the hip joint by the leg plus the cast.

Two blocks each of mass 3.50 kg are fastened to the top of an elevator as in Figure P4.21. (a) If the elevator accelerates upward at 1.60 m/s2, fi nd the tensions T1 and T2 in the upper and lower strings. (b) If the strings can withstand a maximum tension of 85.0 N, what maximum acceleration can the elevator have before the fi rst string breaks?

Two blocks each of mass m are fastened to the top of an elevator as in Figure P4.21. The elevator has an upward acceleration a. The strings have negligible mass. (a) Find the tensions T1 and T2 in the upper and lower strings in terms of m, a, and g. (b) Compare the two tensions and determine which string would break fi rst if a is made suffi ciently large. (c) What are the tensions if the elevator cable breaks?

The distance between two telephone poles is 50.0 m. When a 1.00-kg bird lands on the telephone wire midway between the poles, the wire sags 0.200 m. Draw a freebody diagram of the bird. How much tension does the bird produce in the wire? Ignore the weight of the wire.

Two people are pulling a boat through the water as in Figure P4.24. Each exerts a force of 600 N directed at a 30.0 angle relative to the forward motion of the boat. If the boat moves with constant velocity, fi nd the resistive force F S exerted by the water on the boat.

A 5.0-kg bucket of water is raised from a well by a rope. If the upward acceleration of the bucket is 3.0 m/s2, fi nd the force exerted by the rope on the bucket.

A shopper in a supermarket pushes a loaded cart with a horizontal force of 10 N. The cart has a mass of 30 kg. (a) How far will it move in 3.0 s, starting from rest? (Ignore friction.) (b) How far will it move in 3.0 s if the shopper places his 30-N child in the cart before he begins to push it?

A 2 000-kg car is slowed down uniformly from 20.0 m/s to 5.00 m/s in 4.00 s. (a) What average force acted on the car during that time, and (b) how far did the car travel during that time?

Two packing crates of masses 10.0 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.28. The 5.00-kg crate lies on a smooth incline of angle 40.0. Find the acceleration of the 5.00-kg crate and the tension in the string

Assume the three blocks portrayed in Figure P4.29 move on a frictionless surface and a 42-N force acts as shown on the 3.0-kg block. Determine (a) the accel eration given this system, (b) the tension in the cord connecting the 3.0-kg and the 1.0-kg blocks, and (c) the force exerted by the 1.0-kg block on the 2.0-kg block.

An object of mass 2.0 kg starts from rest and slides down an inclined plane 80 cm long in 0.50 s. What net force is acting on the object along the incline?

A setup similar to the one shown in Figure P4.31 is often used in hospitals to support and apply a traction force to an injured leg. (a) Determine the force of tension in the rope supporting the leg. (b) What is the traction force exerted on the leg? Assume the traction force is horizontal.

Two blocks of masses m1 and m2 (m1 m2) are placed on a frictionless table in contact with each other. A horizontal force of magnitude F is applied to the block of mass m1 in Figure P4.32. (a) If P is the magnitude of the contact force between the blocks, draw the free-body diagrams for each block. (b) What is the net force on the system consisting of both blocks? (c) What is the net force acting 30. An object of mass 2.0 kg starts from rest and slides down an inclined plane 80 cm long in 0.50 s. What net force is acting on the object along the incline? 31. A setup similar to the one shown in Figure P4.31 is often used in hospitals to support and apply a traction force to an injured leg. (a) Determine the force of tension in the rope supporting the leg. (b) What is the traction force exerted on the leg? Assume the traction force is horizontal. on m1? (d) What is the net force acting on m2? (e) Write the x-component of Newtons second law for each block. (f) Solve the resulting system of two equations and two unknowns, expressing the acceleration a and contact force P in terms of the masses and force. (g) How would the answers change if the force had been applied to m2 instead? (Hint: use symmetry; dont calculate!) Is the contact force larger, smaller, or the same in this case? Why?

An 80-kg stuntman jumps from a window of a building situated 30 m above a catching net. Assuming air resistance exerts a 100-N force on the stuntman as he falls, determine his velocity just before he hits the net.

In Figure P4.34, the light, taut, unstretchable cord B joins block 1 and the larger-mass block 2. Cord A exerts a force on block 1 to make it accelerate forward. (a) How does the magnitude of the force exerted by cord A on block 1 compare with the magnitude of the force exerted by cord B on block 2? (b) How does the acceleration of block 1 compare with the acceleration of block 2? (c) Does cord B exert a force on block 1? Explain your answer.

(a) An elevator of mass m moving upward has two forces acting on it: the upward force of tension in the cable and the downward force due to gravity. When the elevator is accelerating upward, which is greater, T or w? (b) When the elevator is moving at a constant velocity upward, which is greater, T or w? (c) When the elevator is moving upward, but the acceleration is downward, which is greater, T or w? (d) Let the elevator have a mass of 1 500 kg and an upward acceleration of 2.5 m/s2. Find T. Is your answer consistent with the answer to part (a)? (e) The elevator of part (d) now moves with a constant upward velocity of 10 m/s. Find T. Is your answer consistent with your answer to part (b)? (f) Having initially moved upward with a constant velocity, the elevator begins to accelerate downward at 1.50 m/s2. Find T. Is your answer consistent with your answer to part (c)?

An object with mass m1 5.00 kg rests on a frictionless horizontal table and is connected to a cable that passes over a pulley and is then fastened to a hanging object with mass m2 10.0 kg, as shown in Figure P4.36. Find the acceleration of each object and the tension in the cable.

A 1 000-kg car is pulling a 300-kg trailer. Together, the car and trailer have an acceleration of 2.15 m/s2 in the forward direction. Neglecting frictional forces on the trailer, determine (a) the net force on the car, (b) the net force on the trailer, (c) the force exerted by the trailer on the car, and (d) the resultant force exerted by the car on the road.

Two objects with masses of 3.00 kg and 5.00 kg are connected by a light string that passes over a frictionless pulley, as in Figure P4.38. Determine (a) the tension in the string, (b) the acceleration of each object, and (c) the distance each object will move in the fi rst second of motion if both objects start from rest.

A dockworker loading crates on a ship fi nds that a 20-kg crate, initially at rest on a horizontal surface, requires a 75-N horizontal force to set it in motion. However, after the crate is in motion, a horizontal force of 60 N is required to keep it moving with a constant speed. Find the coeffi cients of static and kinetic friction between crate and fl oor

In Figure P4.36, m1 10 kg and m2 4.0 kg. The coeffi cient of static friction between m1 and the horizontal surface is 0.50, and the coeffi cient of kinetic friction is 0.30. (a) If the system is released from rest, what will its acceleration be? (b) If the system is set in motion with m2 moving downward, what will be the acceleration of the system?

A 1 000-N crate is being pushed across a level fl oor at a constant speed by a force F S of 300 N at an angle of 20.0 below the horizontal, as shown in Figure P4.41a. (a) What is the coeffi cient of kinetic friction between the crate and the fl oor? (b) If the 300-N force is instead pulling the block at an angle of 20.0 above the horizontal, as shown in Figure P4.41b, what will be the acceleration of the crate? Assume that the coeffi cient of friction is the same as that found in part (a).

A hockey puck is hit on a frozen lake and starts moving with a speed of 12.0 m/s. Five seconds later, its speed is 6.00 m/s. (a) What is its average acceleration? (b) What is the average value of the coeffi cient of kinetic friction between puck and ice? (c) How far does the puck travel during the 5.00-s interval?

Consider a large truck carrying a heavy load, such as steel beams. A signifi cant hazard for the driver is that the load may slide forward, crushing the cab, if the truck stops suddenly in an accident or even in braking. Assume, for example, a 10 000-kg load sits on the fl atbed of a 20 000-kg truck moving at 12.0 m/s. Assume the load is not tied down to the truck and has a coeffi cient of static friction of 0.500 with the truck bed. (a) Calculate the minimum stopping distance for which the load will not slide forward relative to the truck. (b) Is any piece of data unnecessary for the solution?

A crate of mass 45.0 kg is being transported on the fl atbed of a pickup truck. The coeffi cient of static friction between the crate and the trucks fl atbed is 0.350, and the coeffi cient of kinetic friction is 0.320. (a) The truck accelerates forward on level ground. What is the maximum acceleration the truck can have so that the crate does not slide relative to the trucks fl atbed? (b) The truck barely exceeds this acceleration and then moves with constant acceleration, with the crate sliding along its bed. What is the acceleration of the crate relative to the ground?

Objects with masses m1 10.0 kg and m2 5.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.36. If, when the system starts from rest, m2 falls 1.00 m in 1.20 s, determine the coeffi cient of kinetic friction between m1 and the table.

A hockey puck struck by a hockey stick is given an initial speed v0 in the positive x-direction. The coeffi cient of kinetic friction between the ice and the puck is mk. (a) Obtain an expression for the acceleration of the puck. (b) Use the result of part (a) to obtain an expression for the distance d the puck slides. The answer should be in terms of the variables v0, m, and g only.

The coeffi cient of static friction between the 3.00-kg crate and the 35.0 incline of Figure P4.47 is 0.300. What minimum force F S must be applied to the crate perpendicular to the incline to prevent the crate from sliding down the incline?

A student decides to move a box of books into her dormitory room by pulling on a rope attached to the box. She pulls with a force of 80.0 N at an angle of 25.0 above the horizontal. The box has a mass of 25.0 kg, and the coeffi cient of kinetic friction between box and fl oor is 0.300. (a) Find the acceleration of the box. (b) The student now starts moving the box up a 10.0 incline, keeping her 80.0 N force directed at 25.0 above the line of the incline. If the coeffi cient of friction is unchanged, what is the new acceleration of the box?

An object falling under the pull of gravity is acted upon by a frictional force of air resistance. The magnitude of this force is approximately proportional to the speed of the object, which can be written as f bv. Assume b 15 kg/s and m 50 kg. (a) What is the terminal speed the object reaches while falling? (b) Does your answer to part (a) depend on the initial speed of the object? Explain.

A car is traveling at 50.0 km/h on a fl at highway. (a) If the coeffi cient of friction between road and tires on a rainy day is 0.100, what is the minimum distance in which the car will stop? (b) What is the stopping distance when the surface is dry and the coeffi cient of friction is 0.600?

A 3.00-kg block starts from rest at the top of a 30.0 incline and slides 2.00 m down the incline in 1.50 s. Find (a) the acceleration of the block, (b) the coeffi cient of kinetic friction between the block and the incline, (c) the frictional force acting on the block, and (d) the speed of the block after it has slid 2.00 m.

A 2.00-kg block is held in equilibrium on an incline of angle u 60.0 by a horizontal force F S applied in the direction shown in Figure P4.52. If the coeffi cient of static friction between block and incline is ms 0.300, determine (a) the minimum value of F S and (b) the normal force exerted by the incline on the block. t

Find the acceleration reached by each of the two objects shown in Figure P4.53 if the coeffi cient of kinetic friction between the 7.00-kg object and the plane is 0.250.

Objects of masses m1 4.00 kg and m2 9.00 kg are connected by a light string that passes over a frictionless pulley as in Figure P4.54. The object m1 is held at rest on the fl oor, and m2 rests on a fi xed incline of u 40.0. The objects are released from rest, and m2 slides 1.00 m down the incline in 4.00 s. Determine (a) the acceleration of each object, (b) the tension in the string, and (c) the coeffi cient of kinetic friction between m2 and the incline. 5

The person in Figure P4.55 weighs 170 lb. Each crutch makes an angle of 22.0 with the vertical (as seen from the front). Half of the persons weight is supported by the crutches, the other half by the vertical forces exerted by the ground on his feet. Assuming he is at rest and the force exerted by the ground on the crutches acts along the crutches, determine (a) the smallest possible coefficient of friction between crutches and ground and (b) the magnitude of the compression force supported by each crutch.

As a protest against the umpires calls, a baseball pitcher throws a ball straight up into the air at a speed of 20.0 m/s. In the process, he moves his hand through a distance of 1.50 m. If the ball has a mass of 0.150 kg, fi nd the force he exerts on the ball to give it this upward speed.

Three objects are connected on a table as shown in Figure P4.57. The rough table has a coeffi cient of kinetic friction of 0.350. The objects have masses of 4.00 kg, 1.00 kg, and 2.00 kg as shown, and the pulleys are frictionless. (a) Draw a free-body diagram for each object. (b) Determine the acceleration of each object and each objects directions. (c) Determine the tensions in the two cords. (d) If the tabletop were smooth, would the tensions increase, decrease, or remain the same? Explain.

The force exerted by the wind on a sailboat is approximately perpendicular to the sail and proportional to the component of the wind velocity perpendicular to the sail. For the 800-kg sailboat shown in Figure P4.58, the proportionality constant is Fsail 5 a550 N m/sbvwind' Water exerts a force along the keel (bottom) of the boat that prevents it from moving sideways, as shown in the fi gure. Once the boat starts moving forward, water also exerts a drag force backwards on the boat, opposing the forward motion. If a 17-knot wind (1 knot 0.514 m/s) is blowing to the east, what is the initial acceleration of the sailboat?

(a) What is the resultant force exerted by the two cables supporting the traffi c light in Figure P4.59? (b) What is the weight of the light?

(a) What is the minimum force of friction required to hold the system of Figure P4.60 in equilibrium? (b) What coeffi cient of static friction between the 100-N block and the table ensures equilibrium? (c) If the coeffi cient of kinetic friction between the 100-N block and the table is 0.250, what hanging weight should replace the 50.0-N weight to allow the system to move at a constant speed once it is set in motion?

A boy coasts down a hill on a sled, reaching a level surface at the bottom with a speed of 7.0 m/s. If the coeffi cient of friction between the sleds runners and the snow is 0.050 and the boy and sled together weigh 600 N, how far does the sled travel on the level surface before coming to rest?

A 4.00-kg block is pushed along the ceiling with a constant applied force of 85.0 N that acts at an angle of 55.0 with the horizontal, as in Figure P4.62. The block accelerates to the right at 6.00 m/s2. Determine the coeffi cient of kinetic friction between block and ceiling.

A box rests on the back of a truck. The coeffi cient of static friction between the box and the bed of the truck is 0.300. (a) When the truck accelerates forward, what force accelerates the box? (b) Find the maximum acceleration the truck can have before the box slides.

Three objects are connected by light strings as shown in Figure P4.64. The string connecting the 4.00-kg object and the 5.00-kg object passes over a light frictionless pulley. Determine (a) the acceleration of each object and (b) the tension in the two strings.

A frictionless plane is 10.0 m long and inclined at 35.0. A sled starts at the bottom with an initial speed of 5.00 m/s up the incline. When the sled reaches the point at which it momentarily stops, a second sled is released from the top of the incline with an initial speed vi . Both sleds reach the bottom of the incline at the same moment. (a) Determine the distance that the fi rst sled traveled up the incline. (b) Determine the initial speed of the second sled.

A high diver of mass 70.0 kg jumps off a board 10.0 m above the water. If her downward motion is stopped 2.00 s after she enters the water, what average upward force did the water exert on her?

A 2.00-kg aluminum block and a 6.00-kg copper block are connected by a light string over a frictionless pulley. The two blocks are allowed to move on a fi xed steel block wedge (of angle u 30.0) as shown in Figure P4.67. Making use of Table 4.2, determine (a) the acceleration of the two blocks and (b) the tension in the string.

A 3.0-kg object hangs at one end of a rope that is attached to a support on a railroad car. When the car accelerates to the right, the rope makes an angle of 4.0 with the vertical, asa shown in Figure P4.68. Find the acceleration of the car.

Two boxes of fruit on a frictionless horizontal surface are connected by a light string as in Figure P4.69, where m1 10 kg and m2 20 kg. A force of 50 N is applied to the 20-kg box. (a) Determine the acceleration of each box and the tension in the string. (b) Repeat the problem for the case where the coeffi cient of kinetic friction between each box and the surface is 0.10. k

Measuring coeffi cients of friction A coin is placed near one edge of a book lying on a table, and that edge of the book is lifted until the coin just slips down the incline as shown in Figure P4.70. The angle of the incline, uc , called the critical angle, is measured. (a) Draw a free-body diagram for the coin when it is on the verge of slipping and identify all forces acting on it. Your free-body diagram should include a force of static friction acting up the incline. (b) Is the magnitude of the friction force equal to ms n for angles less than uc ? Explain. What can you defi - nitely say about the magnitude of the friction force for any angle u uc ? (c) Show that the coeffi cient of static friction is given by ms tan uc . (d) Once the coin starts to slide down the incline, the angle can be adjusted to a new value u c uc such that the coins moves down the incline with constant speed. How does observation enable you to obtain the coeffi cient of kinetic friction?

A fi sherman poles a boat as he searches for his next catch. He pushes parallel to the length of the light pole, exerting a force of 240 N on the bottom of a shallow lake.The pole lies in the vertical plane containing the boat's keel. At one moment, the pole makes an angle of 35.0 with the vertical and the water exerts a horizontal drag force of 47.5 N on the boat, opposite to its forward velocity of magnitude 0.857 m/s. The mass of the boat including its cargo and the worker is 370 kg. (a) The water exerts a buoyant force vertically upward on the boat. Find the magnitude of this force. (b) Assume the forces are constant over a short interval of time. Find the velocity of the boat 0.450 s after the moment described. (c) If the angle of the pole with respect to the vertical increased but the exerted force against the bottom remained the same, what would happen to buoyant force and the acceleration of the boat?

A rope with mass mr is attached to a block with mass mb as in Figure P4.72. Both the rope and the block rest on a horizontal, frictionless surface. The rope does not stretch. The free end of the rope is pulled to the right with a horizontal force F. (a) Draw free-body diagrams for the rope and the block, noting that the tension in the rope is not uniform. (b) Find the acceleration of the system in terms of mb, mr, and F. (c) Find the magnitude of the force the rope exerts on the block. (d) What happens to the force on the block as the ropes mass approaches zero? What can you state about the tension in a light cord joining a pair of moving objects?

A van accelerates down a hill (Fig. P4.73), going from rest to 30.0 m/s in 6.00 s. During the acceleration, a toy (m 0.100 kg) hangs by a string from the vans ceiling. The acceleration is such that the string remains perpendicular to the ceiling. Determine (a) the angle u and (b) the tension in the string.

An inquisitive physics student, wishing to combine pleasure with scientifi c inquiry, rides on a roller coaster sitting on a bathroom scale. (Do not try this yourself on a roller coaster that forbids loose, heavy packages.) The bottom of the seat in the roller-coaster car is in a plane parallel to the track. The seat has a perpendicular back and a seat belt that fi ts around the students chest in a plane parallel to the bottom of the seat. The student lifts his feet from the fl oor so that the scale reads his weight, 200 lb, when the car is horizontal. At one point during the ride, the car zooms with negligible friction down a straight slope inclined at 30.0 below the horizontal. What does the scale read at that point?

The parachute on a race car of weight 8 820 N opens at the end of a quarter-mile run when the car is traveling at 35 m/s. What total retarding force must be supplied by the parachute to stop the car in a distance of 1 000 m?

On an airplanes takeoff, the combined action of the air around the engines and wings of an airplane exerts an 8 000-N force on the plane, directed upward at an angle of 65.0 above the horizontal. The plane rises with constant velocity in the vertical direction while continuing to accelerate in the horizontal direction. (a) What is the weight of the plane? (b) What is its horizontal acceleration?

The board sandwiched between two other boards in Figure P4.77 weighs 95.5 N. If the coeffi cient of friction between the boards is 0.663, what must be the magnitude of the compression forces (assumed to be horizontal) acting on both sides of the center board to keep it from slipping?

A sled weighing 60.0 N is pulled horizontally across snow so that the coeffi cient of kinetic friction between sled and snow is 0.100. A penguin weighing 70.0 N rides on the sled, as in Figure P4.78. If the coeffi cient of static friction between penguin and sled is 0.700, fi nd the maximum horizontal force that can be exerted on the sled before the penguin begins to slide off.

A 72-kg man stands on a spring scale in an elevator. Starting from rest, the elevator ascends, attaining its maximum speed of 1.2 m/s in 0.80 s. The elevator travels with this constant speed for 5.0 s, undergoes a uniform negative acceleration for 1.5 s, and then comes to rest. What does the spring scale register (a) before the elevator starts to FIGURE P4.77 move? (b) During the fi rst 0.80s of the elevators ascent? (c) While the elevator is traveling at constant speed? (d) During the elevators negative acceleration?

A magician pulls a tablecloth from under a 200-g mug located 30.0 cm from the edge of the cloth. The cloth exerts a friction force of 0.100 N on the mug and is pulled with a constant acceleration of 3.00 m/s2. How far does the mug move relative to the horizontal tabletop before the cloth is completely out from under it? Note that the cloth must move more than 30 cm relative to the tabletop during the process.

An inventive child wants to reach an apple in a tree without climbing the tree. Sitting in a chair connected to a rope that passes over a frictionless pulley (Fig. P4.81), the child pulls on the loose end of the rope with such a force that the spring scale reads 250 N. The childs true weight is 320 N, and the chair weighs 160 N. (a) Show that the acceleration of the system is upward and fi nd its magnitude. (b) Find the force the child exerts on the chair.

A fi re helicopter carries a 620-kg bucket of water at the end of a 20.0-m-long cable. Flying back from a fi re at a constant speed of 40.0 m/s, the cable makes an angle of 40.0 with respect to the vertical. Determine the force exerted by air resistance on the bucket.