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 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, and (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. 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? Figure 8-31 Problems 4 and 14.
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 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, and (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. 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? Figure 8-31 Problems 4 and 14.
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 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, and (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. Would ΔUgfrom 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?
The figure shows a ball with mass m = 0.69 kg attached to the end of a thin rod with length L = 0.99 m and negligible mass. The other
end of the rod is pivoted so that the ball can move in a vertical circle. (a) What 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, what would the answer to (a) be?
The L-shaped object in the figure(Figure 1) consists of three masses connected by light rods.
Find the work that must be done on this object to accelerate it from rest to an angular speed of 2.00 rad/sr about the x axis.
About the y axis.
About the z axis (which is through the origin and perpendicular to the plane of the figure).
The figure shows a thin rod, of length L = 2.20 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy
ball of mass m = 8.10 kg is attached to the other end. The rod is pulled aside to angle 00 = 8° and released with initial velocity V
0. (a) What is the speed of the ball at the lowest point? (b) Does the speed increase, decrease, or remain the same if
%3D
the mass is increased?
3.
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