A train car with mass m 1 = 653 kg is moving to the right with a speed of v 1 =

Question

A train car with mass m1 = 653 kg is moving to the right with a speed of v1 = 7.1 m/s and collides with a second train car with mass m2 = 777 kg. The two cars latch together during the collision.

1)

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

kg-m/s

2)

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

m/s

3)

What is the change in total momentum of the two train system during the collision?

kg-m/s

4)

m/s

5)

Compare the total kinetic energy of the SYSTEM before and after the collision:

KEinitial = KEfinal

KEinitial > KEfinal

KEinitial < KEfinal

Explanation / Answer

m1=653kg, v1=7.1m/s, m2=777kg

(1). Initial momentum p1i = m1 v1i = 4636.3kg.m/s ; p2i = m2 v2i = 0 kg.m/s

(2). Momentum conservation Pinitial = Pfinal

(m1v1 + m2v2)initial = (m1v1 + m2v2)final

m1v1i = m1 x v1f+ m2 x v2f

... Both are latched ,

... v1f = v2f = v

v = ((m1v1i)/(m1 + m2) = 3.24m/s

(3). No external force on the 2 cars system during the collision therefore total momentum will remain constant.

No change in the total momentum of the 2 cars system

(4). v1i = 7.1m/s, v2i = -8.4m/s, v1f = v3 = -3.9m/s, v2f = ?

No external force ... Momentum balance

m1v1i + m2v2i = m1v1f + m2v2f

653 x 7.1 - 777 x 8.4 = - 653 x 3.9 + 777 x v2f

v2f = 0.844m/s

(5). The magnitude of velocity for both cars has decreased therefore KE has decreased

KEinitial > KEfinal

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