A spring of negligible mass has force constant k = 1600 N/m. (a) How far must the spring be compressed for 3.20 J of potential energy to be stored in it? (b) You place the spring vertically with one end on the floor. You then drop a 1.20-kg book onto it from a height of 0.800 m above the top of the spring. Find the maximum distance the spring will be compressed.

Solution 19E Step 1: a) potential energy of the spring, PE = 3.20 J Force constant of the spring, k = 1600 N/m 2 The equation for potential energy in terms of force constant, PE = ½ kx Where, x - change in length for the spring 2 So, we can write, 3.20 J = ½ × 1600 N/m × x 2 2 Rearranging, x = 3.20 J/ 800 N/m = 0.004 m Taking square roots on both sides, x = 0.063 m x = 6.3 cm The spring should be compressed for 6.3 cm to store 3.20 J of PE