Spring compression with given mass

Question

If a spring of negligible mass has force constant k= 7500 N/m

a) How far must the spring be compressed for 500 J of potential energy to be stored in it?

b) If you place the spring vertically with one end on the floor and then drop a 350kg brick onto it from a height of 2.2m above to the top of the spring, how will you find the maximum distance the spring will be compressed?

Answer 1

a) P = k(Δx)²/2; Δx = √2P/k = √2·500J/7500N/m = 0.365 m

b) mgh + mgΔx = k(Δx)²/2; 7500(Δx)²/2 = 350·9.8·2.2 + 350·9.8·Δx; 7500(Δx)² - 6860Δx - 15092 = 0;

Δx = (3430 + √3430² + 7500·15092)/7500 = 1.948 m