Block of mass rests on a horizontal surface

PHYSICS · Multi-part · AP · Physics 1: Algebra-based · Force and Translational Dynamics · Force and Translational Dynamics

Problem

Block

A

of mass

3.0\,\text{kg}

rests on a horizontal surface. It is connected by a light, inextensible string that passes over an ideal (massless, frictionless) pulley at the table’s edge to block

B

of mass

2.0\,\text{kg}

, which hangs vertically. The coefficient of kinetic friction between block

A

and the table is

\mu_k = 0.15

. The acceleration due to gravity is

g = 9.8\,\text{m}\,\text{s}^{-2}

. (1) Part (a) Draw separate free-body diagrams for block

A

and block

B

. Clearly label all forces acting on each block. (2) Part (b) For each block, write an expression of Newton’s second law along the chosen coordinate axes. (3) Part (c) Solve for (i) the magnitude of the common acceleration of the blocks and (ii) the tension in the string. (4) Part (d) Discuss qualitatively how the acceleration found in part (c) would change if the string had significant mass, and explain your reasoning based on the forces acting within the system.

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