Physics

Problem

A light, inextensible string passes over an ideal pulley connecting two blocks. Block X of mass

m_1

rests on a horizontal rough table, while block Y of mass

m_2

hangs freely. The coefficient of kinetic friction between X and the table is

\mu_k

(take

\mu_k<\mu_s

). Assume the system has already started sliding. a. (i) Derive an expression for the magnitude of the common acceleration

a

of the two blocks in terms of

m_1

m_2

\mu_k

, and

g

. b. (ii) Obtain a corresponding expression for the tension

T

in the string while the blocks are in motion. c. (iii) Evaluate

a

and

T

for

m_1 = 3.0\,\text{kg}

m_2 = 2.0\,\text{kg}

, and

\mu_k = 0.20

. (Take

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