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**1. Homework Statement**

A spring scale hung from the ceiling stretches by 6.3 cm when a 1.2 kg mass is hung from it. The 1.2 kg mass is removed and replaced with a 1.4 kg mass. What is the stretch of the spring?

F=mg

U (spring force) = 1/2kx^2

**2. Homework Equations**

The units of cm need to be converted into m, so 6.3cm becomes 0.063m. Units of kg are kept the same.

To solve the problem we need to find k, the spring constant.

**3. The Attempt at a Solution**

First, I'm going to use the first situation with the displacement and mass given to determine the spring constant.

F = mg; F = (1.2kg)(9.8m/s^2); F = 11.76N

F = U;

U = 1/2kx^2

F = 1/2kx^2

k = 2F/x^2

k = 2(11.76N)/0.063m^2

k = 5925.9

From there I plugged the spring constant into the second situation.

F = mg; F = (1.4kg)(9.8m/s^2) = 13.72N

U = 1/2kx^2

x = sqrt of 2*F/k

x = sqrt 2(13.72N)/5925.9

x = 0.068 m or 6.8 cm.

This final answer for displacement is incorrect and I am unsure of my mistake. Did I make a calculation error or set the problem up incorrectly?

Thank you in advance for your help!