Question

two billiard balls, each with a mass of 0.21 kg, collide with each other on a pool table. before the collision, one ball is moving north at 1.7 m/s and the other ball is moving south at 2.6 m/s. what is the momentum of this system after the collision?
a. 0.19 kg·m/s south
b. 0.19 kg·m/s north
c. 0.90 kg·m/s north
d. 0.90 kg·m/s south

Explanation:

Step1: Calculate initial momentum of each ball

Momentum formula: \(p = mv\). Let north be positive.
For the first ball: \(p_1=m\times v_1 = 0.21\times1.7= 0.357\ \text{kg}\cdot\text{m/s}\)
For the second ball: \(p_2=m\times v_2=0.21\times(- 2.6)=-0.546\ \text{kg}\cdot\text{m/s}\)

Step2: Calculate total initial momentum

Total initial momentum \(p_{total}=p_1 + p_2\)
\(p_{total}=0.357-0.546=-0.189\approx - 0.19\ \text{kg}\cdot\text{m/s}\)
According to the law of conservation of momentum (\(p_{initial}=p_{final}\)), the momentum of the system after collision is equal to the total initial momentum.

Answer:

A. \(0.19\ \text{kg}\cdot\text{m/s}\) south