A spring hangs from the ceiling with an unstretched length of x 0 = 0.35 m . A m 1 = 6.3 kg block is hung from the spring, causing the spring to stretch to a length x 1 = 0.50 m . Find the length x 2 of the spring when a m 2 = 3.7 kg block is hung from the spring. For both cases, all vibrations of the spring are allowed to settle down before any measurements are made.

x₂=0.44m

Explanation:

First, we calculate the length the spring is stretch when the first block is hung from it:

Now, since the stretched spring is in equilibrium, we have that the spring restoring force must be equal to the weight of the block:

Solving for the spring constant k, we get:

Next, we use the same relationship, but for the second block, to find the value of the stretched length:

Finally, we sum this to the unstretched length to obtain the length of the spring:

In words, the length of the spring when the second block is hung from it, is 0.44m.

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