Question

A spring has a natural length of 0.1250 m and a spring constant of 2550 N/m. How much potential energy will the spring have if it’s compressed to a length of 0.1125 m?

Answer: (0.119 J)

Answer 1

Answer 2

1. Given:

• Natural length of the spring ($L_0$) = 0.1250 m

• Compressed length ($L$) = 0.1125 m

• Spring constant ($k$) = 2550 N/m

• 
  

2. Calculate the compression distance ($x$):

   $$x=L_0-L=0.1250\text{m}-0.1125\text{m}=0.0125\text{m}$$

4. Use the formula for spring potential energy ($U$):

   $$U=\frac{1}{2}k{x}^2$$

   Plug in the values:

   $$U=\frac{1}{2}(2550\text{N/m})(0.0125\text{m}{)}^2$$$$U=\frac{1}{2}\times 2550\times 0.00015625$$$$U=1275\times 0.00015625\text{J}$$$$U\approx 0.119\text{J}$$

Final Answer: The spring stores 0.119 J of potential energy when compressed