Question

An object attached to the end of a vertical spring causes it to stretch 3.0 cm giving the spring 29 mJ of potential energy. What is the mass of the object? 

 

  

 

Answer 1

We know the energy, so, we can find the spring constant:

$$E=\frac12 kx^2,\\\space\\ k=\frac{2E}{x^2}=64.4\text{ N/m}.$$

Now use Hooke's law to find the mass. The elastic force is equal to the weight, or

$$kx=mg, \\\space\\ m=\frac{kx}{g}=0.197\text{ kg}.$$