PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
Block m1=2.0kg rests on a horizontal tabletop. A second block m2=1.5kg sits on top of m1. A light string is wrapped around m1, passes horizontally over a frictionless pulley at the edge of the table, and supports a hanging block m3 of variable mass. The coefficient of static friction between m1 and the table is μs1=0.42; the coefficient of kinetic friction is μk1=0.30. Between m2 and m1, the coefficients are μs2=0.55 and μk2=0.40. The string remains taut, and the pulley is ideal.
(a) Draw separate free–body diagrams for all three blocks when the system is released from rest.
(b) Derive an expression for the range of values of m3 for which m2 remains at rest relative tom1 while the system accelerates.
(c) For the lower bound of m3 found in part (b), determine the magnitude of the acceleration of the system and the tension in the string.
(d) If m3 exceeds the upper bound found in part (b) so that m2 begins to slide, derive expressions for the acceleration of each block in terms of m3. Simplify your results as much as algebra permits.
(e) Explain qualitatively how the acceleration of m2 changes as m3 is increased well beyond the upper bound, and discuss the physical reason for any limiting behavior you identify.