an 114 g mass is dropped from rest at a height of 64.1 cm above a spring of negligible mass. The mass then compresses the spring to a maximum displacement of 4.1081 cm. What is the spring force constant k of the spring

K = 903.98 N/m

Explanation:

We are given;

Mass; m = 114 g = 0.114 kg

Height; h = 64.1 cm = 0.641m

Maximum displacement; x = 4.1081 cm = 0.041081 m

From law of conservation of energy;

Initial potential energy = final potential energy.

So;

mg (h + x) = ½Kx²

Where k is springs constant.

So, plugging in the relevant values, we have;

0.114 * 9.81 (0.641 + 0.041081) = ½ * K * 0.041081²

0.762798 = 0.00084382428K

K = 0.762798/0.00084382428

K = 903.98 N/m