Find total work done by friction assuming plank is sufficiently long.

Solve this question in both ground frame and C-frame.

Explanation

In ground frame:
let `v` be the final velocity of block & plank when relative motion ceases between block and plank,
applying conservation of linear momentum, `m u=(2m+m)v`
`therefore" "v=u//3`
`w_(f)=`change in `K.E.=K.E._(f)-K.E._(i)`
`w_(f)=(1)/(2)-3m((u)/(3))^(2)-(1)/(2)m u^(2)=-(m u^(2))/(3)`
In C-frame:
Considering block and plank as system
Work done by friction is change in kinetic energy
`w_(f)=`change in `K.E.=K.E._(f)-K.E._(i)`
`K.E._(i)=(1)/(2)mu(u-0)^(2)+((2m+m)v_(c)^(2))/(2)" "(mu=(2mxxm)/(2m+m))`
`K.E._(f)=0+((2m+m)v_(c)^(2))/(2)` (`v_(c)` is constant as external force is zero)
`w_(f)=K.E._(f)-K.E._(i)=-(m u^2)/(3)`
Note: `P_(sys)=` conserved if `f_(ext.=0` although internal friction are doing work.