Momentum Problem - Is it correct?

[AnomalyCoder]

Homework Statement

A 4kg traveling at 14m/s collides with a stationary 8kg cart. The collision causes the 4kg cart to completely stop, and sets the 8kg cart in motion. Determine the velocity of the 8kg cart after the collision.

Homework Equations

m1 = -m2
VFinal-VInitial = m

The Attempt at a Solution

Initially the velocity of the 4kg is 4kg*14m\s, or 56kgm/s.
After it halts completely, therefore a velocity of 0.
m1 = 0-56kgm\s.

Next the 8kg cart; initially it is at 0kg\s.
After it is 8kg*x.
(8x-0) = m2

Thus -56kgm\s = 8x;
x = -7kg/s.

m1 = -m2, therefore -7 becomes 7?

I'm not sure if this is correct. Any help, tips, and resources appreciated.

 

[lineintegral1]

Your units are all over the place. But the general idea is correct. Momentum is conserved because there is no force acted on the system. Therefore, the momentum before the collision equals the momentum after the collision. Thus, since your original mass is 4 kg and it is traveling at 14 m/s, it's momentum is 14 * 4. This must be the same as the other object's momentum afterwards. Therefore, the magnitude of the second object's velocity is simply half of the first object's velocity.

 

[rl.bhat]

Total momentum before collision = total momentum after collision. There is no negative sign.

 

[ashishsinghal]

Total momentum before collision = total momentum after collision. There is no negative sign.

He has used the same concept but written it as:

momentum lost by one body = momentum gained by the other.
since there is "gained" at one place and "lost" at the other there is a negative sign.

 

[rwisz]

Your approach and equations are correct. However, there is a minor mistake in your calculation for the velocity of the 8kg cart after the collision. You have correctly found that the final velocity of the 4kg cart is 0, and the initial velocity of the 8kg cart is 0. So, using the equation VFinal-VInitial = m, we have:

VFinal - 0 = -56kgm/s
VFinal = -56kgm/s

This means that the 8kg cart will have a velocity of -56kgm/s after the collision. This is because the negative sign indicates that the 8kg cart is moving in the opposite direction to the 4kg cart. Therefore, the magnitude of the velocity is still 56kgm/s, but the direction is opposite.

Other than that minor mistake, your solution is correct. Well done!