NEED HELP SOLVING: Question about two train cars (PHYSICS)

Question

A train car with mass m₁ = 618 kg is moving to the right with a speed of v₁ = 7.9 m/s and collides with a second train car. The two cars latch together during the collision and then move off to the right at v_f = 4.8 m/s.

1) What is the initial momentum of the first train car?

2) What is the mass of the second train car?

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Now the same two cars are involved in a second collision. The first car is again moving to the right with a speed of v₁ = 7.9 m/s and collides with the second train car that is now moving to the left with a velocity v₂ = -5.6 m/s before the collision. The two cars latch together at impact.

3) What is the final velocity of the two-car system? (A positive velocity means the two train cars move to the right – a negative velocity me ans the two train cars move to the left.)

Note: Make sure to answer all questions since they correspond with each other make sure to bold the answers and be able to respond in case if its wrong

Answer 1

Hi Nathan.

This question involves the principle of Conservation of Momentum. That's a fancy way of saying that the total momentum never changes, that is, total momentum before the collision equals total momentum after.

Q 1) Momentum of car #1 = m₁v₁ = 618 x 7.9 = 4,882.2 kg m/s

Q 2) To find the mass of car #2, we need to consider the total momentum before and and after the collision.

The speed of car #2 is not given (shame on the questioner!) so we assume it is zero.

Therefore, total momentum before = m₁v₁ + m₂v₂

= 4,882.2 + m₂ x 0

= 4,882.2

After the collision, the 2 trains act as a single body of mass m₁ + m₂

Therefore, total momentum after = (m₁ + m₂) v_f

= (618 + m₂) 4.8

Equating these 2 values: 4,88.2 = (618 + m₂) 4.8

I leave it as an exercise for you to find m₂.

Q 3) This is very similar to the above.

Total momentum before = 618 x 7.9 + m₂ x (-5.6) . . . . . . . . . . and we know the value of m₂

Total momentum after = (m₁ + m₂) v_f . . . . . . . . . . . . . . . . . . v_f = final velocity of the 2-car mass

Fill in the values of m₁ and m₂ , equate the above 2 values, and solve for v_f

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