A block is released from rest from a height `h=5m`. After travelling through the smooth curved surface it moves on the rough horizontal surface through a length `1=8m` and climbs onto the other smooth curved surface through a height `h^'`. If `mu=0.5`, find `h^'`.

Explanation

The forces acting on the block and N, gravity and friction.
`W_f+W_f+W_(gr)=DeltaK`
where `W_N=0`, `W_f=-mumgl`
and `W_(gr)=mg(h-h^')` and `DeltaK=0`
Thus, `-mumgl+mg(h-h^')=0`
`h^'=h-mul=5-1/2xx8=1m`