Cart A has a mass of 8.80 kg and is going to the right at a speed of 2.60 m/s an

Question

Cart A has a mass of 8.80 kg and is going to the right at a speed of 2.60 m/s and cart B has a mass of 4.60 kg and is going to the left with a speed of 3.70 m/s They collide and cart B is seen to now be going to the right with a speed of 2.80 m/s. The collision lasts 65.0 ms.

I have the answers, but do not know how to get them. Can someone please show me step by step on how to get these please? thank you.

A. What is the velocity of Cart A after the collision?

- 0.798 m/s

B. What was the impulse on Cart B?

29.9 kgm/s

c. What was the change in kinetic energy during the collision?

-40.4 J

Explanation / Answer

ua = 2.6 m/s

ub = -3.7 m/s

vb = 2.8 m/s

ma = 8.8 kg

mb = 4.6 kg

from conservation of momentum

maua+mbub = mava+mbvb

8.8*va = 8.8*2.6-4.6*3.7-4.6*2.8 = -7.02

va = -0.797 m/s

cart a is moving left after the collision

b) impulse = chaneg in momentum

I = m(vb-ub) = 4.6(2.8-(-3.7)) = 29.9 kg m/s

c) kinetic energy ki = 1/2*8.8*2.6^2+1/2*4.6*3.7^2 = 61.231 J

kf = 1/2*8.8*0.798^2+1/2*4.6*2.8^2 = 20.83 J

change kf-ki = 20.83-61.231 = -40.401 J

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