Final answer:
To calculate the force applied when a driver with a mass of 100 kg hits an airbag going from a velocity of 6.3 m/s to 0 m/s in 0.35 seconds, we use the impulse-momentum theorem. The impulse is -630 kg·m/s, and dividing by the impulse time gives a force of 1800 N.
Step-by-step explanation:
Calculating the Force Applied During an Impulse
To calculate the force applied when a driver hits the airbag, we need to use the impulse-momentum theorem. The formula for impulse (I) is given by the change in momentum, which is mass (m) times change in velocity (Δv), and impulse is also equal to force (F) times time (t). So, we have:
I = F * t
Given that the change in velocity (Δv) is the final velocity minus the initial velocity and since the car and the driver come to a stop (final velocity is 0 m/s from 6.3 m/s):
Δv = 0 m/s - 6.3 m/s = -6.3 m/s
The negative sign indicates a decrease in velocity. The driver's mass is 100 kg, and the time for the impulse is 0.35 seconds.
So, we can calculate the impulse:
I = m * Δv = 100 kg * (-6.3 m/s) = -630 kg·m/s
The impulse experienced by the driver is then used to find the force:
F = I / t = -630 kg·m/s / 0.35 s = -1800 N
The force applied is therefore 1800 N (the negative sign indicates the direction of the force is opposite to the direction of the initial velocity).