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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
answered-by-expert 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
 
Error converting from MathML to accessible text.
Direction of force makes angle θ with radial force so that , tanθ = Ft / Fr = ( 2 a s ) / [ ( 2 a s2 ) / R ] = ( R / s )

Answered by Thiyagarajan K | 21 May, 2022, 23:31: PM
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