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A 1,240-kg car traveling initially with a speed of 25.0 m/s in an easterly direc

ID: 2033856 • Letter: A

Question

A 1,240-kg car traveling initially with a speed of 25.0 m/s in an easterly direction crashes into the rear end of a 9,200-kg truck moving in the same direction at 20.0 m/s (see figure below). The velocity of the car right after the collision is 18.0 m/s to the east. +25.0 m/s +20.0 m/s +18.0 m/s Before After (a) What is the velocity of the truck right after the collision? (Round your answer to at least three decimal places.) m/s (east) (b) How much mechanical energy is lost in the collision? Account for this loss in energy

Explanation / Answer

Given :-

u1 = initial velocity of car

u2 = initial velocity of truck

v1 = final velocity of car

v2 = final velocity of truck

m1 = mass of the car

m2 = mass of the truck

According to conservation of momentum

m1u1 + m2u2 = m1v1 + m2v2

(1240 kg x 25 m/s) + (9200 kg x 20 m/s) = (1240 kg x 18 m/s) + (9200 kg x v2)

v2 = 20.94 m/s

b)

The energy before collision is

Ei = 1/2m1u1^2 + 1/2m2u2^2

Ei = [0.5 x 1240 x 25^2] + [0.5 x 9200 x 20^2]

Ei = 2227500 J

The energy after collision is

Ef = 1/2m1v1^2 + 1/2m2v2^2

Ef = (0.5 x 1240 x 18)^2 + (0.5 x 9200 x 20.94^2)

Ef = 2217904.56 J

Energy lost in collision is

= Ef - Ei

= 2217904.56 -  2227500 J

= -9595.5 J