A block of mass rests on a horizontal tabletop

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

Problem

A block

A

of mass

4.0\,\text{kg}

rests on a horizontal tabletop. It is connected by a light string that passes over a small, frictionless pulley to a hanging block

B

of mass

m_B

(see verbal description). The coefficients of friction between block

A

and the table are

\mu_s = 0.40

and

\mu_k = 0.25

. Assume the string remains taut at all times. (a) Draw separate free–body diagrams for blocks

A

and

B

while the system is released from rest. (b) Derive an inequality that gives the range of values of

m_B

for which the system remains at rest. (c) Let

m_B = 2.0\,\text{kg}

. Determine the magnitude and direction of the acceleration of each block after release. Show all steps clearly. (d) For the mass in part (c), calculate the tension in the string and the kinetic friction force acting on block

A

once motion has begun. (e) Starting from rest, block

B

descends

0.80\,\text{m}

. Compute its speed at that point, neglecting any rotational inertia of the pulley.

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