A block $B$ is pushed momentarily along a horizontal surface with an initial velocity $v$. If $\mu$ is the coe

Question

A block $B$ is pushed momentarily along a horizontal surface with an initial velocity $v$. If $\mu$ is the coefficient of sliding friction between $B$ and the surface, the block $B$ will come to rest after a time:

Accepted Answer

1. **Identify Forces:** The block moves horizontally. The vertical forces are weight ($mg$) downwards and normal reaction ($N$) upwards. Since there is no vertical motion, $N = mg$.
2. **Frictional Force:** The sliding (kinetic) friction force $f_k$ opposes the motion. The magnitude is given by $f_k = \mu N = \mu mg$ [NCERT Class 11, Physics Part I, Section 5.9].
3. **Determine Retardation:** According to Newton's Second Law ($F = ma$), the retardation $a$ (negative acceleration) caused by friction is:
   $$ ma = -f_k = -\mu mg $$
   $$ a = -\mu g $$
4. **Kinematics:** Use the first equation of motion $v_f = v_i + at$ to find the time $t$ when the block comes to rest ($v_f = 0$).
   $$ 0 = v + (-\mu g)t $$
   $$ \mu g t = v $$
   $$ t = \frac{v}{\mu g} $$
   (Reference: NCERT Class 11, Physics Part I, Chapter 5, Laws of Motion).

Step-by-Step Solution

Practice All PHYSICS Questions