If you double the speed of a vehicle how much does the force in a crash increase by?
2 Answers
The force will be between twice as great and four times as great, depending on some assumptions we make.
Explanation:
The force exerted by a vehicle in a crash will arise from its impulse, a measure of the change in its momentum. Usually the momentum starts high before the collision and ends up at zero after the collision.
The impulse is given by
The impulse will be the change in momentum, from
If we double the velocity, we go from v to 2v, so the expression changes to:
This looks as though the force just doubles, but note that the time taken for the collision is likely to be shorter if the vehicle's velocity is higher. This is not a simple 1:1 relationship because it has to do with how the vehicle crumples, but if it did the time would be half as long:
If that were the case, the force would be 4 times as great.
Quadruple
Explanation:
We know that
We also know that
Solve for
Speed is simply the absolute value of
Square the
We can use
So doubling the speed will quadruple the force.