A block of mass rests on a horizontal table and is connected by a light

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

Problem

A block of mass

m_1

rests on a horizontal table and is connected by a light, inextensible string over a smooth pulley at the table’s edge to a hanging block of mass

m_2

. The coefficient of kinetic friction between

m_1

and the table is

\mu_k

. (a) Taking downward motion of

m_2

as positive, derive an expression for the common acceleration of the two-block system in terms of

m_1

m_2

\mu_k

and

g

. (b) Hence obtain an expression for the tension in the string. (c) For

m_1 = 6\,\text{kg}

m_2 = 3\,\text{kg}

and

\mu_k = 0.15

, calculate the numerical values of the acceleration and the tension. (d) Determine the value of

\mu_k

for which the system would move with uniform velocity once set in motion.