A small cart has two identical wheels of radius that can rotate independently about…
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Energy and Momentum of Rotating Systems · Energy and Momentum of Rotating Systems
Problem
A small cart has two identical wheels of radius r that can rotate independently about their fixed axles. Initially, the cart is held at rest on a horizontal track. The left wheel is suddenly spun up by an internal motor so that its rim moves backward (to the left) relative to the cart at speed u while the right wheel remains free to rotate. Immediately after the motor action ends, the cart is released and allowed to interact with the track solely through friction at the two wheel–ground contact points. Neglect rolling resistance and air drag.
(a) Right after release, identify the direction and type (static or kinetic) of the friction force acting on the left wheel. Justify your answer on the basis of the instantaneous relative motion between the left wheel's rim and the track.
(b) At the same instant, identify the direction and type of the friction force acting on the right wheel. Explain why this force differs from or matches that on the left wheel.
(c) Discuss qualitatively how the translational motion of the cart evolves until both wheels eventually roll without slipping. In your discussion, indicate any changes in the type of friction acting at either wheel during the process.
(d) Rank the magnitudes of the friction forces on the two wheels (left vs. right) during the interval when the cart is still accelerating but slipping persists on the left wheel. Provide reasoning that references how frictional limits are set by the normal force and coefficients of friction.
(e) Once pure rolling is achieved for both wheels, state the value (zero, less than zero, or greater than zero) of the friction forces, and defend your answer conceptually.