A small block P of mass rests on top of a larger block Q of mass
PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics
Problem
A small block P of mass 0.50kg rests on top of a larger block Q of mass 1.5kg, as shown in the side view description below. The surfaces between P and Q are rough with a coefficient of static friction μs=0.40 and a coefficient of kinetic friction μk=0.30. The lower surface of block Q slides on a horizontal tabletop that is essentially frictionless. A horizontal force F is applied to block Q, causing both blocks to accelerate together without P slipping relative to Q.
(a) Draw separate, clearly labeled free-body diagrams for block P and for block Q.
(b) Derive an inequality for the maximum magnitude Fmax of the applied force for which P will not slip. Express your answer in terms of the given quantities and fundamental constants.
(c) Calculate the numerical value of Fmax with proper units.
(d) For the case F=0.60Fmax, determine the magnitude and direction of the frictional force exerted on block P by block Q. Justify your reasoning with reference to the motion of the system and Newton’s laws.