The force required to compress a spring varies directly as the change in the length of the spring. If a force of 30 pounds is required to compress a certain spring 6 ​inches, how much force is required to compress the spring 8 ​inches?

Answer 1

We are given that the force required to compress the spring is directly proportional to the change in length of the spring. This means that the ratio of force to change in length is constant.

Let's call this constant k.

So, we have the equation:

force = k * change in length

We are given that a force of 30 pounds is required to compress the spring 6 inches. Plugging these values into the equation, we get:

30 = k * 6

To find the value of k, we can divide both sides of the equation by 6:

k = 30/6 = 5

Now, we need to find the force required to compress the spring 8 inches. Plugging this value and the value of k into the equation, we get:

force = 5 * 8

Simplifying, we find:

force = 40

Therefore, the force required to compress the spring 8 inches is 40 pounds.