A young girl slides down a rope. As she slides faster and

Problem 1CQ Driving down the road, you hit the brakes suddenly. As a result, your body moves toward the front of the car. Explain, using Newton's laws.

IP Referring to Figure Suppose we would like the acceleration of the satellite to be at an angle of \(25^\circ\), and that the only quantity we can change in the system is the magnitude of \(\mathrm {\vec{F}_1}\). (a) Should the magnitude of \(\mathrm {\vec{F}_1}\) be increased or decreased? Explain. (b) What is the magnitude of the satellite's acceleration in this case? ________________ Equation Transcription: Text Transcription: 25^o vec{F}_1 vec{F}_1

Problem 1P CE An object of mass m is initially at rest. After a force of magnitude F acts on it for a time T, the object has a speed v. Suppose the mass of the object is doubled, and the magnitude of the force acting on it is quadrupled. In terms of T, how long does it take for the object to accelerate from rest to a speed v now?

Problem 2P On a planet far, far away, an astronaut picks up a rock. The rock has a mass of 5.00 kg, and on this particular planet its weight is 40.0 N. Tf the astronaut exerts an upward force of 46.2 N on the rock, what is its acceleration?

Problem 2CQ You've probably seen pictures of someone pulling a tablecloth out from under glasses, plates, and silverware set out for a formal dinner. Perhaps you've even tried it yourself. Using Newton's laws of motion, explain how this stunt works.

Problem 3CQ As you read this, you arc most likely sitting quietly in a chair. Can you conclude, therefore, that you are at rest? Explain.

In a grocery store, you push a 12.3-kg shopping cart with a force of \(10.1 \mathrm{~N}\). If the cart starts at rest, how far does it move in \(2.50 \mathrm{~s}\)?

When a dog gets wet, it shakes its body from head to tail to shed the water. Explain, in terms of Newton’s first law, why this works.

Problem 4P You are pulling your little sister on her sled across an icy (fric-tionless) surface. When you exert a constant horizontal force of 120 N, the sled has an acceleration of 2.5 m/s2. If the sled has a mass of 7.4 kg, what is the mass of your little sister?

Problem 5CQ A young girl slides down a rope. As she slides faster and faster she tightens her grip, increasing the force exerted on her by the rope. What happens when this force is equal in magnitude to her weight? Explain.

Problem 5P · A 0.53-kg billiard ball initially at rest is given a speed of 12 m/s during a time interval of 4.0 ms. What average force acted on the ball during this time?

Problem 6P A 92-kg water skier floating in a lake is pulled from rest to a speed of 12 m/s in a distance of 25 m. What is the net force exerted on the skier, assuming his acceleration is constant?

A block of mass m hangs from a string attached to a ceiling, as shown in Figure 5–16. An identical string hangs down from the bottom of the block. Which string breaks if (a) the lower string is pulled with a slowly increasing force or (b) the lower string is jerked rapidly downward? Explain.

Problem 6CQ A drag-racing car accelerates forward because of the force exerted on it by the road. Why, then, does it need an engine? Explain.

Problem 7P CE Predict/Explain You drop two balls of equal diameter from the same height at the same time. Ball 1 is made of metal and has a greater mass than ball 2, which is made of wood. The upward force due to air resistance is the same for both balls, (a) Is the drop time of ball 1 greater than, less than, or equal to the drop time of ball 2? (b) Choose the best explanation from among the following: I. The acceleration of gravity is the same for all objects, regardless of mass. II. The more massive ball is harder to accelerate. III. Air resistance has less effect on the more massive ball.

Problem 8CQ An astronaut on a space walk discovers that his jet pack no longer works, leaving him stranded 50 m from the spacecraft. If the jet pack is removable, explain how the astronaut can still use it to return to the ship.

Problem 8P IP A 42.0-kg parachutist is moving straight downward with a speed of 3.85 m/s. (a) If the parachutist comes to rest with constant acceleration over a distance of 0.750 m, what force does the ground exert on her? (b) If the parachutist comes to rest over a shorter distance, is the force exerted by the ground greater than, less than, or the same as in part (a)? Explain.

Problem 9CQ Two untethered astronauts on a space walk decide to take a break and play catch with a baseball. Describe what happens as the game of catch progresses.

Problem 10CQ What are the action-reaction forces when a baseball bat hits a fast ball? What is the effect of each force?

Problem 9P IP In baseball, a pitcher can accelerate a 0.15-kg ball from rest to 98 mi/h in a distance of 1.7 m. (a) What is the average force exerted on the ball during the pitch? (b) If the mass of the ball is increased, is the force required of the pitcher increased, decreased, or unchanged? Explain.

Problem 10P A major-league catcher gloves a 92-mi/h pitch and brings it to rest in 0.15 m. If the force exerted by the catcher is 803 N, what is the mass of the ball?

In Figure 5–17 Wilbur asks Mr. Ed, the talking horse, to pull a cart. Mr. Ed replies that he would like to, but the laws of nature just won’t allow it. According to Newton’s third law, he says, if he pulls on the wagon it pulls back on him with an equal force. Clearly, then, the net force is zero and the wagon will stay put. How should Wilbur answer the clever horse?

Driving home from school one day, you spot a ball rolling out into the street (Figure 5–18). You brake for 1.20 s, slowing your 950-kg car from 16.0 m/s to 9.50 m/s. (a) What was the average force exerted on your car during braking? (b) How far did you travel while braking?

Problem 12CQ A whole brick has more mass than half a brick, thus the whole brick is harder to accelerate. Why doesn't a whole brick fall more slowly than half a brick? Explain.

Problem 12P Stopping a 747 A 747 jetliner lands and begins to slow to a stop as it moves along the runway. If its mass is 3.50 × 105 kg, its speed is 27.0 m/s, and the net braking force is 4.30 × 105 N, (a) what is its speed 7.50 s later? (b) How far has it traveled in this time?

Problem 13P IP A drag racer crosses the finish line doing 202 mi/h and promptly deploys her drag chute (the small parachute used for braking), (a) What force must the drag chute exert on the 891-kg car to slow it to 45.0 mi/h in a distance of 185 m? (b) Describe the strategy you used to solve part (a). SECTION 5-4 NEWTON'S THIRD LAW OF MOTION

Problem 13CQ The force exerted by gravity on a whole brick is greater than the force exerted by gravity on half a brick. Why, then, doesn't a whole brick fall faster than half a brick? Explain.

Problem 14CQ Is it possible for an object at rest to have only a single force acting on it? If your answer is yes, provide an example. If your answer is no, explain why not.

Problem 14P CE Predict/Explain A small car collides with a large truck, (a) Is the magnitude of the force experienced by the car greater than, less than, or equal to the magnitude of the force experienced by the truck? (b) Choose the best explanation from among the following: I. Action-reaction forces always have equal magnitude. II. The truck has more mass, and hence the force exerted on it is greater. III. The massive truck exerts a greater force on the lightweight car.

Problem 15CQ Is it possible for an object to be in motion and yet have zero net force acting on it? Explain.

Problem 15P CE Predict/Explain A small car collides with a large truck, (a) Is the acceleration experienced by the car greater than, less than, or equal to the acceleration experienced by the truck? (b) Choose the best explanation from among the following: I. The truck exerts a larger force on the car, giving it the greater acceleration. II. Both vehicles experience the same magnitude of force, therefore the lightweight car experiences the greater acceleration. III. The greater force exerted on the truck gives it the greater acceleration.

Problem 16CQ A bird cage, with a parrot inside, hangs from a scale. The parrot decides to hop to a higher perch. What can you say about the reading on the scale (a) when the parrot jumps, (b) when the parrot is in the air, and (c) when the parrot lands on the second perch? Assume that the scale responds rapidly so that it gives an accurate reading at all times.

Problem 16P You hold a brick at rest in your hand. (a) How many forces act on the brick? (b) Identify these forces, (c) Are these forces equal in magnitude and opposite in direction? (d) Are these forces an action-reaction pair? Explain.

Problem 17CQ Suppose you jump from the cliffs of Acapulco and perform a perfect swan dive. As you fall, you exert an upward force on the Earth equal in magnitude to the downward force the Earth exerts on you. Why, then, does it seem that you are the one doing all the accelerating? Since the forces are the same, why aren't the accelerations?

Problem 17P Referring to Problem 16, you are now accelerating the brick upward, (a) How many forces act on the brick in this case? (b) Identify these forces, (c) Are these forces equal in magnitude and opposite in direction? (d) Are these forces an action-reaction pair? Explain.

Problem 18CQ A friend tells you that since his car is at rest, there are no forces acting on it. How would you reply?

Problem 19CQ Since all objects are "weightless" in orbit, how is it possible for an orbiting astronaut to tell if one object has more mass than another object? Explain.

Problem 18P On vacation, your 1400-kg car pulls a 560-kg trailer away from a stoplight with an acceleration of 1.85 m/s2, (a) What is the net force exerted on the trailer? (b) What force does the traiter exert on the car? (c) What is the net force acting on the car?

Problem 19P IP A 71-kg parent and a 19-kg child meet at the center of an ice rink. They place their hands together and push, (a) Is the force experienced by the child more than, less than, or the same as the force experienced by the parent? (b) Is the acceleration of the child more than, less than, or the same as the acceleration of the parent? Explain, (c) If the acceleration of the child is 2.6 m/s2 in magnitude, what is the magnitude of the parent's acceleration?

A force of magnitude pushes three boxes with masses \(m_1=1.30\ \mathrm {kg}\), \(m_2=3.20\ \mathrm {kg}\) and \(m_3=4.90\ \mathrm {kg}\), as shown in Figure 5-19. Find the magnitude of the contact force (a) between boxes 1 and 2 , and (b) between boxes 2 and 3 . ________________ Equation Transcription: Text Transcription: m_1=1.30 kg m_2=3.20 kg m_3=4.90 kg F=7.50 N

Problem 20CQ To clean a rug, you can hang it from a clothesline and beat it with a tennis racket. Use Newton's laws to explain why beating the rug should have a cleansing effect.

Problem 21CQ If you step off a high board and drop to the water below, you plunge into the water without injury. On the other hand, if you were to drop the same distance onto solid ground, you might break a leg. Use Newton's laws to explain the difference.

Problem 22CQ A moving object is acted on by a net force. Give an example of a situation in which the object moves (a) in the same direction as the net force, (b) at right angles to the net force, or (c) in the opposite direction of the net force.

Problem 22P IP Two boxes sit side-by-side on a smooth horizontal surface. The lighter box has a mass of 5.2 kg; the heavier box has a mass of 7.4 kg. (a) Find the contact force between these boxes when a horizontal force of 5.0 N is applied to the light box. (b) If the 5.0-N force is applied to the heavy box instead, is the contact force between the boxes the same as, greater than, or less than the contact force in part (a)? Explain, (c) Verify your answer to part (b) by calculating the contact force in this case.

A force of magnitude pushes three boxes with masses \(m_1=1.30\ \mathrm {kg}\), \(m_2=3.20\ \mathrm {kg}\) and \(m_3=4.90\ \mathrm {kg}\), as shown in Figure 5-20. Find the magnitude of the contact force (a) between boxes 1 and 2 , and (b) between boxes 2 and 3 . ________________ Equation Transcription: Text Transcription: m_1=1.30 kg m_2=3.20 kg m_3=4.90 kg F=7.50 N

Problem 23P CE A skateboarder on a ramp is accelerated by a nonzero net force. For each of the following statements, state whether it is always true, never true, or sometimes true, (a) The skateboarder is moving in the direction of the net force, (b) The acceleration of the skateboarder is at right angles to the net force. (c) The acceleration of the skateboarder is in the same direction as the net force. (d) The skateboarder is instantaneously at rest.

Problem 23CQ Is it possible for an object to be moving in one direction while the net force acting on it is in another direction? If your answer is yes, provide an example. If your answer is no, explain why not.

Problem 24CQ Since a bucket of water is "weightless" in space, would it hurt to kick the bucket? Explain.

Three objects, A, B, and C, have x and y components of velocity that vary with time as shown in Figure 5–21. What is the direction of the net force acting on (a) object A, (b) object B, and (c) object C, as measured from the positive x axis? (All of the nonzero slopes have the same magnitude.) ________________ Equation Transcription: Text Transcription: v_x v_x v_x v_y v_y v_y

Problem 25P A farm tractor tows a 3700-kg trailer up an 18° incline with a steady speed of 3.2 m/s. What force does the tractor exert on the trailer? (Ignore friction.)

Problem 25CQ In the movie The Rocketeer, a teenager discovers a jet-powered backpack in an old barn. The backpack allows him to fly at incredible speeds. In one scene, however, he uses the backpack to rapidly accelerate an old pickup truck that is being chased by "bad guys." He does this by bracing his arms against the cab of the pickup and firing the backpack, giving the truck the acceleration of a drag racer. Is the physics of this scene "Good," "Bad," or "Ugly?" Explain.

Problem 26CQ List three common objects that have a weight of approximately 1 N.

Problem 26P A surfer "hangs ten," and accelerates down the sloping face of a wave. If the surfer's acceleration is 3.25 m/s2 and friction can be ignored, what is the angle at which the face of the wave is inclined above the horizontal?

A shopper pushes a 7.5-kg shopping cart up a \(13^\circ\) incline, as shown in Figure 5–22. Find the magnitude of the horizontal force, \(\vec {\mathrm F}\), needed to give the cart an acceleration of \(1.41\ \mathrm {m/s^2}\). ________________ Equation Transcription: Text Transcription: 13^o vec{F} 1.41 m/s^2 vec{F} vec{a} 13^o

Two crewmen pull a raft through a lock, as shown in Figure 5–23. One crewman pulls with a force of 130 N at an angle of \(34^\circ\) relative to the forward direction of the raft. The second crewman, on the opposite side of the lock, pulls at an angle of \(45^\circ\). With what force should the second crewman pull so that the net force of the two crewmen is in the forward direction? ________________ Equation Transcription: Text Transcription: 34^o 45^o 45^o 34^o

A hockey puck is acted on by one or more forces, as shown in Figure 5–24. Rank the four cases, A, B, C, and D, in order of the magnitude of the puck’s acceleration, starting with the smallest. Indicate ties where appropriate.

IP A 65-kg skier speeds down a trail, as shown in Figure 5–26. The surface is smooth and inclined at an angle of \(22^\circ\) with the horizontal. (a) Find the direction and magnitude of the net force acting on the skier. (b) Does the net force exerted on the skier increase, decrease, or stay the same as the slope becomes steeper? Explain. ________________ Equation Transcription: Text Transcription: 22^o 22^o

To give a 19-kg child a ride, two teenagers pull on a 3.7-kg sled with ropes, as indicated in Figure 5–25. Both teenagers pull with a force of 55 N at an angle of \(35^\circ\) relative to the forward direction, which is the direction of motion. In addition, the snow exerts a retarding force on the sled that points opposite to the direction of motion, and has a magnitude of 57 N. Find the acceleration of the sled and child. ________________ Equation Transcription: Text Transcription: 35^o vec{a} 35^o 35^o

Problem 31P IP Before practicing his routine on the rings, a 67-kg gymnast stands motionless, with one hand grasping each ring and his feet touching the ground. Both aims slope upward at an angle of 24° above the horizontal, (a) If the force exerted by the rings on each arm has a magnitude of 290 N, and is directed along the length of the arm, what is the magnitude of the force exerted by the floor on his feet? (b) If the angle his arms make with the horizontal is greater that 24°, and everything else remains the same, is the force exerted by the floor on his feet greater than, less than, or the same as the valne found in part (a)? Explain.

Problem 33P An object acted on by three forces moves with constant velocity. One force acting on the object is in the positive x direction and has a magnitude of 6.5 N; a second force has a magnitude of 4.4 N and points in the negative y direction. Find the direction and magnitude of the third force acting on the object.

A train is traveling up a \(3.73^{\circ}\) incline at a speed of \(3.25 \mathrm{~m} / \mathrm{s}\) when the last car breaks free and begins to coast without friction. (a) How long does it take for the last car to come to rest momentarily? (b) How far did the last car travel before momentarily coming to rest?

You pull upward on a stuffed suitcase with a force of \(105 \mathrm{~N}\), and it accelerates upward at \(0.705 \mathrm{~m} / \mathrm{s}^{2}\). What are (a) the mass and (b) the weight of the suitcase?

Problem 38P Suppose a rocket launches with an acceleration of 30.5 m/s2. What is the apparent weight of an 92-kg astronaut aboard this rocket?

The Force Exerted on the Moon Figure 5-27 shows the Earth, Moon, and Sun (not to scale) in their relative positions at the time when the Moon is in its third-quarter phase. Though few people realize it, the force exerted on the Moon by the Sun is actually greater than the force exerted on the Moon by the Earth. In fact, the force exerted on the Moon by the Sun has a magnitude of \(F_\mathrm {SM}=4.34 \times 10^{20}\ \mathrm N\), whereas the force exerted by the Earth has a magnitude of only \(F_{\mathrm {EM}}=1.98 \times 10^{20}\ \mathrm N\). These forces are indicated to scale in Figure Find a) the direction and (b) the magnitude of the net force acting on the Moon. (c) Given that the mass of the Moon is \(M_{\mathrm M}=7.35 \times 10^{22}\ \mathrm {kg}\), find the magnitude of its acceleration at the time of the third quarter phase. ________________ Equation Transcription: Text Transcription: F_{SM}=4.34x10^20 N F_{EM}=1.98x10^20 N M_{M}=7.35x10^22 kg

Problem 37P BIO Brain Growth A newborn baby's brain grows rapidly. In fact, it has been found to increase in mass by about 1.6 mg per minute, (a) How much does the brain's weight increase in one day? (b) How long does it take for the brain's weight to increase by 0.15 N?

Problem 39P At the bow of a ship on a stormy sea, a crewman conducts an experiment by standing on a bathroom scale. In calm waters, the scale reads 182 lb. During the storm, the crewman finds a maximum reading of 225 lb and a minimum reading of 138 lb. Find (a) the maximum upward acceleration and (b) the maximum downward acceleration experienced by the crewman.

As part of a physics experiment, you stand on a bathroom scale in an elevator. Though your normal weight is 610 N, the scale at the moment reads 730 N. (a) Is the acceleration of the elevator upward, downward, or zero? Explain. (b) Calculate the magnitude of the elevator's acceleration. (c) What, if anything, can you say about the velocity of the elevator? Explain.

Flight of the Samara A 1.21-g samara—the winged fruit of a maple tree—falls toward the ground with a constant speed of 1.1 m/s (Figure 5–28). (a) What is the force of air resistance exerted on the samara? (b) If the constant speed of descent is greater than 1.1 m/s, is the force of air resistance greater than, less than, or the same as in part (a)? Explain.

Problem 41P When you weigh yourself on good old terra firma (solid ground), your weight is 142 lb. In an elevator your apparent weight is 121 lb. What are the direction and magnitude of the elevator's acceleration?

Problem 43P When you lift a bowling ball with a force of 82 N, the ball accelerates upward with an acceleration a. If you lift with a force of 92 N, the ball's acceleration is 2a. Find (a) the weight of the bowling ball, and (b) the acceleration a.

Problem 44P A 23-kg suitcase is being pulled with constant speed by a handle that is at an angle of 25° above the horizontal. If the normal force exerted on the suitcase is 180 N, what is the force F applied to the handle?

Problem 45P (a) Draw a free-body diagram for the skier in Problem 32. (b) Determine the normal force acting on the skier.

Problem 46P · A 9.3-kg child sits in a 3.7-kg high chair. (a) Draw a free-body diagram for the child, and find the normal force exerted by the chair on the child. (b) Draw a free-body diagram for the chair, and find the normal force exerted by the floor on the chair.

Figure 5–29 shows the normal force as a function of the angle \(\theta\) for the suitcase shown in Figure 5–13. Determine the magnitude of the force for each of the three curves shown in Figure 5–29. Give your answer in terms of the weight of the suitcase, mg. ________________ Equation Transcription: Text Transcription: theta theta

Problem 53GP CE Predict/Explain Riding in an elevator moving with a constant upward acceleration, you begin a game of darts. (a) Do you have to aim your darts higher than, lower than, or the same as when you play darts on solid ground? (b) Choose the best explanation from among the following: I. The elevator accelerates upward, giving its passengers a greater "effective" acceleration of gravity. II. You have to aim lower to compensate for the upward acceleration of the elevator. III. Since the elevator moves with a constant acceleration, Newton's laws apply within the elevator the same as on the ground.

Problem 49P IP (a) Find the normal force exerted on a 2.9-kg book resting on a surface inclined at 36° above the horizontal. (b) If the angle of the incline is reduced, do you expect the normal force to increase, decrease, or stay the same? Explain.

Problem 50P IP A gardener mows a lawn with an old-fashioned push mower. The handle of the mower makes an angle of 35° with the surface of the lawn. (a) If a 219-N force is applied along the handle of the 19-kg mower, what is the normal force exerted by the lawn on the mower? (b) If the angle between the surface of the lawn and the handle of the mower is increased, does the normal force exerted by the lawn increase, decrease, or stay the same? Explain.

Problem 48P A 5.0-kg bag of potatoes sits on the bottom of a stationary shopping cart. (a) Sketch a free-body diagram for the bag of potatoes. (b) Now suppose the cart moves with a constant velocity. How does this affect your free-body diagram? Explain.

Problem 54GP CE Give the direction of the net force acting on each of the following objects. If the net force is zero, state "zero." (a) A car accelerating northward from a stoplight. (b) A car traveling southward and slowing down. (c) A car traveling westward with constant speed. (d) A skydiver parachuting downward with constant speed. (e) A baseball during its flight from pitcher to catcher (ignoring air resistance).

Problem 55GP ·CE Predict/Explain You jump out of an airplane and open your parachute after an extended period of free fall. (a) To decelerate your fall, must the force exerted on you by the parachute be greater than, less than, or equal to your weight? (b) Choose the best explanation from among the following: I. Parachutes can only exert forces that are less than the weight of the skydiver. II. The parachute exerts a force exactly equal to the skydiver's weight. III. To decelerate after free fall, the net force acting on a skydiver must be upward.

Problem 56GP In a tennis serve, a 0.070-kg ball can be accelerated from rest to 36 m/s over a distance of 0.75 m. Find the magnitude of the average force exerted hy the racket on the ball during the serve.

CE Each of the three identical hockey pucks shown in Figure 5–31 is acted on by a 3-N force. Puck A moves with a speed of 7 m/s in a direction opposite to the force; puck B is instanta- neously at rest; puck C moves with a speed of 7 m/s at right angles to the force. Rank the three pucks in order of the magnitude of their acceleration, starting with the smallest. Indicate ties with an equal sign. ________________ Equation Transcription: Text Transcription: v=7 m/s F= 3 N v=0 F=3 N v=7 m/s F=3 N

Problem 57GP A 51.5-kg swimmer with an initial speed of 1.25 m/s decides to coast until she comes to rest. If she slows with constant acceleration and stops after coasting 2.20 m, what was the force exerted on her by the water?

Problem 59GP IP The VASIMR Rocket NASA plans to use a new type of rocket, a Variable Specific Impulse Magnetoplasma Rocket (VASIMR), on future missions. A VASIMR can produce 1200 N of thrust (force) when in operation. If a VASIMR has a mass of 2.2 × 105 kg, (a) what acceleration will it experience? Assume that the only force acting on the rocket is its own thrust, and that the mass of the rocket is constant. (b) Over what distance must the rocket accelerate from rest to achieve a speed of 9500 m/s? (c) When the rocket has covered one-quarter the acceleration distance found in part (b), is its average speed 1/2, 1/3, or 1/4 its average speed during the final three-quarters of the acceleration distance? Explain.

Problem 61GP At the local grocery store, you push a 14.5-kg shopping cart. You stop for a moment to add a bag of dog food to your cart. With a force of 12.0 N, you now accelerate the cart from rest through a distance of 2.29 m in 3.00 s. What was the mass of the dog food?

An object of mass \(m=5.95\ \mathrm {kg}\) has an acceleration \(\mathrm {\vec{a}=(1.17\ m/s^2)\hat{x}+(-0.664\ m/s^2)\hat{y}}\). Three forces act on this object: \(\mathrm {\vec{F}_1}\), \(\mathrm {\vec{F}_2}\), and \(\mathrm {\vec{F}_3}\). Given that \(\mathrm {\vec{F}_1=(3.22\ N)\hat{x}}\) and \(\mathrm {\vec{F}_2=(-1.55\ N)\hat{x}+(2.05\ N)\hat{y}}\), find \(\(\mathrm {\vec{F}_3}\)\). ________________ Equation Transcription: Text Transcription: m=5.95 kg vec{a}=(1.17 m/s^2)hat{x}+(-0.664 m/s^2)hat{y} vec{F}_1 vec{F}_2 vec{F}_3 vec{F}_1=(3.22 N)hat{x} vec{F}_2=(-1.55 N)hat{x}+(2.05 N)hat{y} vec{F}_3

An apple of mass \(m=0.13\ \mathrm {kg}\) falls out of a tree from a height \(h=3.2\ \mathrm {m}\). (a) What is the magnitude of the force of gravity, , acting on the apple? (b) What is the apple's speed, , just before it lands? (c) Show that the force of gravity times the height, , is equal to \(\frac{1}{2}mv^2\). (We shall investigate the significance of this result in Chapter ) Be sure to show that the dimensions are in agreement as well as the numerical values. ________________ Equation Transcription: Text Transcription: m=0.13 kg h=3.2 m frac{1}{2}mv^2

Problem 63GP IP BIO Grasshopper Liftoff To become airborne, a 2.0-g grasshopper requires a takeoff speed of 2.7 m/s. It acquires this speed by extending its hind legs through a distance of 3.7 cm. (a) What is the average acceleration of the grasshopper during takeoff? (b) Find the magnitude of the average net force exerted on the grasshopper by its hind legs during takeoff. (c) If the mass of the grasshopper increases, does the takeoff acceleration increase, decrease, or stay the same? (d) If the mass of the grasshopper increases, does the required takeoff force increase, decrease, or stay the same? Explain.

Problem 62GP · IP BIO The Force of Running Biomechanical research has shown that when a 67-kg person is running, the force exerted oh each foot as it strikes the ground can be as great as 2300 N. (a) What is the ratio of the force exerted on the foot by the ground to the person's body weight? (b) If the only forces acting on the person are (i) the force exerted by the ground and (ii) the person's weight, what are the magnitude and direction of the person's acceleration? (c) If the acceleration found in part (b) acts for 10.0 ms, what is the resulting change in the vertical component of the person's velocity?

Problem 67GP An apple of mass m = 0.22 kg falls from a tree and hits the ground with a speed of v = 14 m/s. (a) What is the magnitude of the force of gravity, mg, acting on the apple? (b) What is the time, t, required for the apple to reach the ground? (c) Show that the force of gravity times the time, mgt, is equal to mv. (We shall investigate the significance of this result in Chapter 9.) Be sure to show that the dimensions are in agreement as well as the numerical values.

Takeoff from an Aircraft Carrier On an aircraft carrier, a jet can be catapulted from 0 to 155 mi/h in 2.00 s. If the average force exerted by the catapult is \(\mathrm {9.35 \times 10^5\ N}\), what is the mass of the jet? ________________ Equation Transcription: Text Transcription: 9.35x10^5 N

Problem 65GP IP An archer shoots a 0.024-kg arrow at a target with a speed of 54 m/s. When it hits the target, it penetrates to a depth of 0.083 m. (a) What was the average force exerted by the target on the arrow? (b) If the mass of the arrow is doubled, and the force exerted by the target on the arrow remains the same, by what multiplicative factor does the penetration depth change? Explain.

Problem 68GP BIO The Fall of T. rex Paleontologists estimate that if a Tyrnnnosaunis rex were to trip and fall, it would have experienced a force of approximately 260,000 N acting on its torso when it hit the ground. Assuming the torso has a mass of 3800 kg, (a) find the magnitude of the torso's upward acceleration as it comes to rest. (For comparison, humans lose consciousness with an acceleration of about 7g.) (b) Assuming the torso is in freefall for a distance of 1.46 m as it falls to the ground, how much time is required for the torso to come to rest once it contacts the ground?

Problem 69GP Deep Space I The NASA spacecraft Deep Space I was shut down on December 18, 2001, following a three-year journey to the asteroid Braille and the comet Borrelly. This spacecraft used a solar-powered ion engine to produce 0.064 ounces of thrust (force) by stripping electrons from neon atoms and accelerating the resulting ions to 70,000 mi/h. The thrust was only as much as the weight of a couple sheets of paper, but the engine operated continuously for 16,000 hours. As a result, the speed of the spacecraft increased by 7900 mi/h. What was the mass of Deep Space I? (Assume that the mass of the neon gas is negligible.)

Problem 71GP IP While waiting at the airport for your flight to leave, you observe some of the jets as they take off. With your watch you find that it takes about 35 seconds for a plane to go from rest to takeoff speed. In addition, you estimate that the distance re-quired is about 1.5 km. (a) If the mass of a jet is 1.70 × 105 kg, what force is needed for takeoff? (b) Describe the strategy you used to solve part (a).

Problem 70GP Your groceries are in a bag with paper handles. The handles will tear off if a force greater than 51.5 N is applied to them. What is the greatest mass of groceries that can be lifted safely with this bag, given that the bag is raised (a) with constant speed, or (b) with an acceleration of 1.25 m/s2?

Problem 73GP Two boxes are at rest on a smooth, horizontal surface. The boxes are in contact with one another. If box 1 is pushed with a force of magnitude F = 12.00 N, the contact force between the boxes is 8.50 N; if, instead, box 2 is pushed with the force F, the contact force is 12.00 N ? 8.50 N = 3.50 N. In either case, the boxes move together with an acceleration of 1.70 m/s2. What is the mass of (a) box 1 and (b) box 2?

BIO Gecko Feet Researchers have found that a gecko’s foot is covered with hundreds of thousands of small hairs (setae) that allow it to walk up walls and even across ceilings. A single foot pad, which has an area of \(\mathrm {1.0\ cm^2}\), can attach to a wall or ceiling with a force of 11 N. (a) How many 250-g geckos could be suspended from the ceiling by a single foot pad? (b) Estimate the force per square centimeter that your body exerts on the soles of your shoes, and compare with the \(\mathrm {11\ N/cm^2}\) of the sticky gecko foot. ________________ Equation Transcription: Text Transcription: 1.0 cm^2 11 N/cm^2

Problem 74GP IP Responding to an alarm, a 102-kg fireman slides down a pole to the ground floor, 3.3 m below. The fireman starts at rest and lands with a speed of 4.2 m/s. (a) Find the average force exerted on the fireman by the pole. (b) If the landing speed is half that in part (a), is the average force exerted on the fireman by the pole doubled? Explain. (c) Find the average force exerted on the fireman by the pole when the landing speed is 2.1 m/s.

Problem 75GP For a birthday gift, you and some friends take a hot-air balloon ride. One friend is late, so the balloon floats a couple of feet off the ground as you wait. Before this person arrives, the combined weight of the basket and people is 1220 kg, and the balloon is neutrally buoyant. When the late arrival climbs up into the basket, the balloon begins to accelerate downward at 0.56 m/s2. What was the mass of the last person to climb aboard?

Problem 77GP When two people push in the same direction on an object of mass m they cause an acceleration of magnitude a1. When the same people push in opposite directions, the acceleration of the object has a magnitude a2. Determine the magnitude of the force exerted by each of the two people in terms of m, a1 and a2.

Problem 76GP A baseball of mass m and initial speed v strikes a catcher's mitt. If the mitt moves a distance ?x as it brings the ball to rest, what is the average force it exerts on the ball?

The combination of “crumple zones” and air bags/seatbelts might increase the distance over which a person stops in a collision to as great as 1.00 m. What is the magnitude of the force exerted on a 65.0-kg driver who decelerates from 18.0 m/s to 0.00 m/s over a distance of 1.00 m? A. 162 N B. 585 N C. \(1.05 \times 10^4\ \mathrm N\) D. \(2.11 \times 10^4\ \mathrm N\) Equation Transcription: Text Transcription: 1.05x10^4 N 2.11x10^4 N

Problem 78GP · · · An air-track cart of mass m1 = 0.14 kg is moving with a speed v0 = 1.3 m/s to the right when it collides with a cart of mass m2 = 0.25 kg that is at rest. Each cart has a wad of putty on its bumper, and hence they stick together as a result of their collision. Suppose the average contact force between the carts is F = 1.5 N during the collision. (a) What is the acceleration of cart 1? Give direction and magnitude. (b) What is the acceleration of cart 2? Give direction and magnitude. (c) How long does it take for both carts to have the same speed? (Once the carts have the same speed the collision is over and the contact force vanishes.) (d) What is the final speed of the carts, vf? (e) Show that m1v0 is equal to (m1 + m2)vf. (We shall investigate the significance of this result in Chapter 9.)

Problem 80PP A driver who does not wear a seatbelt continues to move forward with a speed of 18.0 m/s (due to inertia) until something solid like the steering wheel is encountered. The driver now comes to rest in a much shorter distance—perhaps only a few centimeters. Find the magnitude of the net force acting on a 65.0-kg driver who is decelerated from 18.0 m/s to rest in 5.00 cm. A. 3240 N B. 1.17 × 104 N C. 2.11 × 105 N D. 4.21 × 105 N

Problem 81PP Suppose the initial speed of the driver is doubled to 36.0 m/s. If the driver still has a mass of 65.0 kg, and comes to rest in 1.00 m, what is the magnitude of the force exerted on the driver during this collision? A. 648 N B. 1170 N C. 2.11 × 104 N D. 4.21 × 104 N

Problem 82PP If both the speed and stopping distance of a driver are doubled, by what factor does the force exerted on the driver change? A. 0.5 B. 1 C. 2 D. 4

Problem 83IP IP Referring to Example 5-4 Suppose that we would like the contact force between the boxes to have a magnitude of 5.00 N, and that the only thing in the system we are allowed to change is the mass of box 2—the mass of box 1 is 10.0 kg and the applied force is 20.0 N. (a) Should the mass of box 2 be increased or decreased? Explain. (b) Find the mass of box 2 that results in a contact force of magnitude 5.00 N. (c) What is the acceleration of the boxes in this case?

IP Referring to Figure 5-9 Suppose the magnitude of \(\mathrm {\vec{F}_2}\) is increased from to , and that everything else in the system remains the same. (a) Do you expect the direction of the satellite's acceleration to be greater than, less than, or equal to \(32^\circ\)? Explain. Find the direction and the magnitude of the satellite's acceleration in this case. ________________ Equation Transcription: Text Transcription: vec{F}_2 32^o

Problem 84IP Referring to Example 5-4 Suppose the force of 20.0 N pushes on two boxes of unknown mass. We know, however, that the acceleration of the boxes is 1.20 m/s2 and the contact force has a magnitude of 4.45 N. Find the mass of (a) box 1 and (b) box 2.

An ant walks slowly away from the top of a bowling ball, as shown in Figure 5–30. If the ant starts to slip when the normal force on its feet drops below one-half its weight, at what angle \(\theta\) does slipping begin? ________________ Equation Transcription: Text Transcription: theta

Problem 52GP ·CE Predict/Explain Riding in an elevator moving upward with constant speed, you begin a game of darts. (a) Do you have to aim your darts higher than, lower than, or the same as when you play darts on solid ground? (b) Choose the best explanation from among the following: I. The elevator rises during the time it takes for the dart to travel to the darf board. II. The elevator moves with constant velocity. Therefore, Newton's laws apply within the elevator in the same way as on the ground. III. You have to aim lower to compensate for the upward speed of the elevator.