Block of mass is stacked on top of block of mass

PHYSICS · Multi-part · A Level · Physics · Mechanics and materials · Mechanics and materials

Problem

Block

A

of mass

2.0\,\text{kg}

is stacked on top of block

B

of mass

4.0\,\text{kg}

, which rests on a horizontal floor. The coefficient of static friction between the blocks is

0.60

, and between block

B

and the floor is

0.40

. A light horizontal rope is attached to block

A

, passes over a massless, frictionless pulley at the edge of the table, and supports a hanging mass

C

of mass

3.0\,\text{kg}

that can move vertically. The rope remains taut throughout the motion. (1) Identify every pair of objects in mutual contact or interaction in this system. For each pair, list the action–reaction force pair that they exert on each other. (2) Draw separate free-body diagrams for blocks

A

B

, and mass

C

. Label all forces with appropriate symbols (e.g.,

T

N_{AB}

) and identify the interacting object responsible for each force. (3) Using your diagrams, derive the set of equations that would allow determination of whether the system moves and, if so, the acceleration. Do not solve the equations. (4) Suppose the system is released from rest and is observed to move without block

A

sliding relative to block

B

. Explain qualitatively what this observation implies about the magnitudes of the forces of friction you identified in part (b).

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