A train car with mass m1 = 663.0 kg is moving to the right with a speed of v1 =

Question

A train car with mass m1 = 663.0 kg is moving to the right with a speed of v1 = 8.8 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 = 5.3 m/s. 1) What is the initial momentum of the first train car? kg-m/s 2) What is the mass of the second train car? kg 3) What is the change in kinetic energy of the two train system during the collision? J 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 = 8.8 m/s and collides with the second train car that is now moving to the left with a velocity v2 = -6.2 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

Explanation / Answer

1) Intital momentum of 1st car = m1 * v1 = 669 * 8.9 = 5954.1 kg m /s

2) Assuming that the 2nd car was initially at rest...So by momentum conservation :

669 * 8.9 = (669 + m2) * 5.3

So, m2 = 454.41 kg

3)Initial KE = 0.5 * m1 * v1^2 = 26495.745 J

Final KE = 0.5 * (m1 + m2) * vf^2 = 15778.293 J

So change in KE = -10717.45 J

4) By conservation of momemtum :

669 * 8.9 - 454.41 * 6.4 = 1123.415 * vf

So, vf = 2.714 m/s...to the right

5) The velocity of train car was larger before collisoin...hence its momentum has decreased...so B.p1 initial > p1 final

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