How much gentler does an airbag actually make a crash? Numbers settle it. The same passenger, the same crash, stopped twice: once with the airbag, once without.
Here is the test case. A 60 kg passenger is moving at 10 m/s when the car crashes. With the airbag, the passenger stops in 0.5 s; without it, the dashboard stops them in 0.05 s.
The momentum change has the same size in both stops: the passenger's momentum falls from 600 kg·m/s to zero, so the change has size 600 kg·m/s.
What average force does each stop take? Well, there is an equation for exactly this: F = Δp/Δt, the second law in momentum form.
Divide the same momentum change by each stopping time in turn. The longer stop must give the smaller force, because the same number is being divided by a bigger time.
The airbag does not shrink the momentum change; it stretches the stop.
A 60 kg passenger moving at 10 m/s is stopped by an airbag in 0.5 s. Calculate the average net force on the passenger.
Write down the values in the question:
m = 60 kg
v = 10 m/s, falling to 0 m/s
Δt = 0.5 s
F = ?
Find the size of the momentum change:
Δp = 60 × 10
Δp = 600 kg·m/s
Write down the equation:
F = Δp/Δt
Substitute in the values:
F = 600 / 0.5
Simplify:
F = 1200 N
The average net force on the passenger is 1200 N.
The same passenger in the same crash, without the airbag: the dashboard stops them in 0.05 s. Calculate the average net force.
The momentum change is the same as before:
Δp = 600 kg·m/s
Write down the equation:
F = Δp/Δt
Substitute in the values:
F = 600 / 0.05
Simplify:
F = 12000 N
The average net force is 12000 N.
Here is the whole comparison again: the same 60 kg passenger, the same crash, one momentum change of 600 kg·m/s. The airbag stop takes ten times the time, 0.5 s against 0.05 s, so its average force is one tenth: 1200 N against 12000 N.
A 50 kg go-kart rider hits a padded barrier at 8.0 m/s and is brought to rest in 0.4 s. Enter the average net force on the rider in N.
The same rider and the same crash, but the barrier is bare concrete and the stop takes 0.05 s. Enter the average net force on the rider in N.
A 70 kg passenger moving at 6.0 m/s is brought to rest by a seat belt and airbag together in 0.3 s. Enter the average net force on the passenger in N.
An 80 kg driver moving at 4.5 m/s is stopped by an airbag in 0.2 s. Enter the average net force on the driver in N.
A 55 kg passenger is moving at 12 m/s when a crash begins. The crumple zone and airbag together stretch the passenger's stop to 0.6 s. Enter the average net force on the passenger in N.
A crash stops a 60 kg test dummy moving at 9.0 m/s. With an airbag the stop takes 0.45 s; without it, 0.09 s. How many times greater is the average force without the airbag? Enter the number.