Question

the kinetic energy K of a particle moving along a circle of radius R depends on the distance covered s as K=as2.What will be the force acting on particle

Answer 1

Given K.E = 1/2 mv² = as²

= mv² = 2as²

now differenciating with respect to t

2mv = dv/dt = 4as ds/dt = 4asv

mat = 2 as

Hence Ft = 2 as  here (Ft = tangential force)  ..... 1>

centripetal force = Fc = mac = mv²/R = 2 mas²/ mR = 2as²/R ..... 2>

now net force of particle is = √Ft² + F² c = √(2as)² + (2as²/R)²

= 2 as(√1 + s²/R² or 2as(1 + s²/R²) raise to power 1/2

Answer 2

Explanation:

Given K.E = 1/2 mv² = as²

= mv² = 2as²

now differenciating with respect to t

2mv = dv/dt = 4as ds/dt = 4asv

mat = 2 as

Hence Ft = 2 as  here (Ft = tangential force)  ..... 1>

centripetal force = Fc = mac = mv²/R = 2 mas²/ mR = 2as²/R ..... 2>

now net force of particle is = √Ft² + F² c = √(2as)² + (2as²/R)²

= 2 as(√1 + s²/R² or 2as(1 + s²/R²) raise to power 1/2

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