Question

A certain spring has a spring constant k1 = 660 N/m as the spring is stretched from x = 0 to x1 = 35 cm. The spring constant then changes to k2 = 250 N/m as the spring is stretched to x2 = 65 cm. From x2 = 65 cm to x3 = 89 cm the spring force is constant at F3 = 105 N.

Write an equation for the work done in stretching the spring from x1 to x2.
Calculate the work done, in joules, in stretching the spring from x1 to x2.
Calculate the work, in joules, necessary to stretch the spring from x = 0 to x3.

Answer 1

The equation for the work done in stretching a spring is derived from the potential energy equation. Calculating the work done involves finding the difference between the potential energies at the initial and final positions of the spring. The work done can be determined using the formula: Work = (1/2 k2*x2^2) - (1/2 k1*x1^2).

Step-by-step explanation:

To calculate the work done in stretching the spring from x1 to x2, we can use the equation for the potential energy of a spring:

PEs = 1/2 kx2

Where PEs is the potential energy stored in the spring, k is the spring constant, and x is the displacement of the spring from its equilibrium position.

In this case, the work done in stretching the spring from x1 to x2 is given by:

Work = PEs2 - PEs1

Where PEs2 is the potential energy at x2 and PEs1 is the potential energy at x1.

Plugging in the given values:

PEs1 = 1/2 k1x12

PEs2 = 1/2 k2x22

So the equation for the work done in stretching the spring from x1 to x2 is:

Work = (1/2 k2x22) - (1/2 k1x12)