What is the momentum (magnitude and direction )

[marisa29]

Homework Statement

1) A 4000kg freight car, moving at 4.0 m/s northwards, collides and couples with a 6000 kg freight car, which was initially at rest.
a) What is the momentum (magnitude and direction ) of the 4000 kg freight car before the collision?
b) What is the momentum of the two couples freight cars after the collision( magnitude and direction)
c) What is the common final speed of the two cars?
d) Extra credit consider the situation where the second (6000 kg) freight car was initially moving southwards at 2.0 m/s . After the collision the two freight cars couple together.

Homework Equations

momentum=mxv

The Attempt at a Solution

A) since before it hits would it just be 4000kg x 4.0 m/s = 16000 /NOrthwards
B) would we just add the two momentum so mv+mv and since the second it at rest would at just be 16000
C) m1v1+ m2v2/ m1+m2
so 1.6m/s

 

[Poop-Loops]

Yes, so p = m*v

m1v1 + m2v2 = 16000 like you said.

Now you equate 16000 = (m1 + m2)*v3 since now they are both together and have to move at the same speed. So you are right, you get 1.6m/s

 

[Moetasim]

D) Same as above, m1v1+ m2v2/ m1+m2
so the same as above 1.6 m/s

Your attempt at a solution is mostly correct. Here is a more detailed explanation:

A) Before the collision, the 4000 kg freight car has a momentum of 16000 kg⋅m/s northwards. This is because momentum is calculated by multiplying mass (m) by velocity (v), so 4000 kg x 4.0 m/s = 16000 kg⋅m/s northwards.

B) After the collision, the two freight cars are coupled together and have a combined mass of 10000 kg (4000 kg + 6000 kg). Therefore, their combined momentum is the sum of their individual momentums before the collision. This means that the momentum of the two coupled freight cars is also 16000 kg⋅m/s northwards.

C) To find the common final speed of the two cars, we can use the conservation of momentum principle, which states that the total momentum of a closed system remains constant before and after a collision. This means that the total momentum before the collision (16000 kg⋅m/s northwards) must be equal to the total momentum after the collision (16000 kg⋅m/s northwards). We can set up an equation to solve for the final velocity (v):

4000 kg x 4.0 m/s + 6000 kg x 0 m/s = 10000 kg x v

Solving for v, we get v = 1.6 m/s. This is the common final speed of the two cars after the collision.

D) In this scenario, the second freight car is initially moving southwards at 2.0 m/s. This means that it has a momentum of 6000 kg x (-2.0 m/s) = -12000 kg⋅m/s southwards. After the collision, the two cars are coupled together and have a combined mass of 10000 kg. The total momentum after the collision must still be 16000 kg⋅m/s northwards, as in part B. This means that the two cars must have a combined velocity of 1.6 m/s northwards. We can set up an equation to solve for the final velocity (v) of the coupled cars:

4000 kg x