A car is approaching a truck moving in the same direction on a one lane straight

Question

A car is approaching a truck moving in the same direction on a one lane straight road. The car driver looks at his cellphone momentarily (!!) and misjudges the distance resulting in a collision. The cars don’t stick together after the collision, the front end of the car is dented during the collision however. The car’s mass is 1200 kg and it was moving with a velocity of 25.0 m/s {+i} before the collision, and the truck’s mass and speed were 9000 kg and 20.0 m/s {+i} respectively.

a. If the car’s velocity drops to 18.0 m/s {+i} momentarily, what is the velocity of the truck just after the collision?

b. How much Energy is lost to the deformation of the car’s front end?

c. Calculate the Impulse (magnitude and direction) that the car experiences during the collision.

Explanation / Answer

Mass of car = 1200 kg

initial velocity = 25 m/s

mass of truck = 9000 kg

initial velocity of truck = 20 m/s

velocity of car after collision = 18 m/s

let the velocity of truck after collision be v

By conservation of momentum

1200 * 25 + 9000 * 20 = 1200 * 18 + 9000 * v

=> 9000 v = 188400

=> v = (1884/90) = 20.93 m/s

a) so the velocity of the truck just after the collision = 20.93 m/s

b) Loss of energy = initial total KE - final total KE

= 0.5*1200*252 + 0.5*9000*202 - 0.5*1200*182 - 0.5*9000*(1884/90)2 = 8680 J

Energy is lost to the deformation of the car’s front end = 8680 J

c) Impulse = change in momentum = 1200*(18-25) = - 8400 kg m/s

Impulse (magnitude and direction) that the car experiences during the collision = 8400 kgm/s in negative x direction = - 8400 i kg m/s

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