Solved: A pendulum consists of a small object hanging from

Find the work done by a 45.0-N force in pulling the suitcase in Figure 6.2a at an angle 50.0 for a distance s 75.0 m. R

The weight lifter in Figure 6.3a is bench-pressing a barbell whose weight is 710 N. In part b of the figure, he raises the barbell a distance of 0.65 m above his chest, and in part c he lowers it the same distance. The weight is raised and lowered at a constant velocity. Determine the work done on the barbell by the weight lifter during (a) the lifting phase and (b) the lowering phase.

Figure 6.4a shows a 120-kg crate on the flatbed of a truck that is moving with an acceleration of a 1.5 m/s2 along the positive x axis. The crate does not slip with respect to the truck as the truck undergoes a displacement whose magnitude is s 65 m. What is the total work done on the crate by all of the forces acting on it? R

Two forces 1 and 2 are acting on the box shown in the drawing, causing the box to move across the floor. The two force vectors are drawn to scale. Which one of the following statements is correct? (a) 2 does more work than 1 does. (b) 1 does more work than 2 does. (c) Both forces do the same amount of work. (d) Neither force does any work.

A box is being moved with a velocity by a force (in the same direction as ) along a level horizontal floor. The normal force is N, the kinetic frictional force is k, and the weight is . Which one of the following statements is correct? (a) does positive work, N and k do zero work, and does negative work. (b) N does positive work, and k do zero work, and does negative work. (c) k does positive work, N and do zero work, and does negative work. (d) does positive work, N and do zero work, and k does negative work.

A force does positive work on a particle that has a displacement pointing in the x direction. This same force does negative work on a particle that has a displacement pointing in the y direction. In which quadrant of the x, y coordinate system does the force lie? (a) First (b) Second (c) Third (d) Fourth

A suitcase is hanging straight down from your hand as you ride an escalator. Your hand exerts a force on the suitcase, and this force does work. This work is (a) positive when you ride up and negative when you ride down, (b) negative when you ride up and positive when you ride down, (c) positive when you ride up or down, (d) negative when you ride up or down.

The space probe Deep Space 1 was launched October 24, 1998, and it used a type of engine called an ion propulsion drive. An ion propulsion drive generates only a weak force (or thrust), but can do so for long periods of time using only small amounts of fuel. Suppose the probe, which has a mass of 474 kg, is traveling at an initial speed of 275 m/s. No forces act on it except the 5.60 102 -N thrust of its engine. This external force is directed parallel to the displacement , which has a magnitude of 2.42 109 m (see Figure 6.6). Determine the final speed of the probe, assuming that its mass remains nearly constant.

A 58-kg skier is coasting down a 25 slope, as Figure 6.7a shows. Near the top of the slope, her speed is 3.6 m/s. She accelerates down the slope because of the gravitational force, even though a kinetic frictional force of magnitude 71 N opposes her motion. Ignoring air resistance, determine the speed at a point that is displaced 57 m downhill.

Figure 6.9 illustrates a satellite moving about the earth in a circular orbit and in an elliptical orbit. The only external force that acts on the satellite is the gravitational force. In which orbit does the kinetic energy of the satellite change, (a) the circular orbit or (b) the elliptical orbit?

A sailboat is moving at a constant velocity. Is work being done by a net external force acting on the boat?

A ball has a speed of 15 m/s. Only one external force acts on the ball. After this force acts, the speed of the ball is 7 m/s. Has the force done (a) positive, (b) zero, or (c) negative work on the ball?

A rocket is at rest on the launch pad. When the rocket is launched, its kinetic energy increases. Consider all of the forces acting on the rocket during the launch, and decide whether the following statement is true or false: The amount by which the kinetic energy of the rocket increases during the launch is equal to the work done by the force generated by the rockets engine

A net external force acts on a particle that is moving along a straight line. This net force is not zero. Which one of the following statements is correct? (a) The velocity, but not the kinetic energy, of the particle is changing. (b) The kinetic energy, but not the velocity, of the particle is changing. (c) Both the velocity and the kinetic energy of the particle are changing

A gymnast springs vertically upward from a trampoline as in Figure 6.12a. The gymnast leaves the trampoline at a height of 1.20 m and reaches a maximum height of 4.80 m before falling back down. All heights are measured with respect to the ground. Ignoring air resistance, determine the initial speed v0 with which the gymnast leaves the trampoline.

In a simulation on earth, an astronaut in his space suit climbs up a vertical ladder. On the moon, the same astronaut makes the exact same climb. Which one of the following statements correctly describes how the gravitational potential energy of the astronaut changes during the climb? (a) It changes by a greater amount on the earth. (b) It changes by a greater amount on the moon. (c) The change is the same in both cases.

A motorcyclist is trying to leap across the canyon shown in Figure 6.16 by driving horizontally off the cliff at a speed of 38.0 m/s. Ignoring air resistance, find the speed with which the cycle strikes the ground on the other side.

A rope is tied to a tree limb. It is used by a swimmer who, starting from rest, swings down toward the water below, as in Figure 6.17. Only two forces act on him during his descent, the nonconservative force , which is due to the tension in the rope, and his weight, which is due to the conservative gravitational force. There is no air resistance. His initial height h0 and final height hf are known. Can we use the principle of conservation of mechanical energy to find his speed vf at the point where he lets go of the rope, even though a nonconservative external force is present? (a) Yes. (b) No.

The Kingda Ka is a giant among roller coasters (see Figure 6.18). Located in Jackson Township, New Jersey, the ride includes a vertical drop of 127 m. Suppose that the coaster has a speed of 6.0 m/s at the top of the drop. Neglect friction and air resistance and find the speed of the riders at the bottom.

Identify the external conservative and nonconservative forces that act on the object. For this principle to apply, the total work done by nonconservative forces must be zero, Wnc 0 J. A nonconservative force that is perpendicular to the displacement of the object does no work, for example.

Choose the location where the gravitational potential energy is taken to be zero. This location is arbitrary but must not be changed during the course of solving a problem.

Set the final total mechanical energy of the object equal to the initial total mechanical energy, as in Equations 6.9a and 6.9b. The total mechanical energy is the sum of the kinetic and potential energies.

Suppose the total mechanical energy of an object is conserved. Which one or more of the following statements is/are true? (a) If the kinetic energy decreases, the gravitational potential energy increases. (b) If the gravitational potential energy decreases, the kinetic energy increases. (c) If the kinetic energy does not change, the gravitational potential energy also does not change.

In Example 10 the Kingda Ka roller coaster starts with a speed of 6.0 m/s at the top of the drop and attains a speed of 50.3 m/s when it reaches the bottom. If the roller coaster were then to start up an identical hill, what speed would it attain when it reached the top? Assume that friction and air resistance are absent. (a) Greater than 6.0 m/s (b) Exactly 6.0 m/s (c) Between 0 m/s and 6.0 m/s (d) 0 m/s

The drawing shows an empty fuel tank about to be released by three different jet planes. At the moment of release, each plane has the same speed, and each tank is at the same height above the ground. However, the directions of the velocities of the planes are different. Which tank has the largest speed upon hitting the ground? Ignore friction and air resistance. (a) A (b) B (c) C (d) Each tank hits the ground with the same speed.

In which one or more of the following situations is the principle of conservation of mechanical energy obeyed? (a) An object moves uphill with an increasing speed. (b) An object moves uphill with a decreasing speed. (c) An object moves uphill with a constant speed. (d) An object moves downhill with an increasing speed. (e) An object moves downhill with a decreasing speed. (f) An object moves downhill with a constant speed.

In Example 10, we ignored nonconservative forces, such as friction. In reality, however, such forces are present when the roller coaster descends. The actual speed of the riders at the bottom is 45.0 m/s, which is less than that determined in Example 10. Assuming again that the coaster has a speed of 6.0 m/s at the top, find the work done by nonconservative forces on a 55.0-kg rider during the descent from a height h0 to a height hf, where h0  hf 127 m.

A 0.20-kg rocket in a fireworks display is launched from rest and follows an erratic flight path to reach the point P, as Figure 6.19 shows. Point P is 29 m above the starting point. In the process, 425 J of work is done on the rocket by the nonconservative force generated by the burning propellant. Ignoring air resistance and the mass lost due to the burning propellant, find the speed vf of the rocket at the point P.

A net external nonconservative force does positive work on a particle. Based solely on this information, you are justified in reaching only one of the following conclusions. Which one is it? (a) The kinetic and potential energies of the particle both decrease. (b) The kinetic and potential energies of the particle both increase. (c) Neither the kinetic nor the potential energy of the particle changes. (d) The total mechanical energy of the particle decreases. (e) The total mechanical energy of the particle increases.

In one case, a sports car, its engine running, is driven up a hill at a constant speed. In another case, a truck approaches a hill, and its driver turns off the engine at the bottom of the hill. The truck then coasts up the hill. Which vehicle is obeying the principle of conservation of mechanical energy? Ignore friction and air resistance. (a) Both the sports car and the truck (b) Only the sports car (c) Only the truck

A car, starting from rest, accelerates in the x direction (see Figure 6.20). It has a mass of 1.10  103 kg and maintains an acceleration of 4.60 m/s2 for 5.00 s. Assume that a single horizontal force (not shown) accelerates the vehicle. Determine the average power generated by this force.

Engine A has a greater power rating than engine B. Which one of the following statements correctly describes the abilities of these engines to do work? (a) Engines A and B can do the same amount of work, but engine A can do it more quickly. (b) Engines A and B can do the same amount of work in the same amount of time. (c) In the same amount of time, engine B can do more work than engine A.

Is it correct to conclude that one engine is doing twice the work that another is doing just because it is generating twice the power? (a) Yes (b) No

Find the work that the archer must do in drawing back the string of the compound bow in Figure 6.21a from 0 to 0.500 m.

The skateboarder in Figure 6.23a is coasting down a ramp, and there are three forces acting on her: her weight (magnitude 675 N), a frictional force (magnitude 125 N) that opposes her motion, and a normal force (magnitude 612 N). Determine the net work done by the three forces when she coasts for a distance of 9.2 m. F

Figure 6.23b shows each force, along with the displacement of the skateboarder. By examining these diagrams and without doing any numerical calculations, determine whether the work done by each force is positive, negative, or zero. Provide a reason for each answer.

Figure 6.24 shows a 0.41-kg block sliding from A to B along a frictionless surface. When the block reaches B, it continues to slide along the horizontal surface BC where a kinetic frictional force acts. As a result, the block slows down, coming to rest at C. The kinetic energy of the block at A is 37 J, and the heights of A and B are 12.0 and 7.0 m above the ground, respectively. (a) What is the kinetic energy of the block when it reaches B? (b) How much work does the kinetic frictional force do during the BC segment of the trip?

Is the total mechanical energy of the block conserved as the block goes from A to B? Why or why not?

When the block reaches point B, has its kinetic energy increased, decreased, or remained the same relative to what it had at A? Provide a reason for your answer.

Is the total mechanical energy of the block conserved as the block goes from B to C? Justify your answer.

The same force pushes in three different ways on a box moving with a velocity , as the drawings show. Rank the work done by the force in ascending order (smallest first): (a) A, B, C (b) A, C, B (c) B, A, C (d) C, B, A (e) C, A, B

Consider the force shown in the drawing. This force acts on an object that can move along the positive or negative x axis, or along the positive or negative y axis. The work done by this force is positive when the displacement of the object is along the _______ axis or along the __________ axis: (a) x, y (b) x, y (c) x, y (d) x, y Sec

Two forces 1 and 2 act on a particle. As a result the speed of the particle increases. Which one of the following is NOT possible? (a) The work done by 1 is positive, and the work done by 2 is zero. (b) The work done by 1 is zero, and the work done by 2 is positive. (c) The work done by each force is positive. (d) The work done by each force is negative. (e) The work done by 1 is positive, and the work done by 2 is negative.

Force 1 acts on a particle and does work W1. Force 2 acts simultaneously on the particle and does work W2. The speed of the particle does not change. Which one of the following must be true? (a) W1 is zero and W2 is positive (b) W1 W2 (c) W1 is positive and W2 is zero (d) W1 is positive and W2 is positive Se

A person is riding on a Ferris wheel. When the wheel makes one complete turn, the net work done on the person by the gravitational force ____________. (a) is positive (b) is negative (c) is zero (d) depends on how fast the wheel moves (e) depends on the diameter of the wheel

In which one of the following circumstances could mechanical energy not possibly be conserved, even if friction and air resistance are absent? (a) A car moves up a hill, its velocity continually decreasing along the way. (b) A car moves down a hill, its velocity continually increasing along the way. (c) A car moves along level ground at a constant velocity. (d) A car moves up a hill at a constant velocity.

A ball is fixed to the end of a string, which is attached to the ceiling at point P. As the drawing shows, the ball is projected downward at A with the launch speed v0. Traveling on a circular path, the ball comes to a halt at point B. What enables the ball to reach point B, which is above point A? Ignore friction and air resistance. (a) The work done by the tension in the string (b) The balls initial gravitational potential energy (c) The balls initial kinetic energy (d) The work done by the gravitational force

In which one of the following circumstances does the principle of conservation of mechanical energy apply, even though a nonconservative force acts on the moving object? (a) The nonconservative force points in the same direction as the displacement of the object. (b) The nonconservative force is perpendicular to the displacement of the object. (c) The nonconservative force has a direction that is opposite to the displacement of the object. (d) The nonconservative force has a component that points in the same direction as the displacement of the object. (e) The nonconservative force has a component that points opposite to the displacement of the object.

A 92.0-kg skydiver with an open parachute falls straight downward through a vertical height of 325 m. The skydivers velocity remains constant. What is the work done by the nonconservative force of air resistance, which is the only nonconservative force acting? (a) 2.93  105 J (b) 0 J (c) 2.93  105 J (d) The answer is not obtainable, because insufficient information about the skydivers speed is given.

The power needed to accelerate a projectile from rest to its launch speed v in a time t is 43.0 W. How much power is needed to accelerate the same projectile from rest to a launch speed of 2v in a time of ?

During a tug-of-war, team A pulls on team B by applying a force of 1100 N to the rope between them. The rope remains parallel to the ground. How much work does team A do if they pull team B toward them a distance of 2.0 m?

You are moving into an apartment and take the elevator to the 6th floor. Suppose your weight is 685 N and that of your belongings is 915 N. (a) Determine the work done by the elevator in lifting you and your belongings up to the 6th floor (15.2 m) at a constant velocity. (b) How much work does the elevator do on you alone (without belongings) on the downward trip, which is also made at a constant velocity?

The brakes of a truck cause it to slow down by applying a retarding force of 3.0 103 N to the truck over a distance of 850 m. What is the work done by this force on the truck? Is the work positive or negative? Why?

A 75.0-kg man is riding an escalator in a shopping mall. The escalator moves the man at a constant velocity from ground level to the floor above, a vertical height of 4.60 m. What is the work done on the man by (a) the gravitational force and (b) the escalator?

Suppose in Figure 6.2 that 1.10 103 J of work is done by the force (magnitude  30.0 N) in moving the suitcase a distance of 50.0 m. At what angle is the force oriented with respect to the ground? 6

A person pushes a 16.0-kg shopping cart at a constant velocity for a distance of 22.0 m. She pushes in a direction 29.0 below the horizontal. A 48.0-N frictional force opposes the motion of the cart. (a) What is the magnitude of the force that the shopper exerts? Determine the work done by (b) the pushing force, (c) the frictional force, and (d) the gravitational force.

The drawing shows a plane diving toward the ground and then climbing back upward. During each of these motions, the lift force acts perpendicular to the displacement , which has the same magnitude, 1.7 103 m, in each case. The engines of the plane exert a thrust , which points in the direction of the displacement and has the same magnitude during the dive and the climb. The weight of the plane has a magnitude of 5.9 104 N. In both motions, net work is performed due to the combined action of the forces , , and . (a) Is more net work done during the dive or the climb? Explain. (b) Find the difference between the net work done during the dive and the climb.

A person pulls a toboggan for a distance of 35.0 m along the snow with a rope directed 25.0 above the snow. The tension in the rope is 94.0 N. (a) How much work is done on the toboggan by the tension force?(b) How much work is done if the same tension is directed parallel to the snow?

As a sailboat sails 52 m due north, a breeze exerts a constant force 1 on the boats sails. This force is directed at an angle west of due north. A force 2 of the same magnitude directed due north would do the same amount of work on the sailboat over a distance of just 47 m. What is the angle between the direction of the force 1 and due north?

A 55-kg box is being pushed a distance of 7.0 m across the floor by a force whose magnitude is 160 N. The force is parallel to the displacement of the box. The coefficient of kinetic friction is 0.25. Determine the work done on the box by each of the four forces that act on the box. Be sure to include the proper plus or minus sign for the work done by each force.

A 1.00 102 -kg crate is being pushed across a horizontal floor P B P B by a force that makes an angle of 30.0 below the horizontal. The coefficient of kinetic friction is 0.200. What should be the magnitude of , so that the net work done by it and the kinetic frictional force is zero?

A 1200-kg car is being driven up a 5.0 hill. The frictional force is directed opposite to the motion of the car and has a magnitude of f  524 N. A force is applied to the car by the road and propels the car forward. In addition to these two forces, two other forces act on the car: its weight and the normal force directed perpendicular to the road surface. The length of the road up the hill is 290 m. What should be the magnitude of , so that the net work done by all the forces acting on the car is 150 kJ?

A fighter jet is launched from an aircraft carrier with the aid of its own engines and a steam-powered catapult. The thrust of its engines is 2.3 105 N. In being launched from rest it moves through a distance of 87 m and has a kinetic energy of 4.5 107 J at lift-off. What is the work done on the jet by the catapult? 1

A golf club strikes a 0.045-kg golf ball in order to launch it from the tee. For simplicity, assume that the average net force applied to the ball acts parallel to the balls motion, has a magnitude of 6800 N, and is in contact with the ball for a distance of 0.010 m. With what speed does the ball leave the club?

It takes 185 kJ of work to accelerate a car from 23.0 m/s to 28.0 m/s. What is the cars mass?

Starting from rest, a 1.9 104 -kg flea springs straight upward. While the flea is pushing off from the ground, the ground exerts an average upward force of 0.38 N on it. This force does 2.4 104 J of work on the flea. (a) What is the fleas speed when it leaves the ground? (b) How far upward does the flea move while it is pushing off? Ignore both air resistance and the fleas weight. 17

A water-skier is being pulled by a tow rope attached to a boat. As the driver pushes the throttle forward, the skier accelerates. A 70.3-kg water-skier has an initial speed of 6.10 m/s. Later, the speed increases to 11.3 m/s. Determine the work done by the net external force acting on the skier.

As background for this problem, review Conceptual Example 6. A 7420-kg satellite has an elliptical orbit, as in Figure 6.9b. The point on the orbit that is farthest from the earth is called the apogee and is at the far right side of the drawing. The point on the orbit that is closest to the earth is called the perigee and is at the left side of the drawing. Suppose that the speed of the satellite is 2820 m/s at the apogee and 8450 m/s at the perigee. Find the work done by the gravitational force when the satellite moves from (a) the apogee to the perigee and (b) the perigee to the apogee.

The hammer throw is a track-and-field event in which a 7.3-kg ball (the hammer), starting from rest, is whirled around in a circle several times and released. It then moves upward on the familiar curving path of projectile motion. In one throw, the hammer is given a speed of 29 m/s. For comparison, a .22 caliber bullet has a mass of 2.6 g and, starting from rest, exits the barrel of a gun at a speed of 410 m/s. Determine the work done to launch the motion of (a) the hammer and (b) the bullet.

A 16-kg sled is being pulled along the horizontal snow-covered ground by a horizontal force of 24 N. Starting from rest, the sled attains a speed of 2.0 m/s in 8.0 m. Find the coefficient of kinetic friction between the runners of the sled and the snow

An asteroid is moving along a straight line. A force acts along the displacement of the asteroid and slows it down. The asteroid has a mass of 4.5 104 kg, and the force causes its speed to change from 7100 to 5500 m/s. (a) What is the work done by the force? (b) If the asteroid slows down over a distance of 1.8 106 m, determine the magnitude of the force.

The concepts in this problem are similar to those in Multiple-Concept Example 4, except that the force doing the work in this problem is the tension in the cable. A rescue helicopter lifts a 79-kg person straight up by means of a cable. The person has an upward acceleration of 0.70 m/s2 and is lifted from rest through a distance of 11 m. (a) What is the tension in the cable? How much work is done by (b) the tension in the cable and (c) the persons weight? (d) Use the workenergy theorem and find the final speed of the person.

A 6200-kg satellite is in a circular earth orbit that has a radius of 3.3 107 m. A net external force must act on the satellite to make it change to a circular orbit that has a radius of 7.0 106 m. What work W must the net external force do? Note that the work determined here is not the work Wlift done by the satellites engines to change the orbit. Instead, the work W is W  Wlift  Wgravitational, where Wgravitational is the work done by the gravitational force. *

Consult Multiple-Concept Example 5 for insight into solving this problem. A skier slides horizontally along the snow for a distance of 21 m before coming to rest. The coefficient of kinetic friction between the skier and the snow is k  0.050. Initially, how fast was the skier going?

A sled is being pulled across a horizontal patch of snow. Friction is negligible. The pulling force points in the same direction as the sleds displacement, which is along the x axis. As a result, the kinetic energy of the sled increases by 38%. By what percentage would the sleds kinetic energy have increased if this force had pointed 62 above the x axis?

Under the influence of its drive force, a snowmobile is moving at a constant velocity along a horizontal patch of snow. When the drive force is shut off, the snowmobile coasts to a halt. The snowmobile and its rider have a mass of 136 kg. Under the influence of a drive force of 205 N, it is moving at a constant velocity whose magnitude is 5.50 m/s. The drive force is then shut off. Find (a) the distance in which the snowmobile coasts to a halt and (b) the time required to do so.

The model airplane in Figure 5.6 is flying at a speed of 22 m/s on a horizontal circle of radius 16 m. The mass of the plane is 0.90 kg. The person holding the guideline pulls it in until the radius becomes 14 m. The plane speeds up, and the tension in the guideline becomes four times greater. What is the net work done on the plane?

Multiple-Concept Example 5 reviews many of the concepts that play roles in this problem. An extreme skier, starting from rest, coasts down a mountain slope that makes an angle of 25.0 with the horizontal. The coefficient of kinetic friction between her skis and the snow is 0.200. She coasts down a distance of 10.4 m before coming to the edge of a cliff. Without slowing down, she skis off the cliff and lands downhill at a point whose vertical distance is 3.50 m below the edge. How fast is she going just before she lands?

A 75.0-kg skier rides a 2830-m-long lift to the top of a mountain. The lift makes an angle of 14.6 with the horizontal. What is the change in the skiers gravitational potential energy?

Juggles and Bangles are clowns. Juggles stands on one end of a teeter-totter at rest on the ground. Bangles jumps off a platform 2.5 m above the ground and lands on the other end of the teeter-totter, launching Juggles into the air. Juggles rises to a height of 3.3 m above the ground, at which point he has the same amount of gravitational potential energy as Bangles had before he jumped, assuming both potential energies are measured using the ground as the reference level. Bangles mass is 86 kg. What is Juggles mass?

A 0.60-kg basketball is dropped out of a window that is 6.1 m above the ground. The ball is caught by a person whose hands are 1.5 m above the ground. (a) How much work is done on the ball by its weight? What is the gravitational potential energy of the basketball, relative to the ground, when it is (b) released and (c) caught? (d) How is the change (PEf PE0) in the balls gravitational potential energy related to the work done by its weight?

A pole-vaulter just clears the bar at 5.80 m and falls back to the ground. The change in the vaulters potential energy during the fall is 3.70 103 J. What is his weight? 3

A bicyclist rides 5.0 km due east, while the resistive force from the air has a magnitude of 3.0 N and points due west. The rider then turns around and rides 5.0 km due west, back to her starting point. The resistive force from the air on the return trip has a magnitude of 3.0 N and points due east. (a) Find the work done by the resistive force during the round trip. (b) Based on your answer to part (a), is the resistive force a conservative force? Explain.

Rocket Man has a propulsion unit strapped to his back. He starts from rest on the ground, fires the unit, and accelerates straight upward. At a height of 16 m, his speed is 5.0 m/s. His mass, including the propulsion unit, has the approximately constant value of 136 kg. Find the work done by the force generated by the propulsion unit.

A 55.0-kg skateboarder starts out with a speed of 1.80 m/s. He does 80.0 J of work on himself by pushing with his feet against the ground. In addition, friction does 265 J of work on him. In both cases, the forces doing the work are nonconservative. The final speed of the skateboarder is 6.00 m/s. (a) Calculate the change ( PE  PEf PE0) in the gravitational potential energy. (b) How much has the vertical height of the skater changed, and is the skater above or below the starting point? c

A 35-kg girl is bouncing on a trampoline. During a certain interval after she leaves the surface of the trampoline, her kinetic energy decreases to 210 J from 440 J. How high does she rise during this interval? Neglect air resistance.

A gymnast is swinging on a high bar. The distance between his waist and the bar is 1.1 m, as the drawing shows. At the top of the swing his speed is momentarily zero. Ignoring friction and treating the gymnast as if all of his mass is located at his waist, find his speed at the bottom of the swing

The skateboarder in the drawing starts down the left side of the ramp with an initial speed of 5.4 m/s. Neglect nonconservative forces, such as friction and air resistance, and find the height h of the highest point reached by the skateboarder on the right side of the ramp.

A slingshot fires a pebble from the top of a building at a speed of 14.0 m/s. The building is 31.0 m tall. Ignoring air resistance, find the speed with which the pebble strikes the ground when the pebble is fired (a) horizontally, (b) vertically straight up, and (c) vertically straight down.

The drawing shows two boxes resting on frictionless ramps. One box is relatively light and sits on a steep ramp. The other box is heavier and rests on a ramp that is less steep. The boxes are released from rest at A and allowed to slide down the ramps. The two boxes have masses of 11 and 44 kg. If A and B are 4.5 and 1.5 m, respectively, above the ground, determine the speed of (a) the lighter box and (b) the heavier box when each reaches B. (c) What is the ratio of the kinetic energy of the heavier box to that of the lighter box at B?

A 47.0-g golf ball is driven from the tee with an initial speed of 52.0 m/s and rises to a height of 24.6 m. (a) Neglect air resistance and determine the kinetic energy of the ball at its highest point. (b) What is its speed when it is 8.0 m below its highest point?

Consult Conceptual Example 9 in preparation for this problem. The drawing shows a person who, starting from rest at the top of a cliff, swings down at the end of a rope, releases it, and falls into the water below. There are two paths by which the person can enter the water. Suppose he enters the water at a speed of 13.0 m/s via path 1. How fast is he moving on path 2 when he releases the rope at a height of 5.20 m above the water? Ignore the effects of air resistance.

The drawing shows a skateboarder moving at 5.4 m/s along a horizontal section of a track that is slanted upward by 48 above the horizontal at its end, which is 0.40 m above the ground. When she leaves the track, she follows the characteristic path of projectile motion. Ignoring friction and air resistance, find the maximum height H to which she rises above the end of the track

A small lead ball, attached to a 1.5-m rope, is being whirled in a circle that lies in the vertical plane. The ball is whirled at a constant rate of three revolutions per second and is released on the upward part of the circular motion when it is 0.75 m above the ground. The ball travels straight upward. In the absence of air resistance, to what maximum height above the ground does the ball rise?

A pendulum consists of a small object hanging from the ceiling at the end of a string of negligible mass. The string has a length of 0.75 m. With the string hanging vertically, the object is given an initial velocity of 2.0 m/s parallel to the ground and swings upward on a circular arc. Eventually, the object comes to a momentary halt at a point where the string makes an angle with its initial vertical orientation and then swings back downward. Find the angle .

A semitrailer is coasting downhill along a mountain highway when its brakes fail. The driver pulls onto a runaway-truck ramp that is inclined at an angle of 14.0 above the horizontal. The semitrailer coasts to a stop after traveling 154 m along the ramp. What was the trucks initial speed? Neglect air resistance and friction.

he drawing shows two frictionless inclines that begin at ground level (h 0 m) and slope upward at the same angle . One track is longer than the other, however. Identical blocks are projected up each track with the same initial speed v0. On the longer track the block slides upward until it reaches a maximum height H above the ground. On the shorter track the block slides upward, flies off the end of the track at a height H1 above the ground, and then follows the familiar parabolic trajectory of projectile motion. At the highest point of this trajectory, the block is a height H2 above the end of the track. The initial total mechanical energy of each block is the same and is all kinetic energy. The initial speed of each block is v0 7.00 m/s, and each incline slopes upward at an angle of 50.0. The block on the shorter track leaves the track at a height of H1 1.25 m above the ground. Find (a) the height H for the block on the longer track and (b) the total height H1  H2 for the block on the shorter track. ** 49

A skier starts from rest at the top of a hill. The skier coasts down the hill and up a second hill, as the drawing illustrates. The crest of the second hill is circular, with a radius of r 36 m. Neglect friction and air resistance. What must be the height h of the first hill so that the skier just loses contact with the snow at the crest of the second hill?

A person starts from rest at the top of a large frictionless spherical surface, and slides into the water below (see the drawing). At what angle does the person leave the surface? (Hint: When the person leaves the surface, the normal force is zero.)

A projectile of mass 0.750 kg is shot straight up with an initial speed of 18.0 m/s. (a) How high would it go if there were no air resistance? (b) If the projectile rises to a maximum height of only 11.8 m, determine the magnitude of the average force due to air resistance.

A basketball player makes a jump shot. The 0.600-kg ball is released at a height of 2.00 m above the floor with a speed of 7.20 m/s. The ball goes through the net 3.10 m above the floor at a speed of 4.20 m/s. What is the work done on the ball by air resistance, a nonconservative force?

Starting from rest, a 93-kg firefighter slides down a fire pole. The average frictional force exerted on him by the pole has a magnitude of 810 N, and his speed at the bottom of the pole is 3.4 m/s. How far did he slide down the pole?

A student, starting from rest, slides down a water slide. On the way down, a kinetic frictional force (a nonconservative force) acts on her. The student has a mass of 83.0 kg, and the height of the water slide is 11.8 m. If the kinetic frictional force does 6.50  103 J of work, how fast is the student going at the bottom of the slide?

The (nonconservative) force propelling a 1.50  103 -kg car up a mountain road does 4.70  106 J of work on the car. The car starts from rest at sea level and has a speed of 27.0 m/s at an altitude of 2.00  102 m above sea level. Obtain the work done on the car by the combined forces of friction and air resistance, both of which are nonconservative forces.

In the sport of skeleton a participant jumps onto a sled (known as a skeleton) and proceeds to slide down an icy track, belly down and head first. In the 2010 Winter Olympics, the track had sixteen turns and dropped 126 m in elevation from top to bottom. (a) In the absence of nonconservative forces, such as friction and air resistance, what would be the speed of a rider at the bottom of the track? Assume that the speed at the beginning of the run is relatively small and can be ignored. (b) In reality, the gold-medal winner (Canadian Jon Montgomery) reached the bottom in one heat with a speed of 40.5 m/s (about 91 mi/h). How much work was done on him and his sled (assuming a total mass of 118 kg) by nonconservative forces during this heat?

In attempting to pass the puck to a teammate, a hockey player gives it an initial speed of 1.7 m/s. However, this speed is inadequate to compensate for the kinetic friction between the puck and the ice. As a result, the puck travels only one-half the distance between the players before sliding to a halt. What minimum initial speed should the puck have been given so that it reached the teammate, assuming that the same force of kinetic friction acted on the puck everywhere between the two players?

A pitcher throws a 0.140-kg baseball, and it approaches the bat at a speed of 40.0 m/s. The bat does Wnc 70.0 J of work on the ball in hitting it. Ignoring air resistance, determine the speed of the ball after the ball leaves the bat and is 25.0 m above the point of impact.

A 67.0-kg person jumps from rest off a 3.00-m-high tower straight down into the water. Neglect air resistance. She comes to rest 1.10 m under the surface of the water. Determine the magnitude of the average force that the water exerts on the diver. This force is nonconservative.

At a carnival, you can try to ring a bell by striking a target with a 9.00-kg hammer. In response, a 0.400-kg metal piece is sent upward toward the bell, which is 5.00 m above. Suppose that 25.0% of the hammers kinetic energy is used to do the work of sending the metal piece upward. How fast must the hammer be moving when it strikes the target so that the bell just barely rings?

A truck is traveling at 11.1 m/s down a hill when the brakes on all four wheels lock. The hill makes an angle of 15.0 with respect to the rhorizontal. The coefficient of kinetic friction between the tires and the road is 0.750. How far does the truck skid before coming to a stop?

A person is making homemade ice cream. She exerts a force of magnitude 22 N on the free end of the crank handle on the ice-cream maker, and this end moves on a circular path of radius 0.28 m. The force is always applied parallel to the motion of the handle. If the handle is turned once every 1.3 s, what is the average power being expended?

Bicyclists in the Tour de France do enormous amounts of work during a race. For example, the average power per kilogram generated by seven-time-winner Lance Armstrong (m 75.0 kg) is 6.50 W per kilogram of his body mass. (a) How much work does he do during a 135-km race in which his average speed is 12.0 m/s? (b) Often, the work done is expressed in nutritional Calories rather than in joules. Express the work done in part (a) in terms of nutritional Calories, noting that 1 joule 2.389  104 nutritional Calories. 6

You are working out on a rowing machine. Each time you pull the rowing bar (which simulates the oars) toward you, it moves a distance of 1.2 m in a time of 1.5 s. The readout on the display indicates that the average power you are producing is 82 W. What is the magnitude of the force that you exert on the handle?

A car accelerates uniformly from rest to 20.0 m/s in 5.6 s along a level stretch of road. Ignoring friction, determine the average power required to accelerate the car if (a) the weight of the car is 9.0  103 N and (b) the weight of the car is 1.4  104 N.

A helicopter, starting from rest, accelerates straight up from the roof of a hospital. The lifting force does work in raising the helicopter. An 810-kg helicopter rises from rest to a speed of 7.0 m/s in a time of 3.5 s. During this time it climbs to a height of 8.2 m. What is the average power generated by the lifting force?

Multiple-Concept Example 13 presents useful background for this problem. The cheetah is one of the fastest-accelerating animals, because it can go from rest to 27 m/s (about 60 mi/h) in 4.0 s. If its mass is 110 kg, determine the average power developed by the cheetah during the acceleration phase of its motion. Express your answer in (a) watts and (b) horsepower.

In 2.0 minutes, a ski lift raises four skiers at constant speed to a height of 140 m. The average mass of each skier is 65 kg. What is the average power provided by the tension in the cable pulling the lift?

The motor of a ski boat generates an average power of 7.50  104 W when the boat is moving at a constant speed of 12 m/s. When the boat is pulling a skier at the same speed, the engine must generate an average power of 8.30  104 W. What is the tension in the tow rope that is pulling the skier?

A 1900-kg car experiences a combined force of air resistance and friction that has the same magnitude whether the car goes up or down a hill at 27 m/s. Going up a hill, the cars engine produces 47 hp more power to sustain the constant velocity than it does going down the same hill. At what angle is the hill inclined above the horizontal?

The drawing shows the forcedisplacement graph for two different bows. These graphs give the force that an archer must apply to draw the bowstring. (a) For which bow is more work required to draw the bow fully from s 0 to s 0.50 m? Give your reasoning. (b) Estimate the additional work required for the bow identified in part (a) compared to the other bow. P

The graph shows how the force component F cos along the displacement varies with the magnitude s of the displacement. Find the work done by the force. (Hint: Recall how the area of a triangle is related to the triangles base and height.)

Review Example 14, in which the work done in drawing the bowstring in Figure 6.21 from s 0 to s 0.500 m is determined. In part b of the figure, the force component F cos reaches a maximum value at s 0.306 m. Find the percentage of the total work that is done when the bowstring is moved (a) from s 0 to 0.306 m and (b) from s 0.306 to 0.500 m. 74. T

The force component along the displacement varies with the magnitude of the displacement, as shown in the graph. Find the work done by the force in the interval from (a) 0 to 1.0 m, (b) 1.0 to 2.0 m, and (c) 2.0 to 4.0 m. (Note: In the last interval the force component is negative, so the work is negative.)

A net external force is applied to a 6.00-kg object that is initially at rest. The net force component along the displacement of the object varies with the magnitude of the displacement as shown in the drawing. What is the speed of the object at s 20.0 m? +

A cable lifts a 1200-kg elevator at a constant velocity for a distance of 35 m. What is the work done by (a) the tension in the cable and (b) the elevators weight?

A 2.00-kg rock is released from rest at a height of 20.0 m. Ignore air resistance and determine the kinetic energy, gravitational potential energy, and total mechanical energy at each of the following heights: 20.0, 10.0, and 0 m.

The surfer in the photo is catching a wave. Suppose she starts at the top of the wave with a speed of 1.4 m/s and moves down the wave until her speed increases to 9.5 m/s. The drop in her vertical height is 2.7 m. If her mass is 59 kg, how much work is done by the (nonconservative) force of the wave?

A water-skier, moving at a speed of 9.30 m/s, is being pulled by a tow rope that makes an angle of 37.0 with respect to the velocity of the boat (see the drawing). The tow rope is parallel to the water. The skier is moving in the same direction as the boat. If the tension in the tow rope is 135 N, determine the work that it does in 12.0 s.

When an 81.0-kg adult uses a spiral staircase to climb to the second floor of his house, his gravitational potential energy increases by 2.00  103 J. By how much does the potential energy of an 18.0-kg child increase when the child climbs a normal staircase to the second floor?

A husband and wife take turns pulling their child in a wagon along a horizontal sidewalk. Each exerts a constant force and pulls the wagon through the same displacement. They do the same amount of work, but the husbands pulling force is directed 58 above the horizontal, and the wifes pulling force is directed 38 above the horizontal. The husband pulls with a force whose magnitude is 67 N. What is the magnitude of the pulling force exerted by his wife?

Some gliders are launched from the ground by means of a winch, which rapidly reels in a towing cable attached to the glider. What average power must the winch supply in order to accelerate a 184-kg ultralight glider from rest to 26.0 m/s over a horizontal distance of 48.0 m? Assume that friction and air resistance are negligible, and that the tension in the winch cable is constant.

A basketball of mass 0.60 kg is dropped from rest from a height of 1.05 m. It rebounds to a height of 0.57 m. (a) How much mechanical energy was lost during the collision with the floor? (b) A basketball player dribbles the ball from a height of 1.05 m by exerting a constant downward force on it for a distance of 0.080 m. In dribbling, the player compensates for the mechanical energy lost during each bounce. If the ball now returns to a height of 1.05 m, what is the magnitude of the force?

A 63-kg skier coasts up a snow-covered hill that makes an angle of 25 with the horizontal. The initial speed of the skier is 6.6 m/s. After coasting 1.9 m up the slope, the skier has a speed of 4.4 m/s. (a) Find the work done by the kinetic frictional force that acts on the skis. (b) What is the magnitude of the kinetic frictional force?

A water slide is constructed so that swimmers, starting from rest at the top of the slide, leave the end of the slide traveling horizontally. As the drawing shows, one person hits the water 5.00 m from the end of the slide in a time of 0.500 s after leaving the slide. Ignoring friction and air resistance, find the height H in the drawing.

Conceptual Example 9 provides background for this problem. A swing is made from a rope that will tolerate a maximum tension of 8.00  102 N without breaking. Initially, the swing hangs vertically. The swing is then pulled back at an angle of 60.0 with respect to the vertical and released from rest. What is the mass of the heaviest person who can ride the swing?

Suppose the skateboarder shown in the drawing for Problem 38 reaches a highest point of h 1.80 m above the right side of the semicircular ramp. He then makes an incomplete midair turn and ends up sliding down the right side of the ramp on his back. When the skateboarder reaches the bottom of the ramp, his speed is 6.40 m/s. The skateboarders mass is 61.0 kg, and the radius of the semicircular ramp is 2.70 m. What is the average frictional force exerted on the skateboarder by the ramp?

Two pole-vaulters just clear the bar at the same height. The first lands at a speed of 8.90 m/s, and the second lands at a speed of 9.00 m/s. The first vaulter clears the bar at a speed of 1.00 m/s. Ignore air resistance and friction and determine the speed at which the second vaulter clears the bar.