Question

A spring of negligible mass has force constant k=900 N/m How far must the spring be compressed for 110 J of potential energy to be stored in it? Express your answer to three significant figures and include the appropriate units.

Answer 1

The spring must be compressed by 0.494 meters to store 110 J of energy, calculated using the potential energy formula U = (1/2)kx^2 with the given spring constant of 900 N/m.

Step-by-step explanation:

To calculate how far the spring must be compressed for 110 J of potential energy to be stored in it, you can use the formula for the potential energy stored in a compressed or stretched spring: U = (1/2)kx^2, where U is the potential energy, k is the spring constant, and x is the compression (or stretch) distance from the spring's natural length. You are given a spring with a force constant k=900 N/m and a potential energy of 110 J. By substituting the known values into the potential energy formula and solving for x, we get 110 J = (1/2)(900 N/m)x^2. To find x, you would rearrange the equation: x^2 = (2*110 J) / (900 N/m), x^2 = 0.2444 m^2, x = √0.2444 m^2, x = 0.4944 m. Therefore, the spring must be compressed by 0.494 m (to three significant figures) to store 110 J of potential energy.