Question

A 6.0-kilogram ball and a 3.0-kilogram ball are initially at rest on a frictionless, horizontal surface. Once a compressed spring between the balls is released, the 6.0-kilogram ball moves to the right at 5.0 meters per second. Which of the following is the speed of the 3.0-kilogram ball after the spring is released?

a) 10 m/s
b) 15 m/s
c) 20 m/s
d) 30 m/s

Answer 1

The speed of the 3.0-kilogram ball after the spring is released can be found using the conservation of momentum. Momentum must be conserved, resulting in a speed of 10 m/s in the opposite direction of the 6.0-kilogram ball's velocity.

Step-by-step explanation:

The speed of the 3.0-kilogram ball after the spring is released can be found using the principle of conservation of momentum. Before the spring is released, the system's total momentum is zero since both balls are at rest. After release, the total momentum should remain zero. To find the velocity (v) of the 3.0-kilogram ball, use the equation m1 * v1 + m2 * v2 = 0, where m1 and v1 are the mass and velocity of the 6.0-kilogram ball and m2 and v2 are the mass and velocity of the 3.0-kilogram ball.

(6.0 kg)(5.0 m/s) + (3.0 kg)(v) = 0 solving for v, we get v = -(6.0 kg * 5.0 m/s) / 3.0 kg = -10 m/s. The negative sign indicates that the 3.0-kilogram ball moves in the opposite direction to the 6.0-kilogram ball. Therefore, the correct answer is a) 10 m/s.