A train car with mass m 1 = 571 kg is moving to the right with a speed of v 1 =

Question

A train car with mass m1 = 571 kg is moving to the right with a speed of v1 = 8.9 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 vf = 5.6 m/s.

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

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

3)What is the change in kinetic energy of the two train system during the collision?

4/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 = 8.9 m/s and collides with the second train car that is now moving to the left with a velocity v2 = -6.4 m/s before the collision. The two cars latch together at impact.

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 means the two train cars move to the left.)

5)

Compare the magnitude of the momentum of train car 1 before and after the collision:

p1 initial = p1 final

p1 initial > p1 final

p1 initial < p1 final

Explanation / Answer

Momentum equals mass times velocity.

The momentum of the first car can be calculated as (571)(8.9)= 5081.9 kg*m/s

To find the mass of the second train car, you have to set up an equation for conservation of momentum. Split the problem into two parts--Before the collision, and after the collision.

Before= the momentum of the first train car = 5081.9
After= the momentum of the combined cars= (571+m2)(5.6)

Now, set the before and after equal to each other.

5081.9=(571+m2)(5.6)
5081.9=3197.6+5.6m2
m2= 336.48 kg

So, the mass of the second car is 336.48 kg

The change in kinetic energy can be defined as the kinetic energy after- the kinetic energy before
So, since kinetic energy equals 1/2mv^2, the change is--

1/2( 336.48+571)(5.6)^2-1/2(336.48+571).=13775.54 N

So, the change in kinetic energy is 13775.54 N.

m1u1 + m2u2 = (m1+m2) V
571*8.9 - 336.48*6.4 = 907.48*V
V = + 3.22 m/s
positive means the two train cars move to the right

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