Question

A car with mass M_C = 1.26 x 10³ kg runs into the back of a truck with mass M_T = 3.23 x 10³ kg that is initially at rest. Immediately after the collision, the car is moving with a speed of 1.09 m/s and the truck is moving with a speed of 3.29 m/s, both in the direction the car was initially traveling.

What is the total kinetic energy lost in the collision? (Of course, the change in energy is negative but give your answer as a positive number, the magnitude of the change in energy.)

Answer 1

here,

mass of car , mc = 1260 kg

mass of truck , mt = 2320 kg

final speed of car , vc = 1.09 m/s

final speed of truck , vt = 3.29 m/s

let the initial speed of car be v

using conservation of momentum

mc * v = mc * vc + mt * vt

1260 * v = 1260 * 1.09 + 2320 * 3.29

solving for v

v = 7.15 m/s

the total kinetic energy lost , dKE = KEi - KEf

dKE = 0.5 * mc * v^2 - ( 0.5 * mc * vc^2 + 0.5 * mt * vt^2)

dKE = 0.5 * ( 1260 * 7.15^2 - (1260 * 1.09^2 + 2320 * 3.29^2))

dKE = 1.89 * 10^4 J

the total kinetic energy lost is 1.89 * 10^4 J