Question

carts on a track
a collision is an incident where two objects hit each other and the net external force is zero or negligible. the total momentum of a system of objects is conserved when there is no net force on the system. collisions can happen between many different types of objects. consider a frictionless track with two carts of equal mass in a physics lab.
a student observes a collision in which the first cart collides with the second cart. the first cart has a speed, v, and the second cart is initially at rest. both carts have a mass, m. immediately after the collision, the carts stick together and move at a speed of v/2.
was momentum conserved in the system? what can you conclude about the presence of external forces acting on the two - cart system?

Explanation:

Step1: Calculate initial momentum

The initial momentum of the first - cart is $p_1 = mv$ and the second cart is initially at rest so $p_2=0$. The total initial momentum $p_{i}=mv + 0=mv$.

Step2: Calculate final momentum

After the collision, the two carts stick together. The combined mass is $m + m=2m$ and the velocity is $\frac{v}{2}$. So the final momentum $p_{f}=(m + m)\times\frac{v}{2}=2m\times\frac{v}{2}=mv$.

Step3: Analyze momentum conservation

Since $p_{i}=mv$ and $p_{f}=mv$, we have $p_{i}=p_{f}$. According to the law of conservation of momentum, if the total initial momentum of a system is equal to the total final momentum of the system, momentum is conserved. Also, since momentum is conserved, we can conclude that the net external force acting on the two - cart system is zero or negligible (because the law of conservation of momentum holds when there is no net external force on the system).

Answer:

Momentum was conserved in the system. We can conclude that the net external force acting on the two - cart system is zero or negligible.