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.

Explanation

Work done by force P in displacing the block by 7m
`W_(1) (Fcostheta)s=Pxx7xxcos30^(@)=(7sqrt(3))/(2)Pj`
work done by gravity
`W_(2)(mg sintheta)S=50xx9.8xx(1)/(2)xx7=1715j`
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))`
`or6.06 + 1715 = 2500 therefore P=129.5N`