Q4.17 Dissipation (S)
A block of mass 10 kg slides a distance 1 m down a 45∘ slope. The coefficient of kinetic friction between the block and slope is 0.2. By how much does the kinetic energy of the block increase?Solution
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Solution
As in question Q4.16, the magnitude of the normal reaction exerted by the sloping surface on the block is
FN=mgcosθ.
The magnitude of the frictional force is
FF=μkmgcosθ
In travelling d=1m down the slope, the block drops a vertical distance
of . The gravitational potential energy thus changes
by
. In the absence of friction,
all of this would appear as an increase in kinetic energy. But in 1 m
of motion down the slope, the frictional force dissipates FFd=13.9 J of
mechanical energy, leaving 55.4 J as kinetic energy.
(Note that the frictional force is path dependent; a different path means
a different answer.)