Solved: Seat belts and air bags save lives by reducing the

Problem 1CQ An object is subject to two forces that do not point in opposite directions. Is it possible to choose their magnitudes so that the object is in equilibrium? Explain.

Problem 1P The three ropes in Figure P5.1 are tied to a small, very light ring. Two of the ropes are anchored to walls at right angles, and the third rope pulls as shown. What are , the magnitudes of the tension forces in the first two ropes?

Problem 2CQ Are the objects described here in static equilibrium, dynamic equilibrium, or not in equilibrium at all? a. A girder is lifted at constant speed by a crane. b. A girder is lowered by a crane. It is slowing down. c. You’re straining to hold a 200 lb barbell over your head. d. A jet plane has reached its cruising speed and altitude. e. A rock is falling into the Grand Canyon. f. A box in the back of a truck doesn’t slide as the truck stops.

Problem 2P The three ropes in Figure P5.2 are tied to a small, very light ring. Two of these ropes are anchored to walls at right angles with the tensions shown in the figure. What are the magnitude and direction of the tension in the third rope?

Problem 3CQ What forces are acting on you right now? What net force is acting on you right now?

Problem 3P A 20 kg loudspeaker is suspended 2.0 m below the ceiling by two cables that are each 30° from vertical. What is the tension in the cables?

Problem 4CQ Decide whether each of the following is true or false. Give a reason! a. The mass of an object depends on its location. b. The weight of an object depends on its location. c. Mass and weight describe the same thing in different units.

Problem 4P A 1000 kg steel beam is sup-ported by the two ropes shown in Figure 4. Each rope can support a maximum sustained tension of 5600 N. Do the ropes break? FIGURE 4

Problem 5CQ An astronaut takes his bathroom scale to the moon and then stands on it. Is the reading of the scale his true weight? Explain.

Problem 5P A cable is used to raise a 25 kg urn from an underwater archeological site. There is a 25 N drag force from the water as the urn is raised at a constant speed. What is the tension in the cable?

Problem 6CQ A light block of mass m and a heavy block of mass M are attached to the ends of a rope. A student holds the heavier block and lets the lighter block hang below it, as shown in Figure Q5.6 . Then she lets go. Air resistance can be neglected. a. What is the tension in the rope while the blocks are falling, before either hits the ground? b. Would your answer be different if she had been holding the lighter block initially?

Problem 6P When you bend your knee, the quadriceps muscle is stretched. This increases the tension in the quadriceps tendon attached to your kneecap (patella), which, in turn, increases the tension in the patella tendon that attaches your kneecap to your lower leg bone (tibia). Simultaneously, the end of your upper leg bone (femur) pushes outward on the patella. Figure P5.5 shows how these parts of a knee joint are arranged. What size force does the femur exert on the kneecap if the tendons are oriented as in the figure and the tension in each tendon is 60 N?

Problem 7CQ Four balls are thrown straight up. Figure 7 is a "snapshot" showing their velocities. They have the same size but different mass. Air resistance is negligible. Rank in order, from largest to smallest, the magnitudes of the net forces, Fnet1,Fnet2, Fnet3, Fnet4, acting on the balls. Some may be equal. Give your answer in the form A > B = C > D, and state your reasoning. FIGURE 7

Problem 7P The two angled ropes used to support the crate in Figure 7 can withstand a maximum tension of 1500 N before they break. What is the largest mass the ropes can support? FIGURE 7

Problem 8CQ Suppose you attempt to pour out 100 g of salt, using a pan balance for measurements, while in an elevator that is accelerating upward. Will the quantity of salt be too much, too little, or the correct amount? Explain.

Problem 8P A force with x-component Fx acts on a 500 g object as it moves along the x-axis. The object’s acceleration graph (ax versus t)is shown in Figure 8. Draw a graph of Fx versus t. FIGURE 8

Problem 9CQ a. Can the normal force on an object be directed horizontally? If not, why not? If so, provide an example. b. Can the normal force on an object be directed downward? If not, why not? If so, provide an example.

Problem 9P A force with x-component acts on a 500 g object as it moves along the x-axis. The object’s acceleration graph ( versus t) is shown in Figure P5.9. Draw a graph of versus t.

Problem 10CQ A ball is thrown straight up. Taking the drag force of air into account, does it take longer for the ball to travel to the top of its motion or for it to fall back down again?

Problem 10P A force with x-component Fx acts on a 500 g object as it moves along the x-axis. A graph of Fxversus t is shown in Figure 10. Draw an acceleration graph (ax versus t)for this object. FIGURE 10

Problem 11CQ Three objects move through the air as shown in Figure Q5.12 . Rank in order, from largest to smallest, the three drag forces . Some may be equal. Give your answer in the form A < B = C and state your reasoning.

Problem 11P The forces in Figure P5.10 are acting on a 2.0 kg object. What is , the x-component of the object’s acceleration?

Problem 12CQ A skydiver is falling at her terminal speed. Right after she opens her parachute, which has a very large area, what is the direction of the net force on her?

Problem 12P The forces in Figure P5.11 are acting on a 2.0 kg object. Find the values of , the x- and y-components of the object’s acceleration.

Problem 13CQ Raindrops can fall at different speeds; some fall quite quickly, others quite slowly. Why might this be true?

Problem 13P A horizontal rope is tied to a 50 kg box on frictionless ice. What is the tension in the rope if a. The box is at rest? b. The box moves at a steady 5.0 m/s? c. The box has ?

Problem 14CQ An airplane moves through the air at a constant speed. The jet engine’s thrust applies a force in the direction of motion. Reducing thrust will cause the plane to fly at a slower—but still constant—speed. Explain why this is so.

Problem 14P A crate pushed along the floor with velocity vu i slides a distance d after the pushing force is removed. a. If the mass of the crate is doubled but the initial velocity is not changed, what distance does the crate slide before stopping? Explain. b. If the initial velocity of the crate is doubled to 2vu i but the mass is not changed, what distance does the crate slide before stopping? Explain.

Problem 15CQ Is it possible for an object to travel in air faster than its terminal speed? If not, why not? If so, explain how this might happen.

Problem 15P In a head-on collision, a car stops in 0.10 s from a speed of 14 m/s. The driver has a mass of 70 kg, and is, fortunately, tightly strapped into his seat. What force is applied to the driver by his seat belt during that fraction of a second?

Problem 16CQ For Questions 17 through 20, determine the tension in the rope at the point indicated with a dot. • All objects are at rest. • The strings and pulleys are massless, and the pulleys are frictionless.

Problem 16P An astronaut’s weight on earth is 800 N. What is his weight on Mars, where ?

Problem 17CQ For Questions 17 through 20, determine the tension in the rope at the point indicated with a dot. • All objects are at rest. • The strings and pulleys are massless, and the pulleys are frictionless.

Problem 17P A woman has a mass of 55.0 kg. a. What is her weight on earth? b. What are her mass and her weight on the moon, where ?

Problem 18CQ For Questions 17 through 20, determine the tension in the rope at the point indicated with a dot. • All objects are at rest. • The strings and pulleys are massless, and the pulleys are frictionless.

Problem 18P A box with a 75 kg passenger inside is launched straight up into the air by a giant rubber band. After the box has left the rubber band but is still moving upward, a. What is the passenger’s true weight? b. What is the passenger’s apparent weight?

Problem 19CQ For Questions 17 through 20, determine the tension in the rope at the point indicated with a dot. • All objects are at rest. • The strings and pulleys are massless, and the pulleys are frictionless.

Problem 20CQ In Figure Q5.21 , block 2 is moving to the right. There is no friction between the floor and block 2, but there is a friction force between blocks 1 and 2. In which direction is the kinetic friction force on block 1? On block 2? Explain.

Problem 19P a. How much force does an 80 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 ?

Problem 21MCQ The wood block in Figure Q5.22 is at rest on a wood ramp. In which direction is the static friction force on block 1? A. Up the slope. B. Down the slope. C. The friction force is zero. D. There’s not enough information to tell.

Problem 20P It takes the elevator in a skyscraper 4.0 s to reach its cruising speed of 10 m/s. A 60 kg passenger gets aboard on the ground floor. What is the passenger’s apparent weight a. Before the elevator starts moving? b. While the elevator is speeding up? c. After the elevator reaches its cruising speed?

Problem 21P Zach, whose mass is 80 kg, is in an elevator descending at 10 m/s. The elevator takes 3.0 s to brake to a stop at the first floor. a. What is Zach’s apparent weight before the elevator starts braking? b. What is Zach’s apparent weight while the elevator is braking?

A 2.0 kg ball is suspended by two light strings as shown in Figure Q5.22. What is the tension \(T\) in the angled string? A.9.5N B. 15N C. 20N D.26N E. 30N

Problem 22P Figure P5.23 shows the velocity graph of a 75 kg passenger in an elevator. What is the passenger’s apparent weight at t = 1.0 s? At 5.0 s? At 9.0 s?

Problem 23MCQ While standing in a low tunnel, you raise your arms and push against the ceiling with a force of 100 N. Your mass is 70 kg. a. What force does the ceiling exert on you? A. 10 N B. 100 N C. 690 N D. 790 N E. 980 N b. What force does the floor exert on you? A. 10 N B. 100 N C. 690 N D. 790 N E. 980 N

Problem 23P a. A 0.60 kg bullfrog is sitting at rest on a level log. How large is the normal force of the log on the frog? b. A second 0.60 kg bullfrog is on a log tilted 30° above horizontal. How large is the normal force of the log on this frog?

Problem 24MCQ A 5.0 kg dog sits on the floor of an elevator that is accelerating downward at . a. What is the magnitude of the normal force of the elevator floor on the dog? A. 34 N B. 43 N C. 49 N D. 55 N E. 74 N b. What is the magnitude of the force of the dog on the elevator floor? A. 4.2 N B. 49 N C. 55 N D. 43 N E. 74 N

Problem 24P A 23 kg child goes down a straight slide inclined 38° above horizontal. The child is acted on by his weight, the normal force from the slide, and kinetic friction. a. Draw a free-body diagram of the child. b. How large is the normal force of the slide on the child?

Problem 25MCQ A 3.0 kg puck slides due east on a horizontal frictionless surface at a constant speed of 4.5 m/s. Then a force of magnitude 6.0 N, directed due north, is applied for 1.5 s. Afterward, a. What is the northward component of the puck’s velocity? A. 0.50 m/s B. 2.0 m/s C. 3.0 m/s D. 4.0 m/s E. 4.5 m/s b. What is the speed of the puck? A. 4.9 m/s B. 5.4 m/s C. 6.2 m/s D. 7.5 m/s E. 11 m/s

Problem 25P Bonnie and Clyde are sliding a 300 kg bank safe across the floor to their getaway car. The safe slides with a constant speed if Clyde pushes from behind with 385 N of force while Bonnie pulls forward on a rope with 350 N of force. What is the safe’s coefficient of kinetic friction on the bank floor?

Problem 26MCQ A rocket in space, initially at rest, fires its main engines at a constant thrust. As it burns fuel, the mass of the rocket decreases. Which of the graphs in Figure 26 best represents the velocity of the rocket as a function of time? FIGURE 26

Problem 26P A 4000 kg truck is parked on a 7.0° slope. How big is the friction force on the truck?

Problem 27MCQ Eric has a mass of 60 kg. He is standing on a scale in an elevator that is accelerating downward at . What is the approximate reading on the scale? A. 0 N B. 400 N C. 500 N D. 600 N

Problem 27P A 1000 kg car traveling at a speed of 40 m/s skids to a halt on wet concrete where . How long are the skid marks?

Problem 28MCQ The two blocks in Figure Q5.28 are at rest on frictionless surfaces. What must be the mass of the right block in order that the two blocks remain stationary? A. 4.9 kg B. 6.1 kg C. 7.9 kg D. 9.8 kg E. 12 kg

Problem 28P A stubborn 120 kg pig sits down and refuses to move. To drag the pig to the barn, the exasperated farmer ties a rope around the pig and pulls with his maximum force of 800 N. The coefficients of friction between the pig and the ground are . Is the farmer able to move the pig?

Problem 29MCQ A football player at practice pushes a 60 kg blocking sled across the field at a constant speed. The coefficient of kinetic friction between the grass and the sled is 0.30. How much force must he apply to the sled? A. 18 N B. 60 N C. 180 N D. 600 N

Problem 29P A 10 kg crate is placed on a horizontal conveyor belt. The materials are such that . a. Draw a free-body diagram showing all the forces on the crate if the conveyer belt runs at constant speed. b. Draw a free-body diagram showing all the forces on the crate if the conveyer belt is speeding up. c. What is the maximum acceleration the belt can have without the crate slipping? d. If the acceleration of the belt exceeds the value determined in part c, what is the acceleration of the crate?

Problem 30MCQ Two football players are pushing a 60 kg blocking sled across the field at a constant speed of 2.0 m/s. The coefficient of kinetic friction between the grass and the sled is 0.30. Once they stop pushing, how far will the sled slide before coming to rest? A. 0.20 m B. 0.68 m C. 1.0 m D. 6.6 m

Problem 30P What is the minimum downward force on the box in Figure P5.33 that will keep it from slipping? The coefficients of static and kinetic friction between the box and the floor are 0.35 and 0.25, respectively.

Problem 31MCQ Land Rover ads used to claim that their vehicles could climb a slope of 45°. For this to be possible, what must be the minimum coefficient of static friction between the vehicle’s tires and the road? A. 0.5 B. 0.7 C. 0.9 D. 1.0

Problem 31P What is the drag force on a 1.6-m-wide, 1.4-m-high car traveling at

Problem 32MCQ A truck is traveling at 30 m/s on a slippery road. The driver slams on the brakes and the truck starts to skid. If the coefficient of kinetic friction between the tires and the road is 0.20, how far will the truck skid before stopping? A. 230 m B. 300 m C. 450 m D. 680 m

Problem 32P A 22-cm-diameter bowling ball has a terminal speed of 77 m/s. What is the ball’s mass?

Problem 33P A 75 kg skydiver can be modeled as a rectangular “box” with dimensions 20 cm × 40 cm ×1.8 m. What is his terminal speed if he falls feet first?

Problem 34P 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?

Problem 35P 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?

Problem 36P What is the tension in the rope of Figure P5.42?

Problem 37P A 2.0-m-long, 500 g rope pulls a 10 kg block of ice across a horizontal, frictionless surface. The block accelerates at . How much force pulls forward on (a) the block of ice, (b) the rope?

Problem 38P Figure P5.44 shows two 1.00 kg blocks connected by a rope. A second rope hangs beneath the lower block. Both ropes have a mass of 250 g. The entire assembly is accelerated upward at . 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?

Problem 39P Each of 100 identical blocks sitting on a frictionless surface is connected to the next block by a massless string. The first block is pulled with a force of 100 N. a. What is the tension in the string connecting block 100 to block 99? b. What is the tension in the string connecting block 50 to block 51?

Problem 40P Two blocks on a frictionless table, A and B, are connected by a massless string. When block A is pulled with a certain force, dragging block B, the tension in the string is 24 N. When block B is pulled by the same force, dragging block A, the tension is 18 N. What is the ratio of the blocks’ masses?

Problem 41GP ||| A 500 kg piano is being lowered into position by a crane while two people steady it with ropes pulling to the sides. Bob’s rope pulls to the left, 15° below horizontal, with 500 N of tension. Ellen’s rope pulls toward the right, 25° below horizontal. a. What tension must Ellen maintain in her rope to keep the piano descending vertically at constant speed? b. What is the tension in the vertical main cable supporting the piano?

Problem 42GP Dana has a sports medal suspended by a long ribbon from her rearview mirror. As she accelerates onto the highway, she notices that the medal is hanging at an angle of 10° from the vertical. a. Does the medal lean toward or away from the windshield? Explain. b. What is her acceleration?

Problem 43GP Figure P5.49 shows the velocity graph of a 2.0 kg object as it moves along the x-axis. What is the net force acting on this object at t = 1 s? At 4 s? At 7 s?

Problem 44GP Figure 44 shows the net force acting on a 2.0 kg object as it moves along the x-axis. The object is at rest at the origin at t = 0 s. What are its acceleration and velocity at t = 6.0 s? FIGURE 44

Problem 45GP A 50 kg box hangs from a rope. What is the tension in the rope if a. The box is at rest? b. The box has ?

Problem 46GP A 50 kg box hangs from a rope. What is the tension in the rope if a. The box moves up at a steady 5.0 m/s? b. The box has and is slowing down at ?

Problem 47GP Your forehead can withstand a force of about 6.0 kN before fracturing, while your cheekbone can only withstand about 1.3 kN. a. If a 140 g baseball strikes your head at 30 m/s and stops in 0.0015 s, what is the magnitude of the ball’s acceleration? b. What is the magnitude of the force that stops the baseball? c. What force does the baseball apply to your head? Explain. d. Are you in danger of a fracture if the ball hits you in the forehead? In the cheek?

Problem 48GP Seat belts and air bags save lives by reducing the forces exerted on the driver and passengers in an automobile collision. Cars are designed with a “crumple zone” in the front of the car. In the event of an impact, the passenger compartment decelerates over a distance of about 1 m as the front of the car crumples. An occupant restrained by seat belts and air bags decelerates with the car. By contrast, an unrestrained occupant keeps moving forward with no loss of speed (Newton’s first law!) until hitting the dashboard or windshield, as we saw in Figure 4.2. These are unyielding surfaces, and the unfortunate occupant then decelerates over a distance of only about 5 mm. a. A 60 kg person is in a head-on collision. The car’s speed at impact is 15 m/s. Estimate the net force on the person if he or she is wearing a seat belt and if the air bag deploys. b. Estimate the net force that ultimately stops the person if he or she is not restrained by a seat belt or air bag. c. How do these two forces compare to the person’s weight?

Problem 49GP 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 forward 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 50GP 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 51GP What thrust does a 200 g model rocket need in order to have a vertical acceleration of 10.0 m/s2 a. On earth? b. On the moon, where g = 1.62 m/s2?

Problem 52GP A 20,000 kg rocket has a rocket motor that generates of thrust. a. What is the rocket’s initial upward acceleration? b. At an altitude of 5.0 km the rocket’s acceleration has increased to . What mass of fuel has it burned?

Problem 53GP You’ve always wondered about the acceleration of the elevators in the 101-story-tall Empire State Building. One day, while visiting New York, you take your bathroom scale into the elevator and stand on it. The scale reads 150 lb as the door closes. The reading varies between 120 lb and 170 lb as the elevator travels 101 floors. a. What is the magnitude of the acceleration as the elevator starts upward? b. What is the magnitude of the acceleration as the elevator brakes to a stop?

Problem 54GP A 23 kg child goes down a straight slide inclined 38° above horizontal. The child is acted on by his weight, the normal force from the slide, kinetic friction, and a horizontal rope exerting a 30 N force as shown in Figure P5.59. How large is the normal force of the slide on the child?

Problem 55GP Josh starts his sled at the top of a 3.0-m-high hill that has a constant slope of 25°. After reaching the bottom, he slides across a horizontal patch of snow. Ignore friction on the hill, but assume that the coefficient of kinetic friction between his sled and the horizontal patch of snow is 0.050. How far from the base of the hill does he end up?

Problem 56GP A wood block, after being given a starting push, slides down a wood ramp at a constant speed. What is the angle of the ramp above horizontal?

Researchers often use force plates to measure the forces that people exert against the floor during movement. A force plate works like a bathroom scale, but it keeps a record of how the reading changes with time. Figure P5.64 shows the data from a force plate as a woman jumps straight up and then lands. a. What was the vertical component of her acceleration during push-off? b. What was the vertical component of her acceleration while in the air? c. What was the vertical component of her acceleration during the landing? d. What was her speed as her feet left the force plate? e. How high did she jump?

Problem 58GP A 77 kg sprinter is running the 100 m dash. At one instant, early in the race, his acceleration is 4.7 m/s2. a. What total force does the track surface exert on the sprinter? Assume his acceleration is parallel to the ground. Give your answer as a magnitude and an angle with respect to the horizontal. b. This force is applied to one foot (the other foot is in the air), which for a fraction of a second is stationary with respect to the track surface. Because the foot is stationary, the net force on it must be zero. Thus the force of the lower leg bone on the foot is equal but opposite to the force of the track on the foot. If the lower leg bone is 60° from horizontal, what are the components of the leg’s force on the foot in the directions parallel and perpendicular to the leg? (Force components perpendicular to the leg can cause dislocation of the anide joint.)

Problem 59GP Sam, whose mass is 75 kg, takes off across level snow on his jet-powered skis. The skis have a thrust of 200 N and a coefficient of kinetic friction on snow of 0.10. Unfortunately, the skis run out of fuel after only 10 s. a. What is Sam’s top speed? b. How far has Sam traveled when he finally coasts to a stop?

Problem 60GP A person with compromised pinch strength in his fingers can only exert a normal force of 6.0 N to either side of a pinch-held object, such as the book shown in Figure P5.65. What is the greatest mass book he can hold onto vertically before it slips out of his fingers? The coefficient of static friction of the surface between the fingers and the book cover is 0.80.

Problem 61GP A 1.0 kg wood block is pressed against a vertical wood wall by a 12 N force as shown in Figure P5.67. If the block is initially at rest, will it move upward, move downward, or stay at rest?

Problem 62GP A 50,000 kg locomotive, with steel wheels, is traveling at 10 m/s on steel rails when its engine and brakes both fail. How far will the locomotive roll before it comes to a stop?

Problem 63GP An Airbus A320 jetliner has a takeoff mass of 75,000 kg. It reaches its takeoff speed of 82 m/s (180 mph) in 35 s. What is the thrust of the engines? You can neglect air resistance but not rolling friction.

Problem 64GP A 2.0 kg wood block is launched up a wooden ramp that is inclined at a 35° angle. The block’s initial speed is 10 m/s. a. What vertical height does the block reach above its starting point? b. What speed does it have when it slides back down to its starting point?

Problem 65GP Two blocks are at rest on a frictionless incline, as shown in Figure P5.69. What are the tensions in the two strings?

Problem 66GP Two identical 2.0 kg blocks are stacked as shown in Figure P5.71. The bottom block is free to slide on a frictionless surface. The coefficient of static friction between the blocks is 0.35. What is the maximum horizontal force that can be applied to the lower block without the upper block slipping?

Problem 67GP A wood block is sliding up a wood ramp. If the angle of the ramp is very steep, the block will reverse direction at some point and slide back down. If the angle of the ramp is shallow, the block will stop when it reaches the highest point of its motion. What is the smallest ramp angle, measured from the horizontal, for which the block will slide back down after reaching its highest point?

Problem 68GP The fastest recorded skydive was by an Air Force officer who jumped from a helium balloon at an elevation of 103,000 ft, three times higher than airliners fly. Because the density of air is so low at these altitudes, he reached a speed of 614 mph at an elevation of 90,000 ft, then gradually slowed as the air became more dense. Assume that he fell in the spread-eagle position of Example 5.15 and that his low-altitude terminal speed is 125 mph. Use this information to determine the density of air at 90,000 ft.

Problem 69GP A 2.7 g Ping-Pong ball has a diameter of 4.0 cm. a. The ball is shot straight up at twice its terminal speed. What is its initial acceleration? b. The ball is shot straight down at twice its terminal speed. What is its initial acceleration?

Problem 70GP Two blocks are connected by a string as in Figure P5.74. What is the upper block’s acceleration if the coefficient of kinetic friction between the block and the table is 0.20?

Problem 71GP The 10 kg block in Figure 71 slides down a frictionless ramp. What is its acceleration? FIGURE 71

Problem 72GP A 2.0 kg wood block is pulled along a wood floor at a steady speed. A second wood block, with mass 3.0 kg, is attached to the first by a horizontal string. What is the magnitude of the force pulling on the first block?

Problem 73GP A magician pulls a tablecloth out from under some dishes. How far do the dishes move during the 0.25 s it takes to pull out the tablecloth? The coefficient of kinetic friction between the cloth and the dishes is ?k = 0.12.

Problem 74GP The 100 kg block in Figure P5.76 takes 6.0 s to reach the floor after being released from rest. What is the mass of the block on the left?

Problem 75GP Problems show free-body diagrams. For each, a. Write a realistic dynamics problem for which this is the correct free-body diagram. Your problem should ask a question that can be answered with a value of position or velocity (such as “How far?” or “How fast? ”), and should give sufficient information to allow a solution. b. Solve your problem! FIGURE 75

Problem 76GP Problems show free-body diagrams. For each, a. Write a realistic dynamics problem for which this is the correct free-body diagram. Your problem should ask a question that can be answered with a value of position or velocity (such as “How far?” or “How fast? ”), and should give sufficient information to allow a solution. b. Solve your problem! FIGURE 76

Problem 77GP In Problems you are given the dynamics equations that are used to solve a problem. For each of these, you are to a. Write a realistic problem for which these are the correct equations. b. Draw the free-body diagram and the pictorial representation for your problem. c. Finish the solution of the problem. ?0.80n = (1500 kg)ax n ? (1500 kg)(9.8 m/s2) = 0

Problem 78GP In Problems you are given the dynamics equations that are used to solve a problem. For each of these, you are to a. Write a realistic problem for which these are the correct equations. b. Draw the free-body diagram and the pictorial representation for your problem. c. Finish the solution of the problem. In Problems you are given the dynamics equations that are used to solve a problem. For each of these, you are to a. Write a realistic problem for which these are the correct equations. b. Draw the free-body diagram and the pictorial representation for your problem. c. Finish the solution of the problem. T ? 0.2n ? (20kg)(9.8m/s2)sin20° = (20kg)(2.0m/s2) n ? (20 kg)(9.8 m/s2) cos20° = 0

Problem 79GP In Problems you are given the dynamics equations that are used to solve a problem. For each of these, you are to a. Write a realistic problem for which these are the correct equations. b. Draw the free-body diagram and the pictorial representation for your problem. c. Finish the solution of the problem. (100 N)cos30° ? fk = (20 kg)ax n + (100 N) sin30° ? (20 kg)(9.8 m/s2) = 0 fk = 0.20n

Problem 80PP Sliding on the Ice In the winter sport of curling, players give a 20 kg stone a push across a sheet of ice. The stone moves approximately 40 m before coming to rest. The final position of the stone, in principle, only depends on the initial speed at which it is launched and the force of friction between the ice and the stone, but team members can use brooms to sweep the ice in front of the stone to adjust its speed and trajectory a bit; they must do this without touching the stone. Judicious sweeping can lengthen the travel of the stone by 3 m. A curler pushes a stone to a speed of 3.0 m/s over a time of 2.0 s. Ignoring the force of friction, how much force must the curler apply to the stone to bring it up to speed? A. 3.0 N B. 15 N C. 30 N D. 150 N

Problem 81PP Sliding on the Ice In the winter sport of curling, players give a 20 kg stone a push across a sheet of ice. The stone moves approximately 40 m before coming to rest. The final position of the stone, in principle, only depends on the initial speed at which it is launched and the force of friction between the ice and the stone, but team members can use brooms to sweep the ice in front of the stone to adjust its speed and trajectory a bit; they must do this without touching the stone. Judicious sweeping can lengthen the travel of the stone by 3 m. The sweepers in a curling competition adjust the trajectory of the stone by A. Decreasing the coefficient of friction between the stone and the ice. B. Increasing the coefficient of friction between the stone and the ice. C. Changing friction from kinetic to static. D. Changing friction from static to kinetic.

Problem 82PP Sliding on the Ice In the winter sport of curling, players give a 20 kg stone a push across a sheet of ice. The stone moves approximately 40 m before coming to rest. The final position of the stone, in principle, only depends on the initial speed at which it is launched and the force of friction between the ice and the stone, but team members can use brooms to sweep the ice in front of the stone to adjust its speed and trajectory a bit; they must do this without touching the stone. Judicious sweeping can lengthen the travel of the stone by 3 m. Suppose the stone is launched with a speed of 3 m/s and travels 40 m before coming to rest. What is the approximate magnitude of the friction force on the stone? A. 0 N B. 2 N C. 20 N D. 200 N

Problem 83PP Sliding on the Ice In the winter sport of curling, players give a 20 kg stone a push across a sheet of ice. The stone moves approximately 40 m before coming to rest. The final position of the stone, in principle, only depends on the initial speed at which it is launched and the force of friction between the ice and the stone, but team members can use brooms to sweep the ice in front of the stone to adjust its speed and trajectory a bit; they must do this without touching the stone. Judicious sweeping can lengthen the travel of the stone by 3 m. Suppose the stone’s mass is increased to 40 kg, but it is launched at the same 3 m/s. Which one of the following is true? A. The stone would now travel a longer distance before coming to rest. B. The stone would now travel a shorter distance before coming to rest. C. The coefficient of friction would now be greater.