Question

As a section of an workout program to toughen their pectoral muscles a person stretches a spring which has a spring constant k = 520 N/m. Write an equation for the work necessary to stretch the spring from the relaxed state to a distance x1.

Answer 1

To develop the problem it is necessary to apply the concepts related to Hooke's Law. For which it is understood that

`F = kx`

Where,

k = Spring constant

x = Displacement of Spring

By the theorem of work we understand that it is the force realized when there is the path of an object therefore

`dW =Fdx`

Our value of F is

`dW = (kx)dx`

Integrating

`W = k\int\limit_0^(x_1) xdx`

Therefore the expresion is

`W = (kx_1^2)/(2)`