Question

If it requires 6.0 J of work to stretch a particular spring by 0.02 m from its equilibrium length, how much more work will be required to stretch it an additional 0.04 m?

A) 0.60 J
B) 3.0 J
C) 6.0 J
D) 12.0 J

Answer 1

The additional work required to stretch the spring an additional 0.04 m is 3.0 J.

Step-by-step explanation:

To calculate the work required to stretch the spring an additional distance of 0.04 m, we can use the formula for work done by a spring force:

Work = 1/2 * k * (x^2 - x0^2)

Where:

k is the spring constant, x is the final displacement, and x0 is the initial displacement.

In this case, we are given the initial work (6.0 J) and initial displacement (0.02 m). We need to find the final displacement to calculate the additional work.

Using the formula above, we can set up the equation:

6.0 J = 1/2 * k * (0.02 m)^2

Solving for the spring constant:

k = (2 * 6.0 J) / (0.02 m)^2

k = 600 N/m

Now, we can calculate the additional work:

Additional work = 1/2 * 600 N/m * ((0.02 m + 0.04 m)^2 - 0.02 m^2)

Additional work = 3.0 J