Net/Everyday Forces

Question

You hang a spring from a tree and measure its length to be 1.0m. You suspend 15kg from the spring and i stretches to a new length of 1.4m. Find the spring constant for this spring.

Answer 1

Hi Hailey,

We know a few things from the word problem. Firstly, we know that the initial length of the spring without any weight on it is 1 meter. Therefore, we can write that:

length (initial) = 1.0m

We know that the mass of the weight that is applied to the spring is 15kg. Therefore, we can write that:

mass (weight) = 15kg

Finally, we know that the final displacement of the spring after the weight is applied is 1.4 meters. Therefore, we can write that:

length (final) = 1.4 m

Now, Hooke's Law states that the Force applied to a spring is equal to the spring constant times the displacement of the spring from its natural state:

F = kx

We know that the only force applied to the spring is applied the by the force generated by gravity acting on the weight, which we can calculate as follows:

F = mg

We know that the final length of the spring after it is stretched is 1.4 m, and that without anything applied to the spring, the length is 1.0 m. Therefore, to calculate the length that the spring is displaced after the weight is placed on it, we do the following:

x = 1.4 - 1.0

x = .4 m

Applying the Force that was calculated above to Hooke's Law, we get:

F = kx

mg = kx

Solving for k, the spring constant, we get:

k = mg/x

Plug in the appropriate values and solve for k!

Thanks, and I hope this helps.