Chapter_8_09 - Chapter 8 8.2 Figure 8-31 shows a ball with...

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Chapter 8 8.2 Figure 8-31 shows a ball with mass m = 0.341 kg attached to the end of a thin rod with length L = 0.452 m and negligible mass. The other end of the rod is pivoted so that the ball can move in a vertical circle The rod is held horizontally as sown and then given enough of a downward push to cause the ball to swing down and around and just reach the vertically up position with zero speed there. How much work is done on the ball by the gravitational force from the initial point (a) the lowest point, (b) the highest point, and (c) the point on the right level with the initial point? If the gravitation potential energy of the ball-earth system is taken to be zero at the initial point, what is it when the ball reaches (d) the lowest point, (e) the highest point and (f) the point on the right level with the initial point? (g) Suppose the rod were pushed harder sot that the ball passed through the highest point with nonzero speed. Would Δ U g from the lowest point to the highest point then be greater than, less than, or the same as it was when the ball stopped at the highest point. Since the gravitational force is conservative, the work done and change in potential energy only depend on the initial and ±nal position. (a) Work done in moving from initial position to lowest position W = mgL = 1.51 J (b) Work done in moving from initial position to highest position W = mgL = 1.51 J (c) Work done in moving from initial position to level position W = 0 De±ning the potential to be zero at the initial point is actually de±ning the initial height as zero height. In that case (d) Potential at lowest point U = mgy = mg ( L ) = 1.51 J (e) Potential at highest point U = mgy = mg ( L ) = 1.51 J (f) Potential at level point U = mgy = mg (0) = 0 J (g) The work and potential are not dependent on velocity in this problem. The answers are unchanged.
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8.3 In Fig 8-32, a 2.00g ice fake is released ±rom the edge o± a hemispherical bowl whose radius is 22 cm. The fake=bowl contact is ±rictionless. (a) how much work is done on the fake by the gravitation ±orce during the fake’s descent to the bottom o± the bowl? (b) What is the change in the potential energy o± the fake Earth system during the descent? (c) I± that potential energy is taken to be zero at the bottom o± the bowl, what is its value when the fake is released? (d) I± instead, the potential energy is taken to be zero at the release point, what is its value when the fake reaches the bottom o± the bowl (e) I± the mass o± the fake were doubled, would the magnitudes o± the answers to (a) through (d) increase, decrease, or remain the same? a) The work done is W = −Δ U = ( U f U i ) = (0 mgy ) = 2 × 10 3 9.8 m / s 2 0.22 m = 4.312 × 10 3 J For this part o± the problem, assume the bottom o± the bowl is zero height U f = 0 U i = mgR W = ( U f U i ) = mgR b) See part (a).
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Chapter_8_09 - Chapter 8 8.2 Figure 8-31 shows a ball with...

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