Q5.9 Road Accident (S)
In a road accident, a car of mass 2000 kg, travelling south, collides in the middle of a junction with a truck of 6000 kg travelling west. The wreckage of the vehicles locks together and skids off the road along a line pointing exactly southwest. Later a witness tells the police that the truck had entered the intersection at exactly 50 mph- Is it likely that the witness is correct?
- If the witness is correct, what fraction of the initial kinetic energy was converted into other forms of energy by the collision?
Hint
Reveal
Hide

Hint
Consider momenta before and after the collision for each component and investigate the consequences.Solution
Reveal
Hide

Solution
First we need a diagram:- Let’s see if we can calculate the speed of the truck from the data
given.
- Firstly, since the collision made such a mess, it it probably unwise to assume energy was conserved between the truck and car. A fair amount of noise and heat would have been generated.
- Let’s calculate the components of the momentum before and after the collision, taking S and W as the positive directions. Let’s also denote the initial speed of the car and truck by vc and vt respectively, and the final speed of the combined wreckage as v. The masses of the car and truck are mc and mt respectively.
Resolve each component of momentum in the S and W directions.
South direction:
mcvc=(mc+mt)vcos(45) (*)West direction:
mtvt=(mc+mt)vsin(45)Since sin(45)=cos(45) then
vc=mtvt/mcIf the witness is correct in saying that vt=50mph, then this implies vc=150mph, which seems unreasonably large. Thus it would seem that the witness was mistaken and the truck was actually moving more slowly than 50mph.
Let’s calculate the initial kinetic energy:
The final kinetic energy is
Assuming the witness were correct, we can calculate v the resulting speed of the wreckage from eqn. (*) above, to find
(to 3 s.f).
Thus
and hence the fraction of energy transformed into other forms is
(Ki-Kf)/Ki=5/8