The kinetic energy K of a particle moving along a circle of radius R depends upon the distance s, as K = as2. The force acting on the particle is-
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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/
= 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/
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