A 1 170.0 kg car traveling initially with a speed of 25.000 m/s in an easterly direction crashes into the back of a 9 800.0 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.

(a) What is the velocity of the truck right after the collision? (Give your answer to five significant figures.) m/s east

(b) What is the change in mechanical energy of the car�truck system in the collision? J

(c) Account for this change in mechanical energy.

Explanation:

mass of car, m1 = 1170 kg

mass of truck, m2 = 9800 kg

initial velocity of car, u1 = 25 m/s

initial velocity of truck, u2 = 20 m/s

final velocity of car, v1 = 18 m/s

Let the final velocity of truck is v2.

(a) Use the conservation of momentum

m1 x u1 + m2 x u2 + m1 x v1 + m2 x v2

1170 x 25 + 9800 x 20 = 1170 x 18 + 9800 x v2

29250 + 196000 = 21060 + 9800 v2

v2 = 20.84 m/s

(b) Total kinetic energy before collision,

Ki = 0.5 x 1170 x 25 x 25 + 0.5 x 9800 x 20 x 20

Ki = 365625 + 1960000 = 2325625 J

Total final kinetic energy

Kf = 0.5 x 1170 x 18 x 18 + 0.5 x 9800 x 20.84 x 20.84

Kf = 189540 + 2128097.44

Kf = 2317637.44 J

Change in energy = 2325625 - 2317637.44 = 7987.56 J

(c) It is due to the heat energy

the current is 0.6

voltage ÷ resistance = current

so 12 ÷ 20 = 0.6

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