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

$W = \frac{kx_1^2}{2}$