A student investigates a rotational device whose driving mechanism supplies the…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A student investigates a rotational device whose driving mechanism supplies the following piece-wise constant torque as it turns through a total angle of θ=60∘:
• For 0≤θ<30∘, the applied torque is +4.0N⋅m (counter-clockwise).
• For 30∘≤θ≤60∘, the applied torque is −2.5N⋅m (clockwise, opposite the initial direction).
Treat counter-clockwise rotation as the positive angular direction.
(a) Sketch a qualitative graph of torque versus angular position over the entire 60∘ rotation, labeling numerical values on both axes.
(b) Calculate the work done on the device during the initial 30∘ interval.
(c) Calculate the work done during the final 30∘ interval and determine the net work performed over the full 60∘ rotation.
(d) If the goal is to have zero net work after 60∘, determine the magnitude and direction of a single additional constant torque that must be applied over the final 30∘ interval to achieve this objective. Explain your reasoning.