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the kinetic energy of a particle moving along a circle of radius R depends on the distance covered s as KE = as^2 where a is constant . find force acting on particle as function of s
Asked by keshavgoyal9pro | 21 May, 2022, 19:59: PM
Expert Answer
Let us consider a particle starts from rest and attains kinetic energy ( a s2 ) after moving a distance s in circular path
By work-energy theorem , workdone W = ( a s2 )
Force Ft = dW/ds = ( 2 a s )
Above force Ft is acting along tangential direction .
If kineteic energy at a distance s is (a s2 ) , then we get velocity at a distance s as
(1/2) m v2 = a s2 or v2 = ( 2 a s2 ) /m
Radial force ( centripetal force ) , Fr = m ( v2 / R ) = ( 2 a s2 ) / R
Radial force Fr and tangential force Ft are perpendicular to each other. Hence , resultant force FR is given as
Direction of force makes angle θ with radial force so that , tanθ = Ft / Fr = ( 2 a s ) / [ ( 2 a s2 ) / R ] = ( R / s )
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