A small block of mass `20kg` rests on a bigger block of mass `30kg`, which lies on a smooth horizontal plane. Initially the whole system is at rest. The coefficient of friction between the blocks is `0.5`. The horizontal force `F=50N` is applied on the lower block.

a. Find the work done by fricitonal force on upper block and on the lower block in `t=2s`.
b. Is the magnitude of work done by the frictional force on upper and lower blocks same?
c. Is the work done by the frictional force on the upper block converted to heat or mechanical energy or both?

Answer

a. `40J`; `-40J`; b. yes; c. onley mechanical energy.

Explanation

a. Assume that `20kg` and `30kg` blocks moves together
`a=50/50=1ms^-2`
Frictional force on `20kg` block is `f=20xx1=20N`
The maximum value of frictional force is
`f_(max)=1/2xx20g=100N`
Hence, no slipping is occuring.
The value of frictional force is `f=20N`
Distance travelled in `t=2s`,
`S=1/2xx1xx4=2m`
Work done by frictional force on upper block is
`W_(fri)=20xx2=40J`
Work done by frictional force on lower block is
`-20xx2=-40J`
b. Yes.
c. Work done by frictional force on the upper block is converted to its kinetic energy, so only mechanical energy.