Question

1. two balls collide in elastically. after the collision, the momentum of the system is 18 kg·m/s. before the collision, 1 ball had mass 3 kg and speed 1 m/s. what was the momentum of the second ball before the collision? (2 points) 15 kg·m/s -15 kg·m/s 6 kg·m/s -6 kg·m/s

Explanation:

Step1: Use the law of conservation of momentum

According to the law of conservation of momentum, the total momentum before the collision is equal to the total momentum after the collision. Let \(p_1\) be the momentum of the first ball before the collision and \(p_2\) be the momentum of the second ball before the collision. The total momentum after the collision \(P_{after}=18\space kg\cdot m/s\). The momentum of the first ball before the collision \(p_1 = m_1v_1\), where \(m_1 = 3\space kg\) and \(v_1=1\space m/s\), so \(p_1=3\times1 = 3\space kg\cdot m/s\).
Since \(P_{before}=P_{after}\), and \(P_{before}=p_1 + p_2\), then \(p_2=P_{after}-p_1\).

Step2: Calculate the momentum of the second ball

Substitute \(P_{after} = 18\space kg\cdot m/s\) and \(p_1 = 3\space kg\cdot m/s\) into the formula \(p_2=P_{after}-p_1\).
\(p_2=18 - 3=15\space kg\cdot m/s\)

Answer:

15 kg·m/s