Is bigger better?
You will most likely at some point in your life be involved in a collision. Hopefully it will be a bingle rather than a serious accident. One question that you may ask yourself could be....is it better to have a larger or smaller car.
In reality car collisions are very complex and difficult to model. Nevertheless a simple spreadsheet model does enable us to explore relationships and hence gain useful insight.
By making some simple assumptions we can model the change in momentum and thus the impulse in a collision. We will assume:
a) the greater the impulse on a car, the greater the damage that will be done to the car, and
b) the greater the impulse on you, the greater the damage that will be done to you!
In this investigations you will model a car of mass m, moving with speed v, colliding with a stationary truck of mass M. For simplicity we will assume the vehicles remain together after to accident and that the road is wet and slippery and thus friction is negligible compared to the other forces involved. (That is the car and truck are an isolated system.)
Begin by writing down the conservation of momentum equations and show that the final speed of the tangled wreck is given by
vfinal = mv / (m+M)
You can write the change in momentum of, or impulse acting on, the car as:
impulse = mΔv
= m(vfinal - v)
Open the spreadsheet from the link belowWhere you can use the earlier expression to give you values of vfinal
You need to write excel formulas to do calculations for:
a) converting the car's initial speed to m/s
b) calculate the final in speed
c) calculate the impulse
Questions
1. How is driving a more massive car likely to affect the damage done to the car in this type of collision? What assumptions about the strength of the car are you making here?
2. How is driving a more massive car likely to affect the damage done to you in this type of collision? (Remember that, assuming the car's cabin remains undamaged, you are either restrained by a seat belt or you hit the dashboard. Either way, a sudden change in speed is what you experience.)
3. If your car is made heavier by filling it with heavy (unrestrained) friends, how will this affect the impulse on a) the car and b) your? (Think!, the truck acts directly by pushing on your car, but what happens to you and your friends? At what point do they begin to push on the truck?)
4. What is the likely effect on you and your car if you hit at a greater speed (say 50 km/h)? Explore!