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A body of mass 50 kg starts from rest a...

A body of mass 50 kg starts from rest and slides down a smooth incilined plane. Find the force ..p.. applied at an angle `30^(@)` to the inclined plane so that the body attains a velocity of `10ms^(-1)` after sliding a distance of 7m.

Text Solution

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Work done by force P in displacing the block by 7 m
`W_(1)=(F cos theta)s=P xx 7xx cos 30^(@)=(7sqrt(3))/(2)` PJ
work done by gravity
`W_(2)=(mg sin theta)S=50xx9.8xx(1)/(2)xx7=1715 J`
Using work - energy theorem, `W = Delta` K.E.
or `W_(1)+W_(2)=(1)/(2)m(v_(f)^(2)-v_(i)^(2))`
or `(7sqrt(3))/(2)P+1715=(1)/(2)xx50xx(10^(2)-0^(2))`
or `6.06 P+1715=2500 therefore P=129.5 N`
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