Question

A(n) 116 g ball is dropped from a height of 573 cm above a spring of negligible mass. The ball compresses the spring to a maximunm displacement of 4.35216 cm. The acceleration of gravity is 9.8 m/s? Calculate the spring force constant k. Answer in units of N/m

Answer 1

A(n) = 116 g height = 57.3 cm Maximum displacement = 4.35216 cm acceleration gravity = 9.8 m/s^2 Here in this case, the loss in gravitational potential energy is converted into elastic potential energy of the spring. i.e. mg (h + x) = 1/2 kx^2 (0.1) (9.8) (57.3 + 4.35) times 10^-2 = 1/2 K (4.35 times 10^-2)^2 (0.98) (57.3 + 4.35)times 10^-2 = 1/2 k(0.0435)^2 (0.98) (61.65) times 10^-12 = 1/2 k 18.92 times 10^-4 60.417 times 10^-2 = 1/2 k 18.92 times 10^-4 120.834 = k 18.92 times 10^-2 K = 120.834/18.92 times 10^2 k = 6.3865 times 10^2 almostequalto 638 N/m