Question

An observed and a vehicle, both starts moving together from rest with accelerations `5 m//s^(2)` and `2 m//s^(2)`, respectively. There is a `2 kg` block on the floor of the vehicle, and `mu = 0.3` between their surfaces. Find the work done by friction on the block with respect to the running observer, during first `2` seconds of the motion.
.
A. `24J`
B. `-24J`
C. `16J`
D. `36J`

Answer 1

Correct Answer - B
`f_("limiting")=mumg=0.3xx2.10=6N`
Force needed for accn of `2m//s^(2)`
`F=ma=4N`
So friction force is static `f=4N`
displacement w.r.t observer in `t=2` sec is
`S=U_("rel")t+1/2a_("rel") t^(2)=01/2(-3)xx4=-6m`
`W=vecf.vecS=4(-6)=-24J`