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Determining Potential Energy Values

1E. What is the spring constant of a spring that stores 25 J of elastic potential energy when compressed by 7.S cm from its relaxed length?

2E. You drop a 2.00 kg textbook to a friend who stands on the ground 10.0 m below the textbook with outstretched hands 1.59 m.








3E Flake is released from the edge of a hemispherical bowl whose radius.






4E. A friction less roller coaster of mass ‘m tops the first hill with speed \’0’ How much work does the gravitational force do on it from that point .

5E. Figure 8-27 shows a ball with mass m attached to the end of a thin rod with length L and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle.

6E.Shows a thin rod. of length L and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball  mass m is attached to the other end. The rod is pulled aside  through an angle and released.

Consummation of Mechanical Energy

7E. (a) In Exercise 3. what is the speed of the flake when it reach the bottom of the bowl? (b) If we substituted a second flake with twice the mass, hat would its speed be?

8E. (a) In Exercise 2. what is the speed of the textbook when it reaches the hands? (b) If we substituted a second textbook with twice the mass, what would its speed be? (e) If, instead. the textbook were thrown down. would the answer to (a) increase. decrease.
or remain the same?
9E. (a) In Exercise 5_ “hat initial speed must be given the ball so that it reaches the vertically upward position with zero speed? What then is its speed at (b) the lowest point and (c) the point on the right at which the ball is level with the initial point? (d) If the ball’s mass were doubled. would the answers to (a) through (e) increase. decrease. or remain the same?
10E. In Exercise 4. what is the speed of the coaster at (a) point A.
(b) point B. and (c) point C? (d) How high will it go on the last
hill. which is too high for it to cross? (e) If we substitute a second
coaster with twice the mass. what then are the answers to (a)
through (d)?
E11_ A runaway truck with failed brakes is moving downgrade at just before the driver steers.

12P. (a) In Problem 8, what is the speed of the ball at the lowest point if L = 2.00 m, 8 = 30.0”, and m = 5.00 kg? (b) Does the speed increase, decrease, or remain the same if the mass is increased?
13P. (a) In Problem 7, using energy techniques rather than the techniques of Chapter 4, find the speed of the snowball as it reaches the ground below the cliff. What is that speed (b) if the launch angle is changed to 41.0· below the horizontal and (c) if the mass
is changed to 2.50 kg?

14P. A 5.0 g marble is fired vertically upward using a spring gun. The spring must be compressed 8.0 cm if the marble is to just reach a target 20 m above the marble’s position on the compressed spring. (a) What is the change 6Ug in the gravitational potential energy of the marble-Earth system during the 20 m ascent? (b) What is the change !1Us in the elastic potential energy of the spring during its launch of the marble? (c) What is the spring constant of the spring?

15P. Shows a pendulum of length L. Its bob (which effectively has all the mass) has speed  when the cord makes an angle 80 with the vertical. (a) Derivean expression for the speed of the bob when it is in its lowest position. What is the least value that can have if the pendulum is to swing down and then up (b) to a horizontal position, and (c) to a vertical position with the cord remaining straight? (d) Do the answers to (b) and (c) increase, decrease, or remain the same if 80 is increased by a few degrees?

 18P. A 2.00 kg block is placed against a spring on a friction less 30.0 incline . (The block is not attached to the spring.) The spring, whose spring constant , is compressed 20.0 em and then released. (a) What is the elastic potential energy of the compressed spring? (b) What is the change in the gravitational potential.

19P. Shows an 8.00 kg stone at rest on a spring. The spring is compressed 10.0 by the stone. (a) What is the spring constant? (b) The stone is pushed down an additional 30.0 cm and released. What is the elastic potential energy of the compressed spring just before that release? (c) What is the change in the gravitational potential energy of the stone-Earth system when the stone moves from  release point to its maximum height? (d) What is that maximum height, measured from the release point?

20P. In Problem 6, what are (a) the horizontal component and (b) the vertical component of the net force acting on the block at point Q? (c) At what height h should the block be released.

21P. In Fig. 8-34, a 12 kg block is released from rest on a 30· friction less incline. Below the block is a spring that can be compressed  by a force of 270 N. The block momentarily stops when it compresses the spring by 5.5 cm. (a) How far does the block move down the incline from its rest position to this stopping point? (b) What is the speed of the block just as it touches the spring?

22P. At t = 0 a 1.0 kg ball is thrown from the top of a tall tower with velocity . What is the change in the potential energy of the ball-Earth system between t = 0 and t= 6.0 s?

23P.The string in L = 120 cm long, has a ball attached to one end, and is fixed at its other end. The distance d to the fixed peg at point P is 75.0cm. When the initially stationary ball is released with the string horizontal as shown, it will swing along the dashed arc. What is it speed when it reaches (a) its lowest point and (b) its highest point after the string catches .

24P. A 60 kg skier starts from rest at a height of 20 m above the end of a ski-jump ramp as shown in Fig. 8-36. As the skier leaves the ramp, his velocity makes an angle of 28· with the horizontal.

25P.A 2.0 kg block is dropped from a high! of 40 cm onto a spring of spring constant. Find the maximum distance the spring is compressed.

26P. Tarzan, who weighs 688 N, swings from a cliff at the end of a convenient vine that is 18 m long (Fig. 8-38). From the top of the cliff to the bottom of the swing, he descends by 3.2 m. The: vine will break if the force on II exceeds 950 N. (a) Does the vine break? (b) If no, what is the greatest force on it during the swing? If yes, at what angle with the vertical does it break?

27P.Two children are playing a game in which they try to hit a small box on the floor with a marble fired from a spring-loaded gun that is mounted on a table. The target box is 2.20 m horizontally from the edge of the table see . Bobby compresses the spring 1.10 em, but the center of the marble falls 27.0 em short of the center of the box. How far should Rhoda compress the ping to score a direct hit? Assume that neither the spinning nor the ball encounters friction in the gun.

28P. To make a pendulum, a 300 g ball is attached to one end of a string that has a length of 1.4 m arid negligible mass. (The other end of the string is fixed.) The ball is pulled to one side until the string makes an angle of with the. vertical; then (with the string taut) the ball is released from rest. Find (a) the speed of the ball when the string makes an angle of 20.0 with the vertical and (b) the maximum speed of the ball. (c) What is the angle between the string and the vertical when the speed of the ball is one-third its maximum value?

29P. A rigid rod of length L and negligible mass has a bail with mass m attached to one end and its other end fixed, to font a pendulum. The pendulum is inverted, with the rod straight up, and then released. At the lowest point, what are (a) the ball’s speed and (b) the tension in the rod? (c) The pendulum is next released at rest from a horizontal position. At what angle from the vertical does the tension in the rod equal the weight of the ball?

30. Fly-Fishing and Speed Amplification. If you throw a loose fishing fly, it will travel horizontally only about I m. However, if you throw that fly attached to fishing line by casting the line with a rod, the fly will easily travel horizontally to the full length of the line, say, 20 m.

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