Question

in the physics lab, two 1 kg carts with elastic bumpers are on a frictionless track. one cart moves to the right at 0.5 m/s. it hits the other cart traveling 0.5 m/s to the left. what will happen to their momentum when they collide? (1 point) they will have the same momentum and travel the same directions as before. they will have the same momentum of 0.5 kg · m/s but will travel opposite directions. they will both have a momentum of 0 kg · m/s. one cart will have a momentum of 0 kg · m/s and the other will have a momentum of 0.5 kg · m/s.

Explanation:

Step1: Calculate initial momentum

Let the right - moving cart have velocity \(v_1 = 0.5\ m/s\) and the left - moving cart have velocity \(v_2=- 0.5\ m/s\) (negative because of opposite direction). Mass of each cart \(m = 1\ kg\).
The initial momentum of the system \(p_{initial}=m_1v_1 + m_2v_2\). Substituting \(m_1 = m_2=1\ kg\), \(v_1 = 0.5\ m/s\), \(v_2=-0.5\ m/s\)
\(p_{initial}=1\times0.5+1\times(- 0.5)=0.5 - 0.5=0\ kg\cdot m/s\)

Step2: Apply conservation of momentum

In an elastic collision (since the bumpers are elastic and the track is frictionless, no external forces act on the system in the horizontal direction), the law of conservation of momentum \(p_{initial}=p_{final}\) holds.

Answer:

They will both have a momentum of \(0\ kg\cdot m/s\).