A block is at rest on a horizontal surface

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

Problem

2.5\,\text{kg}

block is at rest on a horizontal surface. Starting from

t = 0

, it is pulled by a horizontal force that varies with time as

F(t) = F_0 \sin \left( \dfrac{\pi t}{2T} \right)

for

0 \le t \le T

and is zero afterwards. Here

F_0 = 20\,\text{N}

and

T = 4\,\text{s}

. The coefficients of friction are

\mu_s = 0.32

and

\mu_k = 0.25

. Take

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

. (i) Obtain an expression for, and hence calculate, the time

t_1

at which the block starts sliding. (ii) Derive an expression for the speed

v(T)

of the block at

t = T

. (iii) Evaluate

v(T)

numerically with the given data.