Why Must Velocities Remain Constant in a Momentum Conservation Demonstration?

[jsmith613]

Homework Statement

A teacher demonstates the conservation of momentum using a collision between a moving an a stationary trolley. Both trolleys stick together AFTER the collision. She measures the velocities using a motion sensor and data logger. Explain why the velcoties before and after the collision must be constant if the principle is to be convincingly demonstrated

Homework Equations

The Attempt at a Solution

the momentum before and after MUST be the same
BUT initially the momentum = mass of moving trolley * its speed

after the total mass of both trolleys is greater than that of the lone trolley so the speed should be less. How does the question make sense

 

[jedishrfu]

okay so if before the collision the first trolley was speeding up what velocity would you use to compute the momentum before the collision?

Would you use the average velocity, the initial velocity or the velocity at the moment of collision?

The question is designed to give you a better understanding of conservation of momentum. In the case of the trolleys, it could be San Francisco and the first trolley is free rolling downhill (meaning it rolls faster and faster) until it collides with the stationary trolley and they both continue to roll which could be downhill, level or uphill.

 

[jsmith613]

okay so if before the collision the first trolley was speeding up what velocity would you use to compute the momentum before the collision?

Would you use the average velocity, the initial velocity or the velocity at the moment of collision?

The question is designed to give you a better understanding of conservation of momentum. In the case of the trolleys, it could be San Francisco and the first trolley is free rolling downhill (meaning it rolls faster and faster) until it collides with the stationary trolley and they both continue to roll which could be downhill, level or uphill.

sorry, I don't get how this is relevant
the trolley is moving at a FIXED speed so the final velocity should be less

NOTE: this is a REAL exam question which is why I am confused

 

[jedishrfu]

Doesn't it say:

"Explain why the velcoties before and after the collision must be constant if the principle is to be convincingly demonstrated."

So my discussion was considering what if they were changing, which velocity would you choose. Using the measurement tools you might wind up with an averaged velocity before and after and you might then conclude that conservation of momentum wasn't conserved.

 

[asteriatic]

I would say that the principle of momentum conservation states that the total momentum of a closed system remains constant before and after a collision. In this scenario, the initial momentum of the moving trolley is equal to the final momentum of the combined trolleys after the collision. This is because the momentum of the stationary trolley is initially zero, and after the collision, the two trolleys stick together and move with a common velocity. Therefore, the total mass of the combined trolleys is greater than that of the lone trolley, resulting in a lower velocity to maintain the same momentum. This demonstrates the conservation of momentum and supports the principle.