A spring 40mm long is stretched by the application of a force. If 10N force is required to stretch the spring through 1mm, then the work done in stretching the spring through 40mm is:

To find the work done in stretching the spring, we can use the formula for work done on a spring, which is based on Hooke's Law. Hooke's Law states that the force required to stretch or compress a spring is proportional to the distance it is stretched or compressed.

Understanding the Calculation

The formula for work done (W) on a spring is:

W = 0.5 × k × x²

Where:

• W = work done
• k = spring constant (force per unit length)
• x = distance stretched or compressed

Finding the Spring Constant

From the problem, we know that a force of 10 N stretches the spring by 1 mm (0.001 m). Thus, the spring constant (k) can be calculated as:

k = F / x = 10 N / 0.001 m = 10000 N/m

Calculating Work Done

Now, we can calculate the work done in stretching the spring through 40 mm (0.04 m):

W = 0.5 × 10000 N/m × (0.04 m)²

W = 0.5 × 10000 × 0.0016 = 8 J

Final Result

The work done in stretching the spring through 40 mm is 8 joules.