Question

An ideal spring has a spring constant \(k=20.0 \mathrm{N} / \mathrm{m}\) What is the amount of work that must be done to stretch the spring \(0.40 \mathrm{m}\) from its relaxed length?

Short answer

Answer: The amount of work that must be done to stretch the spring by 0.40 m is 1.6 Nm.

Step-by-step solution

Write down the given values

We are given the spring constant \(k=20.0 \frac{N}{m}\) and the distance the spring is stretched \(x=0.40 m\).

Write down the formula for work done on a spring

The formula for work done on a spring is: \(W = \frac{1}{2}kx^2\)

Plug the given values into the formula

Using the given values, we can rewrite the formula as: \(W = \frac{1}{2}(20.0 \frac{N}{m})(0.40 m)^2\)

Calculate the work done

Now, compute the work done by: \(W = \frac{1}{2}(20.0 \frac{N}{m})(0.16 m^2) = 1.6 \frac{N}{m} \times m^2 = 1.6 Nm\) So, the amount of work that must be done to stretch the spring \(0.40m\) from its relaxed length is \(1.6 Nm\).