A car of mass 2300 kg collides with a truck of mass 4000 kg, and just after the
ID: 1612082 • Letter: A
Question
A car of mass 2300 kg collides with a truck of mass 4000 kg, and just after the collision the car and truck slide along, stuck together, with no rotation. The car's velocity just before the collision was < 31, 0, 0 > m/s, and the truck's velocity just before the collision was < -10, 0, 29 > m/s.
What is the increase in internal energy of the car and truck (thermal energy and deformation)?
I got the velocity vector after collision as <4.97,0,18.41> But I am confused on how to get internal energy.
Explanation / Answer
let
m1 = 2300 kg
v1 = sqrt(31^2 + 0^2 + 0^2) = 31 m/s
m2 = 4000 kg
v2 = sqrt(10^2 + 0^2 + 29^2)
= 30.7 m/s
Vf = sqrt(4.97^2 + 0.18^2 + 18.41^2) = 19.07 m/s
initial kinetic energy = (1/2)*m1*v1^2 + (1/2)*m2*v2^2
= (1/2)*2300*31^2 + (1/2)*4000*30.7^2
= 2.99*10^6 J
final kinetic energy = (1/2)*(m1+m2)*vf^2
= (1/2)*(2300 + 4000)*19.07^2
= 1.14*10^6 J
increase in internal energy = loss of kinetic energy
= Ki - Kf
= 2.99*10^6 - 1.14*10^6
= 1.85*10^6 J
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