Figure 20 shows an acceleration-versus-force graph for a

Problem 1CQ A hockey puck slides along The surface of the ice. If friction and air resistance are negligible, what force is required to keep the puck moving?

Problem 1P Whiplash injuries during an automobile accident are caused by the inertia of the head. If someone is wearing a seatbelt, her body will tend to move with the car seat. However, her head is free to move until the neck restrains it, causing damage to the neck. Brain damage can also occur. Figure P4.1 shows two sequences of head and neck motion for a passenger in an auto accident. One corresponds to a headon collision, the other to a rear-end collision. Which is which? Explain.

Problem 2CQ If an object is not moving, does that mean that there are no forces acting on it? Explain.

Problem 2P An automobile has a head-on collision. A passenger in the car experiences a compression injury to the brain. Is this injury most likely to be in the front or rear portion of the brain? Explain.

Problem 3CQ An object moves in a straight line at a constant speed. Is it true that there must be no forces of any kind acting on this object? Explain.

Problem 3P In a head-on collision, an infant is much safer in a child safety seat when the seat isinstalled facing the rear of the car. Explain.

Problem 4CQ A ball sits near the front of a child’s wagon. As she pulls on the wagon and it begins to move forward, the ball rolls toward the back of the wagon. Explain why the ball rolls in this direction.

Problems 4 through 6 show two forces acting on an object at rest. Redraw the diagram, then add a third force that will allow the object to remain at rest. Label the new force .

Problem 5CQ If you know all of the forces acting on a moving object, can you tell in which direction the object is moving? If the answer is Yes, explain how. If the answer is No, give an example.

Problem 5P Problems 4 through 6 show two forces acting on an object at rest. Redraw the diagram, then add a third force that will allow the object to remain at rest. Label the new force .

Problem 6CQ Three arrows are shot horizontally. They have left the bow and are traveling parallel to the ground as shown in Figure Q4.4 . Air resistance is negligible. Rank in order, from largest to smallest, the magnitudes of the horizontal forces acting on the arrows. Some may be equal. State your reasoning.

Problem 6P Problems 4 through 6 show two forces acting on an object at rest. Redraw the diagram, then add a third force that will allow the object to remain at rest. Label the new force .

Problem 7CQ A carpenter wishes to tighten the heavy head of his hammer onto its light handle. Which method shown in Figure Q4.5 will better tighten the head? Explain.

Problem 7P A mountain climber is hanging from a rope in the middle of a crevasse. The rope is vertical. Identify the forces on the mountain climber.

Problem 8CQ Internal injuries in vehicular accidents may be due to what is called the “third collision.” The first collision is the vehicle hitting the external object. The second collision is the person hitting something on the inside of the car, such as the dashboard or windshield. This may cause external lacerations. The third collision, possibly the most damaging to the body, is when organs, such as the heart or brain, hit the ribcage, skull, or other confines of the body, bruising the tissues on the leading edge and tearing the organ from its supporting structures on the trailing edge. a. Why is there a third collision? In other words, why are the organs still moving after the second collision? b. If the vehicle was traveling at 60 mph before the first collision, would the organs be traveling faster than, equal to, or slower than 60 mph just before the third collision?

Problem 8P A circus clown hangs from one end of a large spring. The other end is anchored to the ceiling. Identify the forces on the clown.

Problem 9CQ a. Give an example of the motion of an object in which the frictional force on the object is directed opposite to the motion. b. Give an example of the motion of an object in which the frictional force on the object is in the same direction as the motion.

Problem 9P A baseball player is sliding into second base. Identify the forces on the baseball player.

Problem 10CQ Suppose you are an astronaut in deep space, far from any source of gravity. You have two objects that look identical, but one has a large mass and the other a small mass. How can you tell the difference between the two?

Problem 10P A jet plane is speeding down the runway during takeoff. Air resistance is not negligible. Identify the forces on the jet.

Problem 11CQ Jonathan accelerates away from a stop sign. His eight-year-old daughter sits in the passenger seat. On whom does the back of the seat exert a greater force?

Problem 11P A skier is sliding down a 15° slope. Friction is not negligible. Identify the forces on the skier.

Problem 12CQ The weight of a box sitting on the floor points directly down. The normal force of the floor on the box points directly up. Need these two forces have the same magnitude? Explain.

Problem 12P A tennis ball is flying horizontally across the net. Air resistance is not negligible. Identify the forces on the ball.

Problem 13CQ A ball weighs 2.0 N when placed on a scale. It is then thrown straight up. What is its weight at the very top of its motion? Explain.

Problem 13P Figure P4.13 shows an acceleration-versus-force graph for three objects pulled by rubber bands. The mass of object 2 is 0.20 kg. What are the masses of objects 1 and 3? Explain your reasoning.

Problem 14CQ Josh and Taylor, standing face-to-face on frictionless ice, push off each other, causing each to slide backward. Josh is much bigger than Taylor. After the push, which of the two is moving faster?

Problem 14P A constant force applied to object A causes it to accelerate at . The same force applied to object B causes an acceleration of .Applied to object C, it causes an acceleration of . a. Which object has the largest mass? b. Which object has the smallest mass? c. What is the ratio of mass A to mass B ?

Problem 15CQ A person sits on a sloped hillside. Is it ever possible to have the static friction force on this person point down the hill? Explain.

Problem 15P Two rubber bands pulling on an object cause it to accelerate at 1.2 m/s2. a. What will be the object’s acceleration if it is pulled by four rubber bands? b. What will be the acceleration of two of these objects glued together if they are pulled by two rubber bands?

Problem 16CQ Walking without slipping requires a static friction force between your feet (or footwear) and the floor. As described in this chapter, the force on your foot as you push off the floor is forward while the force exerted by your foot on the floor is backward. But what about your other foot, the one moved during a stride? What is the direction of the force on that foot as it comes into contact with the floor? Explain.

Problem 16P A constant force is applied to an object, causing the object to accelerate at . What will the acceleration be if a. The force is halved? b. The object’s mass is halved? c. The force and the object’s mass are both halved? d. The force is halved and the object’s mass is doubled?

Problem 17CQ Figure 4.30 b showed a situation in which the force of the road on the car’s tire points forward. In other situations, the force points backward. Give an example of such a situation.

Problem 17P A constant force is applied to an object, causing the object to accelerate at . What will the acceleration be if a. The force is doubled? b. The object’s mass is doubled? c. The force and the object’s mass are both doubled? d. The force is doubled and the object’s mass is halved?

Problem 18CQ Alyssa pushes to the right on a filing cabinet; the friction force from the floor pushes on it to the left. Because the cabinet doesn’t move, these forces have the same magnitude. Do they form an action/reaction pair? Explain.

Problem 18P A man pulling an empty wagon causes it to accelerate at . What will the acceleration be if he pulls with the same force when the wagon contains a child whose mass is three times that of the wagon?

Problem 19CQ A very smart three-year-old child is given a wagon for her birthday. She refuses to use it. “After all,” she says, “Newton’s third law says that no matter how hard I pull, the wagon will exert an equal but opposite force on me. So I will never be able to get it to move forward.” What would you say to her in reply?

Problem 19P A car has a maximum acceleration of . What will the maximum acceleration be if the car is towing another car of the same mass?

Problem 20CQ Will hanging a magnet in front of an iron cart, as shown in Figure 20, make it go? Explain why or why not. FIGURE 20

Problem 20P Figure 20 shows an acceleration-versus-force graph for a 500 g object. Redraw this graph and add appropriate acceleration values on the vertical scale. FIGURE 20

Problem 21MCQ Figure 21 shows the view looking down onto a frictionless sheet of ice. A puck, tied with a string to point P, slides on the surface of the ice in the circular path shown. If the string suddenly snaps when the puck is in the position shown, which path best represents the puck’s subsequent motion? FIGURE 21

Problem 21P Figure P4.21 shows an object’s acceleration-versus-force graph. What is the object’s mass?

Problem 22MCQ A block has acceleration a when pulled by a string. If two identical blocks are glued together and pulled with twice the original force, their acceleration will be A. (1/4)a B. (1/2)a C. a D. 2 a E. 4 a

Problem 22P Two children fight over a 200 g stuffed bear. The 25 kg boy pulls to the right with a 15 N force and the 20 kg girl pulls to the left with a 17 N force. Ignore all other forces on the bear (such as its weight). a. At this instant, can you say what the velocity of the bear is? If so, what are the magnitude and direction of the velocity? b. At this instant, can you say what the acceleration of the bear is? If so, what are the magnitude and direction of the acceleration?

Problem 23MCQ A 5.0 kg block has an acceleration of when a force is exerted on it. A second block has an acceleration of when subject to the same force. What is the mass of the second block? A. 10 kg B. 5.0 kg C. 2.5 kg D. 7.5 kg

Problem 23P A 1500 kg car is traveling along a straight road at 20 m/s. Two seconds later its speed is 21 m/s. What is the magnitude of the net force acting on the car during this time?

Probem 24MCQ Tennis balls experience a large drag force. A tennis ball is hit so that it goes straight up and then comes back down. The direction of the drag force is A. Always up. B. Up and then down. C. Always down. D. Down and then up.

Problem 24P Very small forces can have tremendous effects on the motion of very small objects. Consider a single electron, with a mass of 9.1 × 10?31 kg, subject to a single force equal to the weight of a penny, 2.5 × 10?2 N. What is the acceleration of the electron?

Problem 25MCQ A person gives a box a shove so that it slides up a ramp, then reverses its motion and slides down. The direction of the force of friction is A. Always down the ramp. B. Up the ramp and then down the ramp. C. Always down the ramp. D. Down the ramp and then up the ramp.

Problem 25P The motion of a very massive object is hardly affected by what would seem to be a substantial force. Consider a supertanker, with a mass of 3.0 × 108 kg. If it is pushed by a rocket motor (see Table 4.2) and is subject to no other forces, what will be the magnitude of its acceleration?

Problem 26MCQ A person is pushing horizontally on a box with a constant force, causing it to slide across the floor with a constant speed. If the person suddenly stops pushing on the box, the box will A. Immediately come to a stop. B. Continue moving at a constant speed for a while, then gradually slow down to a stop. C. Immediately change to a slower but constant speed. D. Immediately begin slowing down and eventually stop.

Problem 26P Problems 27 through 29 show a free-body diagram. For each problem, (a) redraw the free-body diagram and (b) write a short description of a real object for which this is the correct free-body diagram. Use the situations described in Conceptual Examples 4.1, 4.2, and 4.3 as models of what a description should be like.

Problem 27MCQ Rachel is pushing a box across the floor while Jon, at the same time, is hoping to stop the box by pushing in the opposite direction. There is friction between the box and floor. If the box is moving at constant speed, then the magnitude of Rachel’s pushing force is A. Greater than the magnitude of Jon’s force. B. Equal to the magnitude of Jon’s force. C. Less than the magnitude of Jon’s force. D. The question can’t be answered without knowing how large the friction force is.

Problem 27P Problems 27 through 29 show a free-body diagram. For each problem, (a) redraw the free-body diagram and (b) write a short description of a real object for which this is the correct free-body diagram. Use the situations described in Conceptual Examples 4.1, 4.2, and 4.3 as models of what a description should be like.

Problem 28MCQ Dave pushes his four-year-old son Thomas across the snow on a sled. As Dave pushes, Thomas speeds up. Which statement is true? A. The force of Dave on Thomas is larger than the force of Thomas on Dave. B. The force of Thomas on Dave is larger than the force of Dave on Thomas. C. Both forces have the same magnitude. D. It depends on how hard Dave pushes on Thomas.

Problem 28P Problems 27 through 29 show a free-body diagram. For each problem, (a) redraw the free-body diagram and (b) write a short description of a real object for which this is the correct free-body diagram. Use the situations described in Conceptual Examples 4.1, 4.2, and 4.3 as models of what a description should be like.

Problem 29MCQ Figure Q4.29 shows block A sitting on top of block B. A constant force is exerted on block B, causing block B to accelerate to the right. Block A rides on block B without slipping. Which statement is true? A. Block B exerts a friction force on block A, directed to the left. B. Block B exerts a friction force on block A, directed to the right. C. Block B does not exert a friction force on block A.

Problem 29P Problemdescribe a situation. For each problem, identify all the forces acting on the object and draw a free-body diagram of the object. Your car is sitting in the parking lot.

Problem 30P Problemdescribe a situation. For each problem, identify all the forces acting on the object and draw a free-body diagram of the object. Your car is accelerating from a stop.

Problem 31P Problems describe a situation. For each, identify all forces acting on the object and draw a free-body diagram of the object. Your car is slowing to a stop from a high speed.

Problem 32P Problemdescribe a situation. For each problem, identify all the forces acting on the object and draw a free-body diagram of the object. Your physics textbook is sliding across the table.

Problem 33P Problemdescribe a situation. For each problem, identify all the forces acting on the object and draw a free-body diagram of the object. An ascending elevator, hanging from a cable, is coming to a stop.

Problem 34P Problems describe a situation. For each, identify all forces acting on the object and draw a free-body diagram of the object. A skier slides down a slope at a constant speed.

Problem 35P Problemdescribe a situation. For each problem, identify all the forces acting on the object and draw a free-body diagram of the object. You hold a picture motionless against a wall by pressing on it, as shown in Figure P4.36.

Problem 36P A weightlifter stands up from a squatting position while holding a heavy barbell across his shoulders. Identify all the action/reaction pairs of forces between the weight lifter and the barbell.

Problem 37P Three ice skaters, numbered 1, 2, and 3, stand in a line, each with her hands on the shoulders of the skater in front. Skater 3, at the rear, pushes on skater 2. Identify all the action/reaction pairs of forces between the three skaters. Draw a free-body diagram for skater 2, in the middle. Assume the ice is frictionless.

Problem 38P A girl stands on a sofa. Identify all the action/reaction pairs of forces between the girl and the sofa.

Problem 39GP Redraw the motion diagram shown in Figure P4.43, then draw a vector beside it to show the direction of the net force acting on the object. Explain your reasoning.

Problem 40GP Redraw the motion diagram shown in Figure P4.44, then draw a vector beside it to show the direction of the net force acting on the object. Explain your reasoning.

Problem 41GP Redraw the motion diagram shown in Figure P4.45, then draw a vector beside it to show the direction of the net force acting on the object. Explain your reasoning.

Problem 42GP Redraw the motion diagram shown in Figure P4.46, then draw a vector beside it to show the direction of the net force acting on the object. Explain your reasoning.

Problem 43GP Problems show a free-body diagram. For each: a. Redraw the diagram. b. Identify the direction of the acceleration vector and show it as a vector next to your diagram. Or, if appropriate, write c. Write a short description of a real object for which this is the correct free-body diagram. Use Examples 4.7, 4.8, and 4.9 as models of what a description should be like. FIGURE 43

Problem 44GP Problems show a free-body diagram. For each: a. Redraw the diagram. b. Identify the direction of the acceleration vector and show it as a vector next to your diagram. Or, if appropriate, write c. Write a short description of a real object for which this is the correct free-body diagram. Use Examples 4.7, 4.8, and 4.9 as models of what a description should be like. FIGURE 44

Problem 45GP Problems show a free-body diagram. For each: a. Redraw the diagram. b. Identify the direction of the acceleration vector and show it as a vector next to your diagram. Or, if appropriate, write c. Write a short description of a real object for which this is the correct free-body diagram. Use Examples 4.7, 4.8, and 4.9 as models of what a description should be like. FIGURE 45

Problem 46GP Problems show a free-body diagram. For each: a. Redraw the diagram. b. Identify the direction of the acceleration vector and show it as a vector next to your diagram. Or, if appropriate, write c. Write a short description of a real object for which this is the correct free-body diagram. Use Examples 4.7, 4.8, and 4.9 as models of what a description should be like. FIGURE 46

Problem 47GP Problems show a free-body diagram. For each: a. Redraw the diagram. b. Identify the direction of the acceleration vector and show it as a vector next to your diagram. Or, if appropriate, write c. Write a short description of a real object for which this is the correct free-body diagram. Use Examples 4.7, 4.8, and 4.9 as models of what a description should be like. FIGURE 47

Problem 48GP Problems show a free-body diagram. For each: a. Redraw the diagram. b. Identify the direction of the acceleration vector and show it as a vector next to your diagram. Or, if appropriate, write c. Write a short description of a real object for which this is the correct free-body diagram. Use Examples 4.7, 4.8, and 4.9 as models of what a description should be like. FIGURE 48

Problem 49GP Problems show a free-body diagram. For each: a. Redraw the diagram. b. Identify the direction of the acceleration vector and show it as a vector next to your diagram. Or, if appropriate, write c. Write a short description of a real object for which this is the correct free-body diagram. Use Examples 4.7, 4.8, and 4.9 as models of what a description should be like. FIGURE 49

Problem 50GP A student draws the flawed free-body diagram shown in Figure P4.47 to represent the forces acting on a car traveling at constant speed on a level road. Identify the errors in the diagram, then draw a correct free-body diagram for this situation.

Problem 51GP A student draws the flawed free-body diagram shown in Figure P4.48 to represent the forces acting on a golf ball that is traveling upward and to the right a very short time after being hit off the tee. Air resistance is assumed to be relevant. Identify the errors in the diagram, then draw a correct free-body diagram for this situation.

Problem 53GP Problem describe a situation. For each problem, draw a motion diagram, a force identification diagram, and a freebody diagram. A rocket is being launched straight up. Air resistance is not negligible.

Problem 52GP Problem describe a situation. For each problem, draw a motion diagram, a force identification diagram, and a freebody diagram. An elevator, suspended by a single cable, has just left the tenth floor and is speeding up as it descends toward the ground floor.

Problem 54GP Problem describe a situation. For each problem, draw a motion diagram, a force identification diagram, and a freebody diagram. A jet plane is speeding down the runway during takeoff. Air resistance is not negligible.

Problem 55GP Problem describe a situation. For each problem, draw a motion diagram, a force identification diagram, and a freebody diagram. You’ve slammed on the brakes and your car is skidding to a stop while going down a 20° hill.

Problem 56GP Problems describe a situation. For each, draw a motion diagram, a force identification diagram, and a free-body diagram. A skier is going down a 20° slope. A horizontal headwind is blowing in the skier’s face. Friction is small, but not zero.

Problem 57GP Problem describe a situation. For each problem, draw a motion diagram, a force identification diagram, and a freebody diagram. A bale of hay sits on the bed of a trailer. The trailer is starting to accelerate forward, and the bale is slipping toward the back of the trailer.

Problem 58GP Problem describe a situation. For each problem, draw a motion diagram, a force identification diagram, and a freebody diagram. A Styrofoam ball has just been shot straight up. Air resistance is not negligible.

Problem 59GP Problem describe a situation. For each problem, draw a motion diagram, a force identification diagram, and a freebody diagram. A spring-loaded gun shoots a plastic ball. The trigger has just been pulled and the ball is starting to move down the barrel. The barrel is horizontal.

Problem 60GP Problem describe a situation. For each problem, draw a motion diagram, a force identification diagram, and a freebody diagram. A person on a bridge throws a rock straight down toward the water. The rock has just been released.

Problem 61GP Problem describe a situation. For each problem, draw a motion diagram, a force identification diagram, and a freebody diagram. A gymnast has just landed on a trampoline. She’s still moving downward as the trampoline stretches.

Problem 62GP Problem describe a situation. For each problem, draw a motion diagram, a force identification diagram, and a freebody diagram. A heavy box is in the back of a truck. The truck is accelerating to the right. Apply your analysis to the box.

Problem 63GP Problem describe a situation. For each problem, draw a motion diagram, a force identification diagram, and a freebody diagram. A bag of groceries is on the back seat of your car as you stop for a stop light. The bag does not slide. Apply your analysis to the bag.

Problem 64GP A rubber ball bounces. We’d like to understand how the ball bounces. a. A rubber ball has been dropped and is bouncing off the floor. Draw a motion diagram of the ball during the brief time interval that it is in contact with the floor. Show 4 or 5 frames as the ball compresses, then another 4 or 5 frames as it expands. What is the direction of during each of these parts of the motion? b. Draw a picture of the ball in contact with the floor and identify all forces acting on the ball. c. Draw a free-body diagram of the ball during its contact with the ground. Is there a net force acting on the ball? If so, in which direction? d. During contact, is the force of the ground on the ball larger than, smaller than, or equal to the weight of the ball? Use your answers to parts a–c to explain your reasoning.

Problem 65GP If a car stops suddenly, you feel “thrown forward.” We’d like to understand what happens to the passengers as a car stops. Imagine yourself sitting on a very slippery bench inside a car. This bench has no friction, no seat back, and there’s nothing for you to hold on to. a. Draw a picture and identify all of the forces acting on you as the car travels in a straight line at a perfectly steady speed on level ground. b. Draw your free-body diagram. Is there a net force on you? If so, in which direction? c. Repeat parts a and b with the car slowing down. d. Describe what happens to you as the car slows down. e. Use Newton’s laws to explain why you seem to be “thrown forward” as the car stops. Is there really a force pushing you forward?

Problem 66GP The fastest pitched baseball was clocked at 46 m/s. If the pitcher exerted his force (assumed to be horizontal and constant) over a distance of 1.0 m, and a baseball has a mass of 145 g, a. Draw a free-body diagram of the ball during the pitch. b. What force did the pitcher exert on the ball during this record-setting pitch? c. Estimate the force in part b as a fraction of the pitcher’s weight.

Problem 67GP The froghopper, champion leaper of the insect world, can jump straight up at 4.0 m/s. The jump itself lasts a mere 1.0 ms before the insect is clear of the ground. a. Draw a free-body diagram of this mighty leaper while the jump is taking place. b. While the jump is taking place, is the force that the ground exerts on the froghopper greater than, less than, or equal to the insect’s weight? Explain.

Problem 68GP A beach ball is thrown straight up, and some time later it lands on the sand. Is the magnitude of the net force on the ball greatest when it is going up or when it is on the way down? Or is it the same in both cases? Explain. Air resistance should not be neglected for a large, light object.

Problem 69PP A Simple Solution for a Stuck Car If your car is stuck in the mud and you don’t have a winch to pull it out, you can use a piece of rope and a tree to do the trick. First, you tie one end of the rope to your car and the other to a tree, then pull as hard as you can on the middle of the rope, as shown in Figure P4.68a. This technique applies a force to the car much larger than the force that you can apply directly. To see why the car experiences such a large force, look at the forces acting on the center point of the rope, as shown in Figure P4.68b. The sum of the forces is zero, thus the tension is much greater than the force you apply. It is this tension force that acts on the car and, with luck, pulls it free. The sum of the three forces acting on the center point of the rope is assumed to be zero because A. This point has a very small mass. B. Tension forces in a rope always cancel. C. This point is not accelerating. D. The angle of deflection is very small.

Problem 70PP A Simple Solution for a Stuck Car If your car is stuck in the mud and you don’t have a winch to pull it out, you can use a piece of rope and a tree to do the trick. First, you tie one end of the rope to your car and the other to a tree, then pull as hard as you can on the middle of the rope, as shown in Figure P4.68a. This technique applies a force to the car much larger than the force that you can apply directly. To see why the car experiences such a large force, look at the forces acting on the center point of the rope, as shown in Figure P4.68b. The sum of the forces is zero, thus the tension is much greater than the force you apply. It is this tension force that acts on the car and, with luck, pulls it free. When you are pulling on the rope as shown, what is the approximate direction of the tension force on the tree? A. North B. South C. East D. West

Problem 71PP A Simple Solution for a Stuck Car If your car is stuck in the mud and you don’t have a winch to pull it out, you can use a piece of rope and a tree to do the trick. First, you tie one end of the rope to your car and the other to a tree, then pull as hard as you can on the middle of the rope, as shown in Figure P4.68a. This technique applies a force to the car much larger than the force that you can apply directly. To see why the car experiences such a large force, look at the forces acting on the center point of the rope, as shown in Figure P4.68b. The sum of the forces is zero, thus the tension is much greater than the force you apply. It is this tension force that acts on the car and, with luck, pulls it free. Assume that you are pulling on the rope but the car is not moving. What is the approximate direction of the force of the mud on the car? A. North B. South C. East D. West

Problem 72PP A Simple Solution for a Stuck Car If your car is stuck in the mud and you don’t have a winch to pull it out, you can use a piece of rope and a tree to do the trick. First, you tie one end of the rope to your car and the other to a tree, then pull as hard as you can on the middle of the rope, as shown in Figure P4.68a. This technique applies a force to the car much larger than the force that you can apply directly. To see why the car experiences such a large force, look at the forces acting on the center point of the rope, as shown in Figure P4.68b. The sum of the forces is zero, thus the tension is much greater than the force you apply. It is this tension force that acts on the car and, with luck, pulls it free. Suppose your efforts work, and the car begins to move forward out of the mud. As it does so, the force of the car on the rope is A. Zero. B. Less than the force of the rope on the car. C. Equal to the force of the rope on the car. D. Greater than the force of the rope on the car.