Kinetic energy of a particle moving along a circle of radisu R depends on the distance covered as `K =as^(2)` where a is a constant . Find the force acting on the particle as a function of s.

Explanation

`KE = 1/2 (mv)^(2) = cs^(2) Rightarrow v = (sqrt(2C)/m)s`
`a_(t) = (dv)/(dt) = sqrt((2c)/(m)) xx (ds)/(dt) = v sqrt((2c)/(m))`
`F_(t) = ma_(t) = mvsqrt((2C)/(m)) = [m sqrt ((2C)/(m)s]sqrt(2c)/(m) ) = 2cs`
Total force `F = sqrt((F_(t)^(2) + F_(c)^(2)) = sqrt((2cs)^(2) + (mv^(2))/(r))^(2)`
`F = 2cs sqrt(1 + (s^(2))/(r^(2))`