Concepts & Calculations

Note: Each of these problems consists of Concept Questions followed by a related quantitative Problem. The Concept Questions involve little or no mathematics. They focus on the concepts with which the problems deal. Recognizing the concepts is the essential initial step in any proble-msolving technique.

| 80 | Concept Questions You are moving into an apartment and take the elevator to the 6th floor. Does the force exerted on you by the elevator do positive or negative work when the elevator (a) goes up and (b) goes down? Explain your answers. Problem 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? Check to see that your answers are consistent with your answers to the Concept Questions.

| 81 | Concept Questions An asteroid is moving along a straight line. A force acts along the displacement of the asteroid and slows it down. (a) Is the direction of the force the same as or opposite to the direction of the displacement of the asteroid? Why? (b) Does the force do positive, negative, or zero work? Justify your answer. (c) What type of energy is changing as the object slows down? (d) What is the relationship between the work done by this force and the change in the object’s energy?
Problem The asteroid has a mass of , 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 , determine the magnitude of the force. Verify that your answers are consistent with the answers to the Concept Questions.

| 82 | Concept Questions 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. Which box, if either, has (a) the greater speed and (b) the greater kinetic energy at B? Provide a reason for each answer.
Problem 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? Be sure that your answers are consistent with your answers to the Concept Questions.

| 83 | Concept Questions A student, starting from rest, slides down a water slide. On the way down, a kinetic frictional force (a nonconservative force) acts on her. (a) Does the kinetic frictional force do positive, negative, or zero work? Provide a reason for your answer. (b) Does the total mechanical energy of the student increase, decrease, or remain the same as she descends the slide? Why? (c) If the kinetic frictional force does work, how is this work related to the change in the total mechanical energy of the student?
Problem 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 of work, how fast is the student going at the bottom of the slide?

| 84 | Concept Questions A helicopter, starting from rest, accelerates straight up from the roof of a hospital. The lifting force does work in raising the helicopter. (a) What type(s) of energy is (are) changing? Is each type increasing or decreasing? Why? (b) How is (are) the type(s) of energy that is (are) changing related to the work done by the lifting force? (c) If you want to determine the average power generated by the lifting force, what other variable besides the work must be known?
Problem 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?

| 85 | Concept Questions 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) What type of energy is changing? (b) Is the work being done by the net external force acting on the skier positive, zero, or negative? Why? (c) How is this work related to the change in the energy of the skier?
Problem 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.

| 86 | Concept Questions 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. (a) During the coasting phase, what is the net external force acting on the snowmobile? (b) How does the work W done by the net external force depend on the magnitude and direction of the net force and on the displacement of the snowmobile? (c) What is the net force acting on the snowmobile during the constant-velocity phase? Explain. (d) The work–energy theorem is given by (Equation 6.3), where W is the work done by the net external force acting on the snowmobile, m is its mass, and vf and v0 are, respectively, its final and initial speeds. Suppose the net external force, m, and vf and v0 are known. By using only the work–energy theorem, can one determine the time t it takes for the snowmobile to coast to a halt?
Problem 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. Its drive force is shut off. Find (a) the distance in which the snowmobile coasts to a halt and (b) the time required to do so.

| 87 | Concept Questions The drawing shows two frictionless inclines that begin at ground level 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. (a) When the block on the longer track reaches its maximum height, is its final total mechanical energy all kinetic energy, all potential energy, or some of each? Explain. (b)When the block on the shorter track reaches the top of its trajectory after leaving the track, is its final total mechanical energy all kinetic energy, all potential energy, or some of each? Justify your answer. (c) Which is the greater height above the gound: H or H1 + H2? Why?
Problem The initial speed of each block is , and each incline slopes upward at an angle of . The block on the shorter track leaves the track at a height of above the ground. Find (a) the height H for the block on the longer track and (b) the total height for the block on the shorter track. Verify that your answers are consistent with your answers to the Concept Questions.

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