8- A 1 185.0 kg car traveling initially with a speed of 25.000 m/s in an easterl

Question

8-A 1 185.0 kg car traveling initially with a speed of 25.000 m/s in an easterly direction crashes into the back of a 9 500.0 kg truck moving in the same direction at 20.000 m/s. The velocity of the car right after the collision is 18.000 m/s to the east.

1 185.0 kg car traveling initially with a speed of 25.000 m/s in an easterly direction crashes into the back of a 9 500.0 kg truck moving in the same direction at 20.000 m/s. The velocity of the car right after the collision is 18.000 m/s to the east. What is the velocity of the truck right after the collision? (Give your answer to five significant figures.) What is the change in mechanical energy of the car-truck system in the collision?

Explanation / Answer

Part A)

Use consevration of momentum

(mv) + (Mv) = mv' + Mv'

(1185)(25) + (9500)(20) = (1185)(18) + (9500)(v')

v' = 20.873 m/s

Part B)

Use energy before (KE = .5mv^2)

.5mv^2 + .5Mv^2

(.5)(1185)(25)^2 + (.5)(9500)(20)^2 = 2270312.5 J

Energy after

(.5)(1185)(18)^2 + (.5)(9500)(20.873)^2 = 2261460.113 J

Change = 2270312.5 J - 2261460.113 J = 8852.4 J

That is a loss of 8852.4 J or a change of -8852.4 J (Note the negative, your answer key may want that since the energy is lost)

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