A light mechanical winch pulls upward on the free end of a heavy cable of length and…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A light mechanical winch pulls upward on the free end of a heavy cable of length L and total mass M. Immediately after the winch begins to pull, the cable is accelerating upward with constant magnitude a but has not yet begun to move significantly relative to its original straight shape.
The vertical position y is measured upward from the bottom tip of the cable (y=0) to the top end attached to the winch (y=L).
(a) On axes of your own choosing, sketch a graph of tension magnitude T (vertical axis) versus position y (horizontal axis) for the accelerating cable. Label the values at y=0 and y=L clearly.
(b) Describe in words how and why the shape of your graph differs from the tension-versus-position graph for the same cable hanging motionless at rest.
(c) Explain what physical quantity the slope of your graph represents, and discuss how the value of that slope is related to the acceleration a.
(d) Predict qualitatively how the graph would change if instead the cable were accelerating downward while still remaining straight. Justify your prediction.