The spring constant of Spring A is twice as great as the spring constant of Spring B. Both springs are stretched the same amount. How does the force the Spring A applies compare to the force Spring B applies?

The force needed to stretch spring A is going to be twice as much as the force needed to stretch spring B.

Explanation:

We know that the spring constants are related as

The force needed to stretch spring A is given by

Also, the force needed to stretch spring is

Taking the ratio of the forces, we get

Since the equation above becomes

or

This shows that since the spring constant of spring A is twice as large as that of spring B, the force needed is going to be twice as large.