Question

A ball of mass m = 1.60 kg is released from rest at a height h = 77.0 cm above a light vertical spring of force constant k as in Figure [a] shown below. The ball strikes the top of the spring and compresses it a distance d = 8.10 cm as in Figure [b] shown below. Neglecting any energy losses during the collision, find the following.

(a) Find the speed of the ball just as it touches the spring.

I GOT THIS ANSWER: 3.885 m/s

(b) Find the force constant of the spring.

Answer 1

Gravitational acceleration = g = 9.8 m/s²

Mass of the ball = m = 1.6 kg

Height from which the ball was released = h = 77 cm = 0.77 m

Speed of the ball just as it touches the spring = V

By conservation of energy the potential energy lost by the ball is converted into the kinetic energy of the ball.

V = 3.885 m/s

Force constant of the spring = k

Distance the spring compresses = d = 8.1 cm = 0.081 m

By conservation of energy the potential and kinetic energy of the ball as it touches is equal to the potential energy of the spring as the ball compresses the spring.

k = 4068 N/m

k = 4068/1000 kN/m

k = 4.068 kN/m

a) Speed of the ball just as it touches the spring = 3.885 m/s

b) Force constant of the spring = 4.068 kN/m