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Chapter 8: Q1P (page 202)
What is the spring constant of a spring that storesof elastic potential energy when compressed by?
Spring constant is, .
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In Fig. 8-18, a horizontally moving block can take three frictionless routes, differing only in elevation, to reach the dashed finish line. Rank the routes according to (a) the speed of the block at the finish line and (b) the travel time of the block to the finish line, greatest first.
A single conservative forceacts on a 1.0 kg particle that moves along an x axis. The potential energy associated with role="math" localid="1661227819293" is given by , where xis in meters. Atthe particle has a kinetic energy of 2.0 J. (a) What is the mechanical energy of the system? (b) Make a plot of as a function of xfor , and on the same graph draw the line that represents the mechanical energy of the system. Use part (b) to determine (c) the least value of xthe particle can reach and (d) the greatest value of x the particle can reach. Use part (b) to determine (e) the maximum kinetic energy of the particle and (f) the value of xat which it occurs. (g) Determine an expression in newtons and meters for as a function of x. (h) For what (finite) value of xdoes?
In Fig. 8-22, a block slides from A to C along a frictionless ramp, and then it passes through horizontal region CD, where a frictional force act on it. Is the block鈥檚 kinetic energy increasing, decreasing, or constant in (a) region AB, (b) region BC, and (c) region CD? (d) Is the block鈥檚 mechanical energy increasing, decreasing, or constant in those regions?
In Fig 8.54, a block slides along a track from one level to a higher level after passing through an intermediate valley. The track is frictionless until the block reaches the higher level. There a frictional force stops the block in a distance d. The block鈥檚 initial speed , the height difference his 1.1 m, and . Find d.
Figure 8-31 shows a ball with mass attached to the end of a thin rod with lengthand 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 shown 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 to (a) the lowest point (b) the highest point (c) the point on the right level with the initial point?If the gravitational 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 so that the ball passed through the highest point with a nonzero speed. Wouldfrom 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?
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