Question

A spring of unstretched length l has a mass m with one end fixed to a rigid support. assuming spring to be made of a uniform wire, the kinetic energy possessed by it if its free end is pulled with uniform velocity v is?

Answer 1

Answer: mv^2/6

Explanation:

Mass per unit length of spring M' = m.dx/L

Where dx is the small portion of which we are calculating the mass

m=total mass

L=total length

Velocity per unit length of spring would be = V/L

Now if the spring is pulled from the free end, then it will result in expansion

So let the spring expanded with x

Now velocity of spring after expansion

V'= Vx/L

Now KE= M'V'^2/2 (KE=1/2 MV^2)

Integrate (1/2)(M/L)(Vx/L)^2.dx

Limit 0 to L

Solve and you will get the answer

Answer 2

Answer:

1/6 mv² is the answer just integrate the energy from 0 to 1