Question

Derive formula for potential energy stored in a stretched spring

Answer 1

Answer:

Let the extension produced in the spring on the application of force be x,

Then Internal restoring force developed in the spring = - Kx

We know,

work done by the internal restoring force = -Integral F.dx

(The work done by the internal force is negative because the direction of force and displacement are opposite.)

W = - Integral (-kx)dx

W = - (-k) integral x dx

W = k x^2/2

W = 1/2 Kx^2

Since, this work done by the internal restoring force gets stored in the spring as it's potential energy, so P.E = 1/2 kx^2

Answer 2

Expression for Gravitational Potential Energy at Height (h) – Derive ΔU = mgh. When, h<<R, then, R + h = R and g = GM/R2.