Block of mass rests on a horizontal table

PHYSICS · Multi-part · CBSE · Physics · Laws of Motion · Laws of Motion

Problem

Block

A

of mass

m_1=5.0\,\text{kg}

rests on a horizontal table. It is attached by a light, inextensible string that passes over a frictionless pulley at the table’s edge to a hanging block

B

of mass

m_2=3.0\,\text{kg}

. The coefficient of kinetic friction between block

A

and the table is

\mu_k=0.20

. The system is released from rest, and the string remains taut. Respond to the following. (a) Draw separate, fully labeled free-body diagrams for blocks

A

and

B

. (b) Derive an algebraic expression for the magnitude of the acceleration of the system in terms of

m_1

m_2

\mu_k

, and

g

. (c) Using the given numerical values, calculate (i) the acceleration of the system and (ii) the tension in the string. (d) Discuss how the acceleration would change if the mass of block

B

were gradually increased while all other quantities remained the same. Identify the value of

m_2

(in terms of

m_1

and

\mu_k

) at which the direction of acceleration would reverse.

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