Question

A 0.98 kg ball is placed on a vertical 55.71 N/m spring that is compressed 43.14 cm. When the spring is released, how high above its starting point will the ball go?

Answer 1

F = - K X

X = .4314 m compression of spring

F = 55.71 N/m * .4314 m = 24.03 N force to compress spring

E = 1/2 K X^2 energy of compressed spring

E = 1/2 55.71 N / m * (.4314 m)^2 = 5.184 Joules energy of spring

1/2 M V^2 = E energy imparted to ball

V = (2 E / M)^1/2 = 3.25 m/s max speed of ball

M g H = 1/2 M V^2 calculate height of ball after release

H = E / (M g) height above spring

H = 5.184 / (.98 * 9.80) = .540 m height to which ball rises

.540 + .4314 = .972 m height above compression point