Question

scenario 3: 100% elastic collision between two particles of different mass and same initial velocity.
before collision
after collision

1. what is the relationship between the initial and final total momentums in scenario 3?
2. describe the motion of the particles before and after the collation in scenario 3.

Explanation:

Step1: Calculate initial momentum of each particle

The formula for momentum is \(p = mv\).
For particle 1: \(m_1=1.0\space kg\), \(v_1 = 0.50\space m/s\), so \(p_1=m_1v_1=1.0\times0.50 = 0.50\space kg\cdot m/s\)
For particle 2: \(m_2 = 0.5\space kg\), \(v_2=- 0.05\space m/s\), so \(p_2=m_2v_2=0.5\times(-0.05)=-0.025\space kg\cdot m/s\)

Step2: Calculate total initial momentum

\(p_{total - initial}=p_1 + p_2\)
\(p_{total - initial}=0.50+( - 0.025)=0.475\space kg\cdot m/s\)
In an elastic collision, the law of conservation of momentum states that the total initial momentum is equal to the total final momentum.

Answer:

The total initial momentum is equal to the total final momentum. So the relationship between the initial and final total momentums in scenario 3 is that they are equal, i.e., \(p_{total - initial}=p_{total - final}=0.475\space kg\cdot m/s\)