A train car with mass m 1 = 619 kg is moving to the right with a speed of v 1 =

Question

A train car with mass m1 = 619 kg is moving to the right with a speed of v1 = 7 m/s and collides with a second train car with mass m2 = 791 kg. The two cars latch together during the collision.

What is the magnitude of initial momentum of BOTH train cars?

What is the final speed of the train cars latched together?

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 m/s and collides with the second train car that is now moving to the left with a speed of v2 = 8.7 m/s before the collision. The first car rebounds backwards (to the left) at a speed of v3 = 5.5 m/s.

What is the final velocity of the second car? (A positive velocity means the train car moves to the right

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 m/s and collides with the second train car that is now moving to the left with a speed of v2 = 8.7 m/s before the collision. The first car rebounds backwards (to the left) at a speed of v3 = 5.5 m/s. What is the final velocity of the second car? (A positive velocity means the train car moves to the right ?? a negative velocity means the train car moves to the left.) A train car with mass m1 = 619 kg is moving to the right with a speed of v1 = 7 m/s and collides with a second train car with mass m2 = 791 kg. The two cars latch together during the collision. What is the magnitude of initial momentum of BOTH train cars? What is the final speed of the train cars latched together? What is the change in total momentum of the two train system during the collision?

Explanation / Answer

m1 = mass of left car = 619 kg

m2 = mass of right car = 791 kg

V1i = initial velocity of left car = 7 m/s

V2i = initial velocity of right car =0 m/s

V = final velocity of combination.

using conservation of momentum ::

m1 V1i + m2 V2i = (m1 + m2 ) V

619 x 7 + 791 x 0 = (619 +791) V

V = 3.07 m/s

initial momentum of both cars :: m1 V1i + m2 V2i = 619 x 7 + 791 x 0 = 4333 kgm/s

change in momentum =0

m1 = mass of left car = 619 kg

m2 = mass of right car = 791 kg

V1 = initial velocity of left car = 7 m/s

V2 = initial velocity of right car = -8.7 m/s

V3 = final velocity of first car = -5.5 m/s

using conservation of momentum ::

m1 V1 + m2 V2 = m1 V3 + m2 V4

619 x 7 + 791 x (-8.7) = 619 x (-5.5) + 791 V4

V4 = 1.08 m/s       to the right

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