A 1 240.0 kg car traveling initially with a speed of 25.000 m/s in an easterly d

Question

A 1 240.0 kg car traveling initially with a speed of 25.000 m/s in an easterly direction crashes into the back of a 8 500.0 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.

(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.

Please explain step by step. Thank you!

Explanation / Answer

here,

mass of car , mc = 1240 kg

mass of truck, mt = 8500 kg

initial speed of car , uc = 25 m/s

initial speed of truck , ut = 20 m/s

final speed of car , vc = 18 m/s

(a)

let the final speed of truck be vt

using conservation of angular momentum

mc*uc + mt*ut = mc*vc + mt*vt

1240 * 25 + 8500 * 20 = 1240 * 18 + 8500 * vt

vt = 21.021 m/s

the velocity of truck after the collison is 21.021 m/s to the east

(b)

the change in mechanical energy of the car–truck system in the collision , E = final energy - initial energy

E = 0.5 * ( mc*vc^2 + mt*vt^2 - mc*uc^2 + mt*ut^2 )

E = 0.5 * (1240*18^2 + 8500*21.021^2 - 1240*25^2 - 8500*20^2 )

E = - 8619.62 J

the change in mechanical energy of the car–truck system in the collision is - 8619.62 J

c)

the final energy is less than that of initial kinetic energy

than ,

the energy lost in collison may be lost as sound energy or heat energy

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