A heavy swinging door in a restaurant is held open by a torsion spring
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A heavy swinging door in a restaurant is held open by a torsion spring. When the door is displaced by an angle θ from its closed position, the spring exerts a restoring torque τspring that is directly proportional to θ. A person pushes on the door with a constant applied torque τpush in the direction opposite to the spring torque, closing the door slowly from an initial angle θi to the fully closed position θ=0. During the motion, the only significant torques acting on the door are τspring and τpush; friction is negligible.
(a) On your answer sheet, draw qualitatively accurate, separate torque–versus–θ graphs for τspring and τpush over the interval from θ=0 to θ=θi. Label all relevant intercepts and slopes.
(b) Using geometric reasoning based on your graphs, derive an algebraic expression for the net rotational work Wnet done on the door by the person during the closing motion in terms of τpush, θi, and any necessary constants of proportionality for the spring torque.
(c) The manager wants to minimize the work required to close the door without replacing the spring. Suggest one practical change the person could make to reduce the required work and justify your suggestion using your expression from part (b).