Consider the following setup with three identical springs, a ruler for length measurements and three known masses and three unknown masses. You previously explored the force applied by the spring on a mass by hanging each of the known masses on a separate identical spring to determine the spring constant kk. Here we want to determine the mass of some unknowns. You hang each of the unknown colored masses on the same springs you characterized previously. From the displacement of the springs from the original equilibrium position, what is the mass of the green mass

To find the value of the unknown weight, we previously placed the 3 known weights and made a graph of the force against displacement

When hanging the weight is known, we measure the displacement and from the graph we can find the value of the hanging masses

We can also use the equation and multiply the constant K by the displacement and this is the applied weight.

Explanation:

For this problem we will use the translational equilibrium relation

        F –W = 0

        F = W

        W = mg

The spring elastic force is

        F = - k x

We substitute

        k x = m g

Where we see that the force of the spring is equal to the weight of the body.

To find the value of the unknown weight, we previously placed the 3 known weights and made a graph of the force against displacement

When hanging the weight is known, we measure the displacement and from the graph we can find the value of the hanging masses

We can also use the equation and multiply the constant K by the displacement and this is the applied weight.

the answer is b ) square root of 5