Question

An observer and a vehicle, both start moving together from rest (towards right) with acceleration $5m/s^2$ and $2m/s^2$, respectively. There is a $1kg$ block on the floor of the vehicle and coefficient of friction is $\mu =0.3$ between their surfaces. What is the magnitude of the work done (in $J$) by frictional force on the $1kg$ block observed by the running observer, during first second of the motion.

Answer 1

Limiting value of frictional force on the block is $f_r$

$f_{rmax}=\mu mg=0.3\times 10=2N$

Pseudo force acting on block $=m{a}_1=\times 2=N$

Here $f_{rmax}>m{a}_1$ (therefore block do not move relative to vehicle)

Frictional force act $f_r=m{a}_1=2N$

Relative acceleration of vehicle w.r.t man is $a_r=-5+2=-3m/s^2$

Charge in speraation $=y=\frac{1}{2}{a}_r{t}^2$

for $t=1,y=\frac{-1}{2}\times 3\times 1=\frac{-}{2}m$

Work done by frictional force $=f_r\times y=-3J$