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A plank of mass 5 kg in kept on a smooth...

A plank of mass 5 kg in kept on a smooth surface. A block of 1 kg is kept on it and is given a velcoity of 12 m/s. There is friction between the block and the plank. Assuming the plank to be very long, find the magnitude of work done (in Joules) by friction on block till the relative sliding between them stops.

Text Solution

Verified by Experts

The correct Answer is:
70
When relative sliding stops, both move with same velocity.
Only friction acts in horizontal direction.
`:.` for system no extemal force, we can apply conservation of momentum
`1xx12+5xx0=6xxv`
`v=2` m/s
Now work done by friction on block = change in kinetic energy of block
`w=(1)/(2)m(2^(2)-12^(2))=(1)/(2)(1)(4-144)=(1)/(2)(-140)=-70J`
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