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physics
mechanics

Physics 5th edition James S. Walker - Solutions

Discuss the nature of the work done by the equipment shown in this photo. What types of forces are involved?
The work done by a conservative force is indicated in FIGURE 8-23 for a variety of different paths connecting the points A and B. What is the work done by this force(a) On path 1(b) On path 2?
A student lifts a 1.42-kg book from her desk to a bookshelf. If the gravitational potential energy of the book-Earth system increases by 9.08 J, how high is the bookshelf above the desk?
At the local ski slope, an 82.0-kg skier rides a gondola to the top of the mountain. If the lift has a length of 2950 m and makes an angle of 13.1° with the horizontal, what is the change in the gravitational potential energy of the skier-Earth system?
Experiments performed on the wing of a hawkmoth (Manduca sexta) show that it deflects by a distance of x = 4.8 mm when a force of magnitude F = 3.0 mN is applied at the tip, as indicated in FIGURE 8-28. Treating the wing as an ideal spring, find(a) The force constant of the wing and(b) The energy
A vertical spring stores 0.962 J in spring potential energy when a 3.5-kg mass is suspended from it.(a) By what multiplicative factor does the spring potential energy change if the mass attached to the spring is doubled?(b) Verify your answer to part (a) by calculating the spring potential energy
Pushing on the pump of a soap dispenser compresses a small spring. When the spring is compressed 0.50 cm, its potential energy is 0.0025 J. (a) What is the force constant of the spring? (b) What compression is required for the spring potential energy to equal 0.0084 J?
A peacock mantis shrimp smashes its prey with a hammer-like appendage by storing energy in a spring like section of exoskeleton on its appendage. The spring has a force constant of 5.9 × 104 N/m.(a) If the spring stores 0.0103 J of energy, over what distance must the shrimp compress it?(b) What
The work required to stretch a certain spring from an elongation of 4.00 cm to an elongation of 5.00 cm is 30.5 J.(a) Is the work required to increase the elongation of the spring from 5.00 cm to 6.00 cm greater than, less than, or equal to 30.5 J? Explain.(b) Verify your answer to part (a) by
A 0.33-kg pendulum bob is attached to a string 1.2 m long. What is the change in the gravitational potential energy of the system as the bob swings from point A to point B in FIGURE 8-29?
(a) You throw a ball upward and let it fall to the ground. Your friend drops an identical ball straight down to the ground from the same height. Is the change in kinetic energy of your ball greater than, less than, or equal to the change in kinetic energy of your friend's ball? (b) Choose the best
When a ball of mass m is dropped from rest from a height h, its kinetic energy just before landing is K. Now, suppose a second ball of mass 4m is dropped from rest from a height h/4. (a) Just before ball 2 lands, is its kinetic energy 4K, 2K, K, K/2, or K/4? (b) Choose the best explanation from
Calculate the work done by gravity as a 3.2-kg object is moved from point A to point B in FIGURE 8-24 along paths 1, 2, and 3.
For an object moving along the x axis, the potential energy of the frictionless system is shown in FIGURE 8-30. Suppose the object is released from rest at the point A. Rank the other points in the figure in increasing order of the object's speed. Indicate ties where appropriate.
At an amusement park, a swimmer uses a water slide to enter the main pool. If the swimmer starts at rest, slides without friction, and descends through a vertical height of 2.31 m, what is her speed at the bottom of the slide?
A player passes a 0.600-kg basketball downcourt for a fast break. The ball leaves the player's hands with a speed of 8.30 m/s and slows down to 7.10 m/s at its highest point.(a) Ignoring air resistance, how high above the release point is the ball when it is at its maximum height?(b) How would
A skateboarder at a skate park rides along the path shown in FIGURE 8-31. If the speed of the skateboarder at point A is v = 1.4 m/s, what is her speed at point B? Assume that friction is negligible.
Three balls are thrown upward with the same initial speed v0, but at different angles relative to the horizontal, as shown in FIGURE 8-32. Ignoring air resistance, indicate which of the following statements is correct: At the dashed level,(a) Ball 3 has the lowest speed;(b) Ball 1 has the lowest
A 0.21-kg apple falls from a tree to the ground, 4.0 m below. Ignoring air resistance, determine the apple's kinetic energy, K, the gravitational potential energy of the system, U, and the total mechanical energy of the system, E, when the apple's height above the ground is(a) 4.0 m,(b) 3.0 m,(c)
A 2.9-kg block slides with a speed of 2.1 m/s on a frictionless horizontal surface until it encounters a spring.(a) If the block compresses the spring 5.6 cm before coming to rest, what is the force constant of the spring?(b) What initial speed should the block have to compress the spring by 1.4 cm?
A 0.26-kg rock is thrown vertically upward from the top of a cliff that is 32 m high. When it hits the ground at the base of the cliff, the rock has a speed of 29 m/s. Assuming that air resistance can be ignored,(a) The initial speed of the rock(b) The greatest height of the rock as measured from
A 1.40-kg block slides with a speed of 0.950 m/s on a frictionless horizontal surface until it encounters a spring with a force constant of 734 N/m. The block comes to rest after compressing the spring 4.15 cm. Find the spring potential energy, U, the kinetic energy of the block, K, and the total
A 5.76-kg rock is dropped and allowed to fall freely. Find the initial kinetic energy, the final kinetic energy, and the change in kinetic energy for(a) The first 2.00 m of fall(b) The second 2.00 m of fall.
Calculate the work done by friction as a 3.7-kg box is slid along a floor from point A to point B in FIGURE 8-25 along paths 1, 2, and 3. Assume that the coefficient of kinetic friction between the box and the floor is 0.26.
Suppose the pendulum bob in Figure 8-29 has a mass of 0.33 kg and is moving to the right at point B with a speed of 2.4 m/s. Air resistance is negligible.(a) What is the change in the system's gravitational potential energy when the bob reaches point A?(b) What is the speed of the bob at point
The two masses in the Atwood's machine shown in FIGURE 8-33 are initially at rest at the same height. After they are released, the large mass, m2, falls through a height h and hits the floor, and the small mass, m1, rises through a height h.(a) Find the speed of the masses just before m2 lands,
In the previous problem, suppose the masses have an initial speed of 0.20 m/s, and that m2 is moving upward. How high does m2 rise above its initial position before momentarily coming to rest, given that m1 = 3.7 kg and m2 = 4.1 kg?
On reentry, the Space Shuttle's protective heat tiles became extremely hot. (a) Was the mechanical energy of the Shuttle-Earth system when the Shuttle landed greater than, less than, or the same as when it was in orbit? (b) Choose the best explanation from among the following: I. Dropping out of
Catching a wave, a 77-kg surfer starts with a speed of 1.3 m/s, drops through a height of 1.65 m, and ends with a speed of 8.2 m/s. How much nonconservative work was done on the surfer?
At a playground, a 19-kg child plays on a slide that drops through a height of 2.3 m. The child starts at rest at the top of the slide. On the way down, the slide does a nonconservative work of -361 J on the child. What is the child's speed at the bottom of the slide?
Starting at rest at the edge of a swimming pool, a 72.0-kg athlete swims along the surface of the water and reaches a speed of 1.20 m/s by doing the work Wnc1 = + 161 J. Find the nonconservative work, Wnc2, done by the water on the athlete.
A 22,000-kg airplane lands with a speed of 64 m/s on a stationary aircraft carrier deck that is 115 m long. Find the work done by nonconservative forces in stopping the plane.
A 78-kg skateboarder grinds down a hubba ledge that is 2.5 m long and inclined at 19° below the horizontal. Kinetic friction dissipates half of her initial potential energy to thermal and sound energies. What is the coefficient of kinetic friction between her skateboard and the ledge surface?
You ride your bicycle down a hill, maintaining a constant speed the entire time. (a) As you ride, does the gravitational potential energy of the you-bike-Earth system increase, decrease, or stay the same? Explain. (b) Does the kinetic energy of you and your bike increase, decrease, or stay the
A 2.8-kg block is attached to a spring with a force constant of 375 N/m, as shown in FIGURE 8-26.(a) Find the work done by the spring on the block as the block moves from A to B along paths 1 and 2.(b) How do your results depend on the mass of the block? Specifically, if you increase the mass, does
A 111-kg seal at an amusement park slides from rest down a ramp into the pool below. The top of the ramp is 1.75 m higher than the surface of the water, and the ramp is inclined at an angle of 26.5° above the horizontal. If the seal reaches the water with a speed of 4.25 m/s, what are(a) The work
A 1.9-kg rock is released from rest at the surface of a pond 1.8 m deep. As the rock falls, a constant upward force of 4.6 N is exerted on it by water resistance. Calculate the nonconservative work, Wnc, done by water resistance on the rock, the gravitational potential energy of the system, U, the
A 1250-kg car drives up a hill that is 16.2 m high. During the drive, two nonconservative forces do work on the car: (i) The force of friction, (ii) The force generated by the car's engine. The work done by friction is -3.11 × 105 J; the work done by the engine is + 6.44 × 105 J. Find the change
The Outlaw Run roller coaster in Branson, Missouri, features a track that is inclined at 81° below the horizontal and that spans a 49.4-m (162 ft) change in height.(a) If the coefficient of friction for the roller coaster is μk = 0.29, what is the magnitude of the friction force on a 1700-kg
A 1.80-kg block slides on a rough horizontal surface. The block hits a spring with a speed of 2.00 m/s and compresses it a distance of 11.0 cm before coming to rest. If the coefficient of kinetic friction between the block and the surface is μk = 0.560, what is the force constant of the spring?
FIGURE 8-34 shows a potential energy curve as a function of x. In qualitative terms, describe the subsequent motion of an object that starts at rest at point A.
An object moves along the x axis, subject to the potential energy shown in Figure 8-34. The object has a mass of 1.1 kg and starts at rest at point A.(a) What is the object's speed at point B?(b) At point C?(c) At point D?(d) What are the turning points for this object?
A 1.34-kg object moves along the x axis, subject to the potential energy shown in Figure 8-34. If the object's speed at point C is 1.25 m/s, what are the approximate locations of its turning points?
The potential energy of a particle moving along the x axis is shown in Figure 8-34. When the particle is at x = 1.0 m it has 3.6 J of kinetic energy. Give approximate answers to the following questions.(a) What is the total mechanical energy of the system?(b) What is the smallest value of x the
A block of mass m = 0.88 kg is connected to a spring of force constant k = 845 N / m on a smooth, horizontal surface.(a) Plot the potential energy of the spring from x = -5.00 cm to x = 5.00 cm.(b) Determine the turning points of the block if its speed at x = 0 is 1.4 m/s.
(a) Calculate the work done by gravity as a 5.2-kg object is moved from A to B in FIGURE 8-27 along paths 1 and 2.(b) How do your results depend on the mass of the block? Specifically, if you increase the mass, does the work done by gravity increase, decrease, or stay the same?
A ball of mass m = 0.75 kg is thrown straight upward with an initial speed of 8.9 m/s.(a) Plot the gravitational potential energy of the ball from its launch height, y = 0, to the height y = 5.0 m. Let U = 0 correspond to y = 0.(b) Determine the turning point (maximum height) of the ball.
FIGURE 8-35 depicts the potential energy of a 350-kg pallet that slides from rest down a frictionless roller conveyer ramp, then moves across a frictionless horizontal conveyer, and finally encounters a horizontal spring at x = 4.0 m. When the pallet encounters the spring, it momentarily comes to
Figure 8-35 depicts the potential energy of a 655-kg pallet that slides from rest down a frictionless roller conveyer ramp, then moves across a frictionless horizontal conveyer, and finally encounters a horizontal spring at x = 4.0 m.(a) What is the angle of inclination of the conveyer ramp?(b)
You and a friend both solve a problem involving a skier going down a slope. When comparing solutions, you notice that your choice for the y = 0 level is different than the y = 0 level chosen by your friend. Will your answers agree or disagree on the following quantities: (a) The skier's potential
A particle moves under the influence of a conservative force. At point A the particle has a kinetic energy of 12 J; at point B the particle is momentarily at rest, and the potential energy of the system is 25 J; at point C the potential energy of the system is 5 J. (a) What is the potential energy
A sled slides without friction down a small, ice-covered hill. On its first run down the hill, the sled starts from rest at the top of the hill and its speed at the bottom is 7.50 m/s. On a second run, the sled starts with a speed of 1.50 m/s at the top. What is the speed of the sled at the bottom
A 74-kg skier encounters a dip in the snow's surface that has a circular cross section with a radius of curvature of 12 m. If the skier's speed at point A in FIGURE 8-36 is 7.1 m/s, what is the normal force exerted by the snow on the skier at point B? Ignore frictional forces.
The soles of a popular make of running shoe have a force constant of 2.0 × 105 N / m. Treat the soles as ideal springs for the following questions. (a) If a 62-kg person stands in a pair of these shoes, with her weight distributed equally on both feet, how much does she compress the soles? (b) How
The force required to flex a nasal strip and apply it to the nose is 0.25 N; the energy stored in the strip when flexed is 0.0022 J. Assume the strip to be an ideal spring for the following calculations. Find(a) The distance through which the strip is flexed(b) The force constant of the strip.
The water slide shown in FIGURE 8-37 ends at a height of 1.50 m above the pool. If the person starts from rest at point A and lands in the water at point B, what is the height h of the water slide? (Assume the water slide is frictionless.)
In the system shown in Figure 8-26, suppose the block has a mass of 2.7 kg, the spring has a force constant of 480 N/m, and the coefficient of kinetic friction between the block and the floor is 0.16.(a) Find the work done on the block by the spring and by friction as the block is moved from point
A skateboarder starts at point A in FIGURE 8-38 and rises to a height of 2.64 m above the top of the ramp at point B. What was the skateboarder's initial speed at point A?
NASA's Skylab, the largest spacecraft ever to fall back to the Earth, reentered the Earth's atmosphere on July 11, 1979, and broke into a myriad of pieces. One of the largest fragments was a 1770-kg, lead-lined film vault, which landed with an estimated speed of 120 m/s. If its speed at an altitude
Several studies indicate that the elastic properties of tendons can change in response to exercise. In one study, guinea fowl were divided into a group that ran for 30 minutes a day on a treadmill, and a control group that was kept in their cages. After 12 weeks, the researchers measured the
In the Atwood's machine of Problem 31, the mass m2 remains at rest once it hits the floor, but the mass m1 continues moving upward. How much higher does m1 go after m2 has landed? Give your answer for the case h = 1.2 m, m1 = 3.7 kg, and m2 = 4.1 kg.
A 6.60-kg block slides with an initial speed of 2.24 m/s up a ramp inclined at an angle of 18.4° with the horizontal. The coefficient of kinetic friction between the block and the ramp is 0.44. Use energy conservation to find the distance the block slides before coming to rest.
Jeff of the Jungle swings on a 7.6-m vine that initially makes an angle of 37° with the vertical. If Jeff starts at rest and has a mass of 78 kg, what is the tension in the vine at the lowest point of the swing?
A 1.9-kg block slides down a frictionless ramp, as shown in FIGURE 8-40. The top of the ramp is 1.5 m above the ground; the bottom of the ramp is 0.25 m above the ground. The block leaves the ramp moving horizontally, and lands a horizontal distance d away. Find the distance d.
Suppose the ramp in Figure 8-40 is not frictionless. Find the distance d for the case in which friction on the ramp does - 9.7 J of work on the block before it becomes airborne.
A running track at Harvard University uses a surface with a force constant of 2.5 × 105 N / m. This surface is compressed slightly every time a runner's foot lands on it. The force exerted by the foot, according to the Saucony shoe company, has a magnitude of 2700 N for a typical runner. Treating
The resilin in the body of a flea has a force constant of about 24 N/m, and when the flea cocks its jumping legs, the resilin associated with each leg is compressed by approximately 0.12 mm. Given that the flea has a mass of 0.56 mg, and that two legs are used in a jump, estimate the maximum height
(a) Ball 1 is thrown to the ground with an initial downward speed; ball 2 is dropped to the ground from rest. Assuming the balls have the same mass and are released from the same height, is the change in gravitational potential energy of ball 1 greater than, less than, or equal to the change in
A ball of mass m is attached to a string of length L and released from rest at the point A in FIGURE 8-41.(a) Show that the tension in the string when the ball reaches point B is 3mg, independent of the length l.(b) Give a detailed physical explanation for the fact that the tension at point B is
An ice cube is placed on top of an overturned spherical bowl of radius r, as indicated in FIGURE 8-42. If the ice cube slides downward from rest at the top of the bowl, at what angle Î¸ does it separate from the bowl? In other words, at what angle does the normal force between the ice cube and
The two blocks shown in FIGURE 8-43 are moving with an initial speed v.(a) If the system is frictionless, find the distance d the blocks travel before coming to rest. (Let U = 0 correspond to the initial position of block 2.)(b) Is the work done on block 2 by the rope positive, negative, or zero?
(a) A block of mass m slides from rest on a frictionless loop-the-loop track, as shown in FIGURE 8-44. What is the minimum release height, h, required for the block to maintain contact with the track at all times? Give your answer in terms of the radius of the loop, r.(b) Explain why the release
FIGURE 8-45 shows a 1.75-kg block at rest on a ramp of height h. When the block is released, it slides without friction to the bottom of the ramp, and then continues across a surface that is frictionless except for a rough patch of width 10.0 cm that has a coefficient of kinetic friction Î¼k =
In FIGURE 8-46 a 1.2-kg block is held at rest against a spring with a force constant k = 730 N/m. Initially, the spring is compressed a distance d. When the block is released, it slides across a surface that is frictionless except for a rough patch of width 5.0 cm that has a coefficient of kinetic
Treating the model wing as an ideal spring, what is the force constant of the hind wing when a force is applied to its tip?A. 94 N/mB. 130 N/mC. 290 N/mD. 330 N/m
What is the force constant of the hind wing when a force is applied at two-thirds the distance from the base of the wing to the tip?A. 94 N/mB. 130 N/mC. 290 N/mD. 330 N/m
Which of the wings is "stiffer"?A. The hindwingB. The forewingC. Depends on where the force is appliedD. They are equally "stiff"
How much energy is stored in the forewing when a force at the tip deflects it by 3.5 mm?A. 0.766 mJB. 49.0 mJC. 0.219 JD. 1.70 kJ
A mass is attached to the bottom of a vertical spring. This causes the spring to stretch and the mass to move downward.(a) Does the potential energy of the spring increase, decrease, or stay the same during this process? Explain.(b) Does the gravitational potential energy of the Earth-mass system
Consider a spring with a force constant of 955 N/m.(a) Suppose the mass of the block is 1.70 kg, but its initial speed can be varied. What initial speed is required to give a maximum spring compression of 4.00 cm?(b) Suppose the initial speed of the block is 1.09 m/s, but its mass can be varied.
Suppose the block is released from rest with the spring compressed 5.00 cm. The mass of the block is 1.70 kg and the force constant of the spring is 955 N/m.(a) What is the speed of the block when the spring expands to a compression of only 2.50 cm?(b) What is the speed of the block after it leaves
Suppose we would like the landing speed of block 2 to be increased to 1.50 m/s.(a) Should the coefficient of kinetic friction between block 1 and the tabletop be increased or decreased?(b) Find the required coefficient of kinetic friction for a landing speed of 1.50 m/s. Note that m1 = 2.40 kg, m2
Find the gravitational potential energy of an 88-kg person standing atop Mt. Everest at an altitude of 8848 m. Use sea level as the location for y = 0.
An hourglass is turned over, and the sand is allowed to pour from the upper half of the glass to the lower half. If the hourglass is resting on a scale, and the total mass of the hourglass and sand is M, describe the reading on the scale as the sand runs to the bottom.
A tall, slender drinking glass with a thin base is initially empty. (a) Where is the center of mass of the glass? (b) Suppose the glass is now filled slowly with water until it is completely full. Describe the position and motion of the center of mass during the filling process.
In the "Fosbury flop" method of high jumping, named for the track and field star Dick Fosbury, an athlete's center of mass may pass under the bar while the athlete's body passes over the bar. Explain how this is possible.
A system of particles is known to have zero momentum. Does it follow that the kinetic energy of the system is also zero? Explain.
Crash statistics show that it is safer to be riding in a heavy car in an accident than in a light car. Explain in terms of physical principles.
An object at rest on a frictionless surface is struck by a second object. Is it possible for both objects to be at rest after the collision? Explain.
What is the mass of a mallard duck whose speed is 8.9 m/s and whose momentum has a magnitude of 11 kg ∙ m/s?
A net force of 200 N acts on a 100-kg boulder, and a force of the same magnitude acts on a 100-g pebble. (a) Is the change of the boulder's momentum in one second greater than, less than, or equal to the change of the pebble's momentum in the same time period? (b) Choose the best explanation from
Referring to the previous question, (a) Is the change in the boulder's speed in one second greater than, less than, or equal to the change in speed of the pebble in the same time period? (b) Choose the best explanation from among the following: I. The large mass of the boulder results in a small
Two identical cars, each traveling at 16 m/s, slam into a concrete wall and come to rest. In car A the air bag does not deploy and the driver hits the steering wheel; in car B the driver contacts the deployed air bag. (a) Is the impulse delivered by the steering wheel to driver A greater than, less
Force A has a magnitude F and acts for the time Δt, force B has a magnitude 2F and acts for the time Δt/3, force C has a magnitude 5F and acts for the time Δt/10, and force D has a magnitude 10F and acts for the time Δt/100. Rank these forces in order of increasing impulse. Indicate ties where
Find the magnitude of the impulse delivered to a soccer ball when a player kicks it with a force of 1250 N. Assume that the player's foot is in contact with the ball for 5.95 × 10-3 s.
A 0.45-kg croquet ball is initially at rest on the grass. When the ball is struck by a mallet, the average force exerted on it is 270 N. If the ball's speed after being struck is 5.4 m/s, for what amount of time was the mallet in contact with the ball?
When spiking a volleyball, a player changes the velocity of the ball from 4.2 m/s to -24 m/s along a certain direction. If the impulse delivered to the ball by the player is -9.3 kg ∙ m/s, what is the mass of the volleyball?
A force platform measures the horizontal force exerted on a person's foot by the ground. In FIGURE 9-26 we see force-versus-time data taken by a force platform for a person who starts jogging at time t = 0. The impulse imparted to the jogger from t = 0 to t = 0.6 s is 198 N âˆ™ s.(a) What is
If a driver makes contact with a steering wheel during a 35-mph crash, she comes to rest in about Δt = 15 ms. If, during an identical crash, the driver makes contact with an air bag, she comes to rest in about Δ t = 110 ms. What is the ratio Fsw/Fab of the force exerted by the steering wheel to
To make a bounce pass, a player throws a 0.60-kg basketball toward the floor. The ball hits the floor with a speed of 5.4 m/s at an angle of 65° to the vertical. If the ball rebounds with the same speed and angle, what was the impulse delivered to it by the floor?

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