A block of mass M M is placed on a semicircular track and released from rest at point P P , which is at vertical height H 1 H1 above the track’s lowest point. The surfaces of the track and block are considered to be rough such that a coefficient of friction exists between the track and the block. The block slides to a vertical height H 2 H2 on the other side of the track. How does H 2 H2 compare to H 1 H1 ?

Explanation:

A block of mass  M is placed on a semicircular track and released from rest at point  P , which is at vertical height H₁ above the track’s lowest point.

Its initial potential energy = mgH₁

Kinetic energy = 0

Total energy = mgH₁

When  block slides to a vertical height  H₂ on the other side of the track

Its final potential energy = mgH₂

Kinetic energy = 0

Total  final energy = mgH₂

As negative work is done by frictional force while block moves ,

final energy < initial energy

mgH₂ < mgH₁

H₂ < H₁

H₂  will be less than H₁ .

trig 15.3 cos

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