Question

A 2.1 kg mass is attached to a spring with a spring constant of 75.3 N/m. The spring is securely attached on the other end to a vertical wall so that the spring extends and contracts horizontally. The mass is shoved so the mass has a velocity of 3.1 m/s and the spring is streched 0.128 m from its equilibrium, or rest, position when the mass is released. Friction and air resistance are negligible. What is the greatest distance that the spring will be compressed from its eqiuilibrium position after the mass is released?

Answer 1

K = 75.3 N/m g = 9.8 ms^2 when spring is pulled it stores potential energy and when mass in shoved it gets kinetic energy this net energy is stored back as potential energy of spring and gravity E_1 = E_1 1/2 mv^2 + 1/2kx_i^2 -mgx_1 = 1/2 kx^2 + mgx 5 times 2.1 times (3.1)^2 + .5 times 7 times 4x(12.8)^2 -2.1 times 28 times 128 = .5 times 75.4 times x^2 + 2 + 38 x 10.09 + 0.6188 -2.63 = 8.07 = 37.7x^2 + 20.58 x x = 0.264 m