Serious fractures of the leg often need a stretching force

What is an interaction?

What is an interaction diagram?

How do we model ropes and pulleys?

What is Newtons third law?

How is Newtons third law used?

Why is Newtons third law important?

shows a person pushing a large crate across a rough surface. Identify all interactions, show them on an interaction diagram, then draw free-body diagrams of the person and the crate.

A rope of negligible mass pulls a crate across the floor. The rope and crate are the system; the hand pulling the rope is part of the environment. What, if anything, is wrong with the freebody diagrams?

A tow truck uses a rope to pull a car along a horizontal road, as shown in FIGURE 7.8. Identify all interactions, show them on an interaction diagram, then draw free-body diagrams of each object in the system.

A small car is pushing a larger truck that has a dead battery. The mass of the truck is larger than the mass of the car. Which of the following statements is true? a. The car exerts a force on the truck, but the truck doesnt exert a force on the car. b. The car exerts a larger force on the truck than the truck exerts on the car. c. The car exerts the same amount of force on the truck as the truck exerts on the car. d. The truck exerts a larger force on the car than the car exerts on the truck. e. The truck exerts a force on the car, but the car doesnt exert a force on the truck

The hand shown in FIGURE 7.12 pushes boxes A and B to the right across a frictionless table. The mass of B is larger than the mass of A. a. Draw free-body diagrams of A, B, and the hand H, showing only the horizontal forces. Connect action/reaction pairs with dashed lines. b. Rank in order, from largest to smallest, the horizontal forces shown on your free-body diagrams

Boxes A and B are sliding to the right across a frictionless table. The hand H is slowing them down. The mass of A is larger than the mass of B. Rank in order, from largest to smallest, the horizontal forces on A, B, and H. a. FB on H = FH on B = FA on B = FB on A b. FB on H = FH on B 7 FA on B = FB on A c. FB on H = FH on B 6 FA on B = FB on A d. FH on B = FH on A 7 FA on B

You and a friend have just loaded a 200 kg crate filled with priceless art objects into the back of a 2000 kg truck. As you press down on the accelerator, force F u surface on truck propels the truck forward. To keep things simple, call this just F u T. What is the maximum magnitude F u T can have without the crate sliding? The static and kinetic coefficients of friction between the crate and the bed of the truck are 0.80 and 0.30. Rolling friction of the truck is negligible

All three 50 kg blocks are at rest. Is the tension in rope 2 greater than, less than, or equal to the tension in rope 1?

shows a student pulling horizontally with a 100 N force on a rope that is attached to a wall. In FIGURE 7.18b, two students in a tug-of-war pull on opposite ends of a rope with 100 N each. Is the tension in the second rope larger than, smaller than, or the same as that in the first rope?

Blocks A and B in FIGURE 7.22 are connected by massless string 2 and pulled across a frictionless table by massless string 1. B has a larger mass than A. Is the tension in string 2 larger than, smaller than, or equal to the tension in string 1?

Serious fractures of the leg often need a stretching force to keep contracting leg muscles from forcing the broken bones together too hard. This is done using traction, an arrangement of a rope, a weight, and pulleys as shown in FIGURE 7.25. The rope must make the same angle on both sides of the pulley so that the net force on the leg is horizontal, but the angle can be adjusted to control the amount of traction. The doctor has specified 50 N of traction for this patient with a 4.2 kg hanging mass. What is the proper angle?

A 200 kg set used in a play is stored in the loft above the stage. The rope holding the set passes up and over a pulley, then is tied backstage. The director tells a 100 kg stagehand to lower the set. When he unties the rope, the set falls and the unfortunate man is hoisted into the loft. What is the stagehands acceleration?

Bank robbers have pushed a 1000 kg safe to a second-story floor-toceiling window. They plan to break the window, then lower the safe 3.0 m to their truck. Not being too clever, they stack up 500 kg of furniture, tie a rope between the safe and the furniture, and place the rope over a pulley. Then they push the safe out the window. What is the safes speed when it hits the truck? The coefficient of kinetic friction between the furniture and the floor is 0.50.

You find yourself in the middle of a frozen lake with a surface so slippery 1ms = mk = 02 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 feet do. Can you think of a way to get to shore? Use pictures, forces, and Newtons laws to explain your reasoning.

How does a sprinter sprint? What is the forward force on a sprinter as she accelerates? Where does that force come from? Your explanation should include an interaction diagram and a free-body diagram.

How does a rocket take off? What is the upward force on it? Your explanation should include an interaction diagram and free-body diagrams of the rocket and of the parcel of gas being exhausted

How do basketball players jump straight up into the air? Your explanation should include an interaction diagram and a free-body diagram.

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

A mosquito collides head-on with a car traveling 60 mph. Is the magnitude of the mosquitos acceleration larger than, smaller than, or equal to the magnitude of the cars acceleration? Explain

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?

A very smart 3-year-old child is given a wagon for her birthday. She refuses to use it. After all, she says, Newtons 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?

Teams red and blue are having a tug-of-war. According to Newtons 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.

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

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?

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

The hand in FIGURE Q7.13 is pushing on the back of block A. Blocks A and B, with mB 7 mA, 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.

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.

In case a in FIGURE Q7.15, block A is accelerated across a frictionless table by a hanging 10 N weight (1.02 kg). In case b, block A is accelerated across a frictionless table by a steady 10 N tension in the string. The string is massless, and the pulley is massless and frictionless. Is As acceleration in case b greater than, less than, or equal to its acceleration in case a? Explain

For Exercises 1 through 5: a. Draw an interaction diagram. 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 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.

For Exercises 1 through 5: a. Draw an interaction diagram. 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 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

For Exercises 1 through 5: a. Draw an interaction diagram. 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 members of an action/reaction pair.A steel cable with mass is lifting a girder. The girder is speeding up.

For Exercises 1 through 5: a. Draw an interaction diagram. 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 members of an action/reaction pair.Block A in FIGURE EX7.4 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 youll have to decide if theyre part of the system.

For Exercises 1 through 5: a. Draw an interaction diagram. 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 members of an action/reaction pair.Block A in FIGURE EX7.5 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 youll have to decide if theyre part of the system.

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 10 m/s2 ?

Block B in FIGURE EX7.7 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 remains in equilibrium?

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 against the ground with a force of 4500 N. Rolling friction can be neglected. 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?

Blocks with masses of 1 kg, 2 kg, and 3 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 kg block. a. How much force does the 2 kg block exert on the 3 kg block? b. How much force does the 2 kg block exert on the 1 kg block?

A 3000 kg meteorite falls toward the earth. What is the magnitude of the earths acceleration just before impact? The earths mass is

The foot of a 55 kg sprinter is on the ground for 0.25 s while her body accelerates from rest to 2.0 m/s. a. Is the friction between her foot and the ground static friction or kinetic friction? b. What is the magnitude of the friction force?

A steel cable lying flat on the floor drags a 20 kg block across a horizontal, frictionless floor. 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?

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?

The sled dog in FIGURE EX7.14 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?

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?

FIGURE EX7.16 shows two 1.0 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 3.0 m/s2 by force F u . 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?

What is the tension in the rope of FIGURE EX7.17?

A 2.0-m-long, 500 g rope pulls a 10 kg block of ice across a horizontal, frictionless surface. The block accelerates at 2.0 m/s2 . How much force pulls forward on (a) the ice, (b) the rope? Assume that the rope is perfectly horizontal

A woman living in a third-story apartment is moving out. Rather than carrying everything down the stairs, she decides to pack her belongings into crates, attach a frictionless pulley to her balcony railing, and lower the crates by rope. How hard must she pull on the horizontal end of the rope to lower a 25 kg crate at steady speed?

Two blocks are attached to opposite ends of a massless rope that goes over a massless, frictionless, stationary pulley. One of the blocks, with a mass of 6.0 kg, accelerates downward at 3 4 g. What is the mass of the other block?

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 EX7.21. A 2000 kg block is attached to the tensioning pulleys cart, via a rope and pulley, and is suspended in a deep hole. What is the tension in the cable cars cable?

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

A mobile at the art museum has a 2.0 kg steel cat and a 4.0 kg steel dog suspended from a lightweight cable, as shown in FIGURE EX7.23. It is found that u1 = 20 when the center rope is adjusted to be perfectly horizontal. What are the tension and the angle of rope 3?

The 1.0 kg block in FIGURE EX7.24 is tied to the wall with a rope. It sits on top of the 2.0 kg block. The lower block is pulled to the right with a tension force of 20 N. The coefficient of kinetic friction at both the lower and upper surfaces of the 2.0 kg block is mk = 0.40. a. What is the tension in the rope attached to the wall? b. What is the acceleration of the 2.0 kg block?

The 100 kg block in FIGURE EX7.25 takes 6.0 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.

FIGURE P7.26 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. The lower magnet is being pulled upward against the bottom of the table. Suppose that each magnets weight is 2.0 N and that the magnetic force of the lower magnet on the upper magnet is 6.0 N. How hard does the lower magnet push against the table?

FIGURE P7.27 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? The spring is firmly attached to the gliders, and it does not sag.

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

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?

A Federation starship 12.0 * 106 kg2 uses its tractor beam to pull a shuttlecraft 12.0 * 104 kg2 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?

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?

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?

Two packages at UPS start sliding down the 20 ramp shown in FIGURE P7.33. 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?

The two blocks in FIGURE P7.34 are sliding down the incline. What is the tension in the massless string?

The coefficient of static friction is 0.60 between the two blocks in FIGURE P7.35. The coefficient of kinetic friction between the lower block and the floor is 0.20. Force F u 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?

The block of mass M in FIGURE P7.36 slides on a frictionless surface. Find an expression for the tension in the string

The 10.2 kg block in FIGURE P7.37 is held in place by a force applied to a rope passing over two massless, frictionless pulleys. Find the tensions T1 to T5 and the magnitude of force F u .

The coefficient of kinetic friction between the 2.0 kg block in FIGURE P7.38 and the table is 0.30. What is the acceleration of the 2.0 kg block?

FIGURE P7.39 shows a block of mass m resting on a 20 slope. The block has coefficients of friction ms = 0.80 and mk = 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?

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 P7.39. 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?

The 1.0 kg physics book in FIGURE P7.41 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 ms = 0.50 and mk = 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?

The 2000 kg cable car shown in FIGURE P7.42 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 cars speed at the bottom of the hill?

The century-old ascensores in Valparaiso, Chile, are picturesque cable cars built on stilts to keep the passenger compartments level as they go up and down the steep hillsides. As FIGURE P7.43 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?

A 3200 kg helicopter is flying horizontally. A 250 kg crate is suspended from the helicopter by a massless cable that is constantly 20 from vertical. What propulsion force F u prop is being provided by the helicopters rotor? Air resistance can be ignored. Give your answer in component form in a coordinate system where ni points in the direction of motion and nj points upward.

A house painter uses the chair-andpulley arrangement of FIGURE P7.45 to lift himself up the side of a house. The painters mass is 70 kg and the chairs mass is 10 kg. With what force must he pull down on the rope in order to accelerate upward at 0.20 m/s2 ?

A long, 1.0 kg rope hangs from a support that breaks, causing the rope to fall, if the pull exceeds 40 N. A student team has built a 2.0 kg robot mouse that runs up and down the rope. What maximum acceleration can the robot haveboth magnitude and directionwithout the rope falling?

A 50-cm-diameter, 400 g beach ball is dropped with a 4.0 mg ant riding on the top. The ball experiences air resistance, but the ant does not. What is the magnitude of the normal force exerted on the ant when the balls speed is 2.0 m/s?

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 m1 does not slip either up or down along the wedge. All surfaces are frictionless.

A rocket burns fuel at a rate of 5.0 kg/s, expelling the exhaust gases at a speed of 4.0 km/s relative to the rocket. We would like to find the thrust of the rocket engine. a. Model the fuel burning as a steady ejection of small pellets, each with the small mass m. Suppose it takes a short time t to accelerate a pellet (at constant acceleration) to the exhaust speed vex. Further, suppose the rocket is clamped down so that it cant recoil. Find an expression for the magnitude of the force that one pellet exerts on the rocket during the short time while the pellet is being expelled. b. If the rocket is moving, vex is no longer the pellets speed through space but it is still the pellets speed relative to the rocket. By considering the limiting case of m and t approaching zero, in which case the rocket is now burning fuel continuously, calculate the rocket thrust for the values given above.

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.

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.

The lower block in FIGURE CP7.53 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. What is the acceleration of the 2.0 kg block

In FIGURE CP7.54, find an expression for the acceleration of m1. The pulleys are massless and frictionless. Hint: Think carefully about the acceleration constraint.

What is the acceleration of the 3.0 kg block in FIGURE CP7.55 across the frictionless table? Hint: Think carefully about the acceleration constraint.

A 40-cm-diameter, 50-cm-tall, 15 kg hollow cylinder is placed on top of a 40-cm-diameter, 30-cm-tall, 100 kg cylinder of solid aluminum, then the two are sent sliding across frictionless ice. The static and kinetic coefficients of friction between the cylinders are 0.45 and 0.25, respectively. Air resistance cannot be neglected. What is the maximum speed the cylinders can have without the top cylinder sliding off?

FIGURE CP7.57 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 ms = mk = 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?

FIGURE CP7.58 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 a1y, a2y, and a3y. Hint: yA isnt 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: m1 = 2.5 kg, m2 = 1.5 kg, and m3 = 4.0 kg. Find the acceleration of each. d. The 4.0 kg mass would appear to be in equilibrium. Explain why it accelerates.