FIGURE shows two 1.0 kg blocks connected by a rope. A

Problem 1E Exercise describe a situation. For the: a. Draw an interaction diagram, following the steps of Tactics Box 7.1. ________________ b. Identify the “system” on your interaction diagram. ________________ c. Draw a free-body diagram for each object in the system. Use dashed lines to connect the members of an action/reaction pair. A weightlifter stands up at constant speed from a squatting position while holding a heavy barbell across his shoulders.

What is the acceleration of the \(2.0 kg\) block in across the frictionless table? Hint: Think carefully about the acceleration constraint. ________________ Equation Transcription: Text Transcription: 2.0 kg

In FIGURE CP7.54, find an expression for the acceleration of \(m_{1}\). The pulleys are massless and frictionless. Hint: Think carefully about the acceleration constraint. ________________ Equation Transcription: Text Transcription: m_1

FIGURE CP7.57 shows three hanging masses connected by massless strings over two massless, frictionless pulleys. a. Find the acceleration constraint for this system. It is a single equation relating \(a_{1 y}\), \(a_{2 y}\), and \(a_{3 y}\) Hint: \(y_{\mathrm{A}}\) isn't constant. b. Find an expression for the tension in string A. Hint: You should be able to write four second-law equations. These, plus the acceleration constraint, are five equations in five unknowns. c. Suppose: \(m_{1}=2.5 \mathrm{~kg}, m_{2}=1.5 \mathrm{~kg}\), and \(m_{3}=4.0 \mathrm{~kg}\). Find the acceleration of each. d. The \(4.0 \mathrm{~kg}\) mass would appear to be in equilibrium. Explain why it accelerates. ________________ Equation Transcription: Text Transcription: a_{1 y}, a_{2 y} a_{3 y} y_{\mathrm{A}} m_{1}=2.5 \mathrm{~kg}, m_{2}=1.5 \mathrm{~kg} m_{3}=4.0 \mathrm{~kg} 4.0 \mathrm{~kg}

Problem 1CQ You find yourself in the middle of a frozen lake with a surface so slippery (?s = ?k = 0) you cannot walk. However, you happen to have several rocks in your pocket. The ice is extremely hard. It cannot be chipped, and the rocks slip on it just as much as your feel do. Can you think of a way to get to shore? Use pictures, forces, and Newton’s laws to explain your reasoning.

FIGURE CP7.56 shows a 200 g hamster sitting on an 800 g wedge shaped block. The block, in turn, rests on a spring scale. An extra-fine lubricating oil having \(\mu_{\mathrm{s}}=\mu_{\mathrm{k}}=0\) is sprayed on the top surface of the block, causing the hamster to slide down. Friction between the block and the scale is large enough that the block does not slip on the scale. What does the scale read, in grams, as the hamster slides down? ________________ Equation Transcription: Text Transcription: mu_s = mu_k = 0

Problem 2CQ How do you paddle a canoe in the forward direction? Explain. Your explanation should include diagrams showing forces on the water and forces on the paddle.

Problem 2E Exercise describe a situation. For the: a. Draw an interaction diagram, following the steps of Tactics Box 7.1. ________________ b. Identify the “system” on your interaction diagram. ________________ c. Draw a free-body diagram for each object in the system. Use dashed lines to connect the members of an action/reaction pair. A soccer ball and a bowling ball have a head-on collision at this instant. Rolling friction is negligible.

Problem 3CQ How does a rocket take off? What is the upward force on it? Your explanation should include diagrams showing forces on the rocket and forces on the parcel of hot gas that was just expelled from the rocket’s exhaust.

Problem 4CQ How do basketball players jump straight up into the air? Your explanation should include pictures showing forces on the player and forces on the ground.

A mountain climber is using a rope to pull a bag of supplies up a \(45^{\circ}\) slope. The rope is not massless. ________________ Equation Transcription: Text Transcription: 45^circ

| A battery-powered toy car pushes a stuffed rabbit across the floor.

Problem 6CQ A mosquito collides head-on with a car traveling 60 mph. Is the magnitude of the mosquito’s acceleration larger than, smaller than, or equal to the magnitude of the car’s acceleration? Explain.

Block A in Figure EX7.5 is heavier than block B and is sliding down the incline. All surfaces have friction. The rope is massless, and the massless pulley turns on frictionless bearings. The rope and the pulley are among the interacting objects, but you’ll have to decide if they’re part of the system.

Problem 5CQ A mosquito collides head-on with a car traveling 60 mph. Is the force of the mosquito on the car larger than, smaller than, or equal to the force of the car on the mosquito? Explain.

Block A in Figure EX7.6 is sliding down the incline. The rope is massless, and the massless pulley turns on frictionless bearings, but the surface is not frictionless. The rope and the pulley are among the interacting objects, but you’ll have to decide if they’re part of the system.

Problem 8CQ A very smart 3-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?

Block B in Figure EX7.8 rests on a surface for which the static and kinetic coefficients of friction are 0.60 and 0.40, respectively. The ropes are massless. What is the maximum mass of block A for which the system is in equilibrium?

Problem 9E A 1000 kg car pushes a 2000 kg truck that has a dead battery. When the driver steps on the accelerator, the drive wheels of the car push backward against the ground with a force of 4500 N. a. What is the magnitude of the force of the car on the truck? b. What is the magnitude of the force of the truck on the car?

a. How much force does an \(80 \mathrm{~kg}\) astronaut exert on his chair while sitting at rest on the launch pad? b. How much force does the astronaut exert on his chair while accelerating straight up at \(10 \mathrm{~m} / \mathrm{s}^{2}\) ? ________________ Equation Transcription: Text Transcription: 80 kg 10 m/s^2

Problem 7CQ A small car is pushing a large truck. They are speeding up. Is the force of the truck on the car larger than, smaller than, or equal to the force of the car on the truck?

Problem 9CQ Teams red and blue are having a tug-of-war. According to Newton’s third law, the force with which the red team pulls on the blue team exactly equals the force with which the blue team pulls on the red team. How can one team ever win? Explain.

Problem 10E Blocks with masses of 1.0 kg, 2.0 kg, and 3.0 kg are lined up in a row on a frictionless table. All three are pushed forward by a 12 N force applied to the 1.0 kg block. How much force does the 2.0 kg block exert on (a) the 3.0 kg block and (b) the 1.0 kg block?

Will hanging a magnet in front of the iron cart in Figure Q7.10 make it go? Explain.

Problem 11E A massive steel cable drags a 20 kg block across a horizontal, frictionless surface. A 100 N force applied to the cable causes the block to reach a speed of 4.0 m/s in a distance of 2.0 m. What is the mass of the cable?

. Figure Q7.11 shows two masses at rest. The string is massless and the pulley is frictionless. The spring scale reads in \(kg\). What is the reading of the scale? ________________ Equation Transcription: Text Transcription: kg

The hand in FIGURE Q7.13 is pushing on the back of block A. Blocks A and B, with \(m_{B}>m_{A}\), are connected by a massless string and slide on a frictionless surface. Is the force of the string on B larger than, smaller than, or equal to the force of the hand on A? Explain. ________________ Equation Transcription: Text Transcription: m_B > m_A

What is the tension in the rope of Figure EX7.12?

FIGURE EX7.13 shows two \(1.0 \mathrm{~kg}\) blocks connected by a rope. A second rope hangs beneath the lower block. Both ropes have a mass of \(250 \mathrm{~g}\). The entire assembly is accelerated upward at \(3.0 \mathrm{~m} / \mathrm{s}^{2}\) by force \(\vec{F}\). a. What is \(F\) ? b. What is the tension at the top end of rope 1 ? c. What is the tension at the bottom end of rope 1 ? d. What is the tension at the top end of rope 2 ? ________________ Equation Transcription: Text Transcription: 1.0 kg 250 g 3.0 m/ s^2 vec{F} F

Blocks A and B in Figure Q7.14 are connected by a massless string over a massless, frictionless pulley. The blocks have just been released from rest. Will the pulley rotate clockwise, counterclockwise, or not at all? Explain.

Figure Q7.12 shows two masses at rest. The string is massless and the pulley is frictionless. The spring scale reads in kg. What is the reading of the scale?

Problem 14E Jimmy has caught two fish in Yellow Creek. He has tied the line holding the 3.0 kg steelhead trout to the tail of the 1.5 kg carp. To show the fish to a friend, he lifts upward on the carp with a force of 60 N. a. Draw separate free-body diagrams for the trout and the carp. Label all forces, then use dashed lines to connect action/ reaction pairs or forces that act as if they are a pair. ________________ b. Rank in order, from largest to smallest, the magnitudes of all the forces shown on your free-body diagrams. Explain your reasoning.

A 2.0-m-long, \(500 \mathrm{~g}\) rope pulls a \(10 \mathrm{~kg}\) block of ice across a horizontal, frictionless surface. The block accelerates at \(2.0 \mathrm{~m} / \mathrm{s}^{2}\). How much force pulls forward on (a) the ice, (b) the rope? ________________ Equation Transcription: Text Transcription: 500 g 10 kg 2.0 m/s^2

The cable cars in San Francisco are pulled along their tracks by an underground steel cable that moves along at 9.5 mph. The cable is driven by large motors at a central power station and extends, via an intricate pulley arrangement, for several miles beneath the city streets. The length of a cable stretches by up to \(100 ft\) during its lifetime. To keep the tension constant, the cable passes around a \(1.5-m\) diameter “tensioning pulley” that rolls back and forth on rails, as shown in Figure EX7.16. A 2000 kg block is attached to the tensioning pulley’s cart, via a rope and pulley, and is suspended in a deep hole. What is the tension in the cable car’s cable? ________________ Equation Transcription: Text Transcription: 100 ft 1.5 m

A 2.0 kg rope hangs from the ceiling. What is the tension at the midpoint of the rope?

In case a in FIGURE Q7.15, block \(A\) is accelerated across a frictionless table by a hanging \(10 \mathrm{~N}\) weight \((1.02 \mathrm{~kg})\). In case b, block \(A\) is accelerated across a frictionless table by a steady \(10 \mathrm{~N}\) tension in the string. The string is massless, and the pulley is massless and frictionless. Is A's acceleration in case b greater than, less than, or equal to its acceleration in case a? Explain. ________________ Equation Transcription: Text Transcription: A 10 N 1.02 kg A 10 N

||| Figure P7.19 shows two strong magnets on opposite sides of a small table. The long-range attractive force between the magnets keeps the lower magnet in place. a. Draw an interaction diagram and draw free-body diagrams for both magnets and the table. Use dashed lines to connect the members of an action/reaction pair. b. Suppose the weight of the table is \(20 N\), the weight of each magnet is \(2.0 N\), and the magnetic force on the lower magnet is three times its weight. Find the magnitude of each of the forces shown on your free-body diagrams. ________________ Equation Transcription: Text Transcription: 20 N 2.0 N

Problem 20P An 80 kg spacewalking astronaut pushes off a 640 kg satellite, exerting a 100 N force for the 0.50 s it takes him to straighten his arms. How far apart are the astronaut and the satellite after 1.0 min?

Problem 21P A massive steel cable drags a 20 kg block across a horizontal, frictionless surface. A 100 N force applied to the cable causes the block to reach a speed of 4.0 m/s in 2.0 s. What is the difference in tension between the two ends of the cable?

Problem 24P A rope of length L and mass m is suspended from the ceiling. Find an expression for the tension in the rope at position y,measured upward from the free end of the rope.

| Figure P7.22 shows a \(6.0 N\) force pushing two gliders along an air track. The \(200 g\) spring between the gliders is compressed. How much force does the spring exert on (a) glider A and (b) glider B? ________________ Equation Transcription: Text Transcription: 6. 0 N 200 g

A mobile at the art museum has a \(2.0 \mathrm{~kg}\) steel cat and a \(4.0 \mathrm{~kg}\) steel dog suspended from a lightweight cable, as shown in FIGURE EX7.18. It is found that \(\theta_{1}=20^{\circ}\) when the center rope is adjusted to be perfectly horizontal. What are the tension and the angle of rope 3 ?pe is adjusted to be perfectly horizontal. What are the tension and the angle of rope 3 ? ________________ Equation Transcription: Text Transcription: 2. 0 kg 4.0 kg theta_1 = 20^circ

Problem 25P While driving to work last year, I was holding my coffee mug in my left hand while changing the CD with my right hand. Then the cell phone rang, so I placed the mug on the flat part of my dashboard. Then, believe it or not, a deer ran out of the woods and on to the road right in front of me. Fortunately, my reaction time was zero, and I was able to stop from a speed of 20 m/s in a mere 50 m, just barely avoiding the deer. Later tests revealed that the static and kinetic coefficients of friction of the coffee mug on the dash are 0.50 and 0.30, respectively; the coffee and mug had a mass of 0.50 kg; and the mass of the deer was 120 kg. Did my coffee mug slide?

|| The sled dog in Figure P7.23 drags sleds A and B across the snow. The coefficient of friction between the sleds and the snow is 0.10. If the tension in rope 1 is \(150 N\), what is the tension in rope 2? ________________ Equation Transcription: Text Transcription: 150 N

Problem 26P Two-thirds of the weight of a 1500 kg car rests on the drive wheels. What is the maximum acceleration of this car on a concrete surface?

Problem 27P A Federation starship (2.0 × 106 kg) uses its tractor beam to pull a shuttlecraft (2.0 × 104 kg) aboard from a distance of 10 km away. The tractor beam exerts a constant force of 4.0 × 104 N on the shuttlecraft. Both spacecraft are initially at rest. How far does the starship move as it pulls the shuttlecraft aboard?

The two blocks in Figure P7.32 are sliding down the incline. What is the tension in the massless string?

Your forehead can withstand a force of about 6.0 kN before fracturing, while your cheekbone can withstand only about 1.3 kN. Suppose a 140 g baseball traveling at 30 m/s strikes your head and stops in 1.5 ms. a. What is the magnitude of the force that stops the baseball? b. What force does the baseball exert on your head? Explain. c. Are you in danger of a fracture if the ball hits you in the forehead? On the cheek?

Problem 29P Bob, who has a mass of 75 kg, can throw a 500 g rock with a speed of 30 m/s. The distance through which his hand moves as he accelerates the rock from rest until he releases it is 1.0 m. a. What constant force must Bob exert on the rock to throw it with this speed? ________________ b. If Bob is standing on frictionless ice, what is his recoil speed after releasing the rock?

Problem 30P You see the boy next door trying to push a crate down the sidewalk. He can barely keep it moving, and his feet occasionally slip. You start to wonder how heavy the crate is. You call to ask the boy his mass, and he replies “50 kg.” From your recent physics class you estimate that the static and kinetic coefficients of friction are 0.8 and 0.4 for the boy’s shoes, and 0.5 and 0.2 for the crate. Estimate the mass of the crate.

Two packages at UPS start sliding down the 20 ramp shown in Figure P7.31. Package A has a mass of \(5.0 kg\) and a coefficient of friction of 0.20. Package B has a mass of \(10 kg\) and a coefficient of friction of 0.15. How long does it take package A to reach the bottom? ________________ Equation Transcription: Text Transcription: 5.0 kg 10 kg

The \(1.0 \mathrm{~kg}\) block in FIGURE P7.33 is tied to the wall with a rope. It sits on top of the \(2.0 \mathrm{~kg}\) block. The lower block is pulled to the right with a tension force of \(20 \mathrm{~N}\). The coefficient of kinetic friction at both the lower and upper surfaces of the \(2.0 \mathrm{~kg}\) block is \(\mu_{\mathrm{k}}=0.40\). a. What is the tension in the rope holding the \(1.0 \mathrm{~kg}\) block to the wall? b. What is the acceleration of the \(2.0 \mathrm{~kg}\) block? ________________ Equation Transcription: Text Transcription: 1.0 kg 2.0 kg 20 N 2.0 kg mu_k = 0.40 1.0 kg 2.0 kg

The \(100 \mathrm{~kg}\) block in FIGURE P7.38 takes \(6.0 \mathrm{~s}\) to reach the floor after being released from rest. What is the mass of the block on the left? The pulley is massless and frictionless. ________________ Equation Transcription: Text Transcription: 100 kg 6.0 s

The lower block in Figure P7.35 is pulled on by a rope with a tension force of \(20 N\). The coefficient of kinetic friction between the lower block and the surface is 0.30. The coefficient of kinetic friction between the lower block and the upper block is also 0.30. ________________ Equation Transcription: Text Transcription: 20 N

Problem 37P A rope attached to a 20 kg wood sled pulls the sled up a 20° snow-covered hill. A 10 kg wood box rides on top of the sled. If the tension in the rope steadily increases, at what value of the tension does the box slip?

The coefficient of static friction is 0.60 between the two blocks in Figure P7.34. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force \(\vec{F}\) causes both blocks to cross a distance of 5.0 m, starting from rest. What is the least amount of time in which this motion can be completed without the top block sliding on the lower block? ________________ Equation Transcription: Text Transcription: vec{F}

The block of mass \(M\) in Figure P7.36 slides on a frictionless surface. Find an expression for the tension in the string. ________________ Equation Transcription: Text Transcription: M

The 10.2 kg block in Figure P7.39 is held in place by a force applied to a rope passing over two massless, frictionless pulleys. Find the tensions \(T_{1}\) to \(T_{5}\) and the magnitude of force \(\vec{F}\). . ________________ Equation Transcription: Text Transcription: T_1 T_5 vec{F}

The coefficient of kinetic friction between the \(2.0 kg\) block in Figure P7.40 and the table is 0.30. What is the acceleration of the \(2.0 kg\) block? ________________ Equation Transcription: Text Transcription: 2.0 kg 2.0 kg

FIGURE P7.41 shows a block of mass \(m\) resting on a \(20^{\circ}\) slope. The block has coefficients of friction \(\mu_{\mathrm{s}}=0.80\) and \(\mu_{\mathrm{k}}=0.50\) with the surface. It is connected via a massless string over a massless, frictionless pulley to a hanging block of mass 2.0 kg. a. What is the minimum mass \(m\) that will stick and not slip? b. If this minimum mass is nudged ever so slightly, it will start being pulled up the incline. What acceleration will it have? ________________ Equation Transcription: Text Transcription: m 20^circ mu_s =0.80 mu_k = 0.50 m

The \(2000 kg\) cable car shown in Figure P7.44 descends a \(200-m\)-high hill. In addition to its brakes, the cable car controls its speed by pulling an \(1800 kg\) counterweight up the other side of the hill. The rolling friction of both the cable car and the counterweight are negligible. a. How much braking force does the cable car need to descend at constant speed? b. One day the brakes fail just as the cable car leaves the top on its downward journey. What is the runaway car’s speed at the bottom of the hill? ________________ Equation Transcription: Text Transcription: 2000 kg 200 m 1800 kg

A house painter uses the chair-and-pulley arrangement of FIGURE P7.46 to lift himself up the side of a house. The painter's mass is 70 kg and the chair's mass is 10 kg. With what force must he pull down on the rope in order to accelerate upward at \(0.20 \mathrm{~m} / \mathrm{s}^{2}\) ? ________________ Equation Transcription: Text Transcription: 0.20 m/s^2

A \(4.0 kg\) box is on a frictionless 35 slope and is connected via a massless string over a massless, frictionless pulley to a hanging 2.0 kg weight. The picture for this situation is similar to Figure P7.41. a. What is the tension in the string if the \(4.0 kg\) box is held in place, so that it cannot move? b. If the box is then released, which way will it move on the slope? c. What is the tension in the string once the box begins to move? ________________ Equation Transcription: Text Transcription: 4.0 kg 4.0 kg

The century-old ascensores in Valparaiso, Chile, are small cable cars that go up and down the steep hillsides. As Figure P7.45 shows, one car ascends as the other descends. The cars use a two cable arrangement to compensate for friction; one cable passing around a large pulley connects the cars, the second is pulled by a small motor. Suppose the mass of both cars (with passengers) is \(1500 kg\), the coefficient of rolling friction is 0.020, and the cars move at constant speed. What is the tension in (a) the connecting cable and (b) the cable to the motor? ________________ Equation Transcription: Text Transcription: 1500 kg

The 1.0 kg physics book in FIGURE P7.43 is connected by a string to a 500 g coffee cup. The book is given a push up the slope and released with a speed of 3.0 m/s. The coefficients of friction are (\mu_{\mathrm{s}}=0.50\) and \(\mu_{\mathrm{k}}=0.20\). a. How far does the book slide? b. At the highest point, does the book stick to the slope, or does it slide back down? ________________ Equation Transcription: Text Transcription: mu_s =0.50 mu_k = 0.20

Problem 47P Jorge, with mass ?m?,is wearing roller skates whose coefficient of friction with the floor is ???r. He ties a massless rope around his waist, passes it around a frictionless pulley, and grabs hold of the other end, as shown in FIGURE. Jorge then pulls hand over hand on the rope with a constant force ?F.? Find an expression for Jorge’s acceleration toward the wall. FIGURE

Problem 53CP A 100 g ball of clay is thrown horizontally with a speed of 10 m/s toward a 900 g block resting on a frictionless surface. It hits the block and sticks. The clay exerts a constant force on the block during the 10 ms it takes the clay to come to rest relative to the block. After 10 ms, the block and the clay are sliding along the surface as a single system. a. What is their speed after the collision? ________________ b. What is the force of the clay on the block during the collision? ________________ c. What is the force of the block on the clay?

Problem 48P A 70 kg tightrope walker stands at the center of a rope. The rope supports are 10 m apart and the rope sags 10° at each end. The tightrope walker crouches down, then leaps straight up with an acceleration of 8.0 m/s2 to catch a passing trapeze. What is the tension in the rope as he jumps?

|| Find an expression for the magnitude of the horizontal force \(F\) in Figure P7.49 for which \(m_{1}\) does not slip either up or down along the wedge. All surfaces are frictionless. ________________ Equation Transcription: Text Transcription: F m_1

Problems 51 and 52 show the free-body diagrams of two interacting systems. For each of these, you are to a. Write a realistic problem for which these are the correct free body diagrams. Be sure that the answer your problem requests is consistent with the diagrams shown. b. Finish the solution of the problem.

Problems 51 and 52 show the free-body diagrams of two interacting systems. For each of these, you are to a. Write a realistic problem for which these are the correct freebody diagrams. Be sure that the answer your problem requests is consistent with the diagrams shown. b. Finish the solution of the problem.

A \(100 kg\) basketball player can leap straight up in the air to a height of \(80 cm\), as shown in Figure P7.50. You can understand how by analyzing the situation as follows: a. The player bends his legs until the upper part of his body has dropped by \(60 cm\), then he begins his jump. Draw separate free-body diagrams for the player and for the floor as he is jumping, but before his feet leave the ground. b. Is there a net force on the player as he jumps (before his feet leave the ground)? How can that be? Explain. c. With what speed must the player leave the ground to reach a height of \(80\) cm? d. What was his acceleration, assumed to be constant, as he jumped? e. Suppose the player jumps while standing on a bathroom scale that reads in newtons. What does the scale read before he jumps, as he is jumping, and after his feet leave the ground? ________________ Equation Transcription: Text Transcription: 100 kg 80 cm 60 cm 80 cm