Energy transformations?

[Yoda]

A car equipped with a driver's air bag, hits a large tree while travelling horizontally at 15m/s. The drivers head has a mass of 8kg. We have a force vs x graph which is 16000N at when x=.20m and 8000N when x=.10m. Calculate the maximum compression distance of the airbag in this collision.

[Yacoubb]

A car equipped with a driver's air bag, hits a large tree while travelling horizontally at 15m/s. The drivers head has a mass of 8kg. We have a force vs x graph which is 16000N at when x=.20m and 8000N when x=.10m. Calculate the maximum compression distance of the airbag in this collision.

1. Calculate kinetic energy:

KE = 0.5mv² = 0.5 * 8kg * (15)² = 900 J

Now, Kinetic Energy is equal to Elastic Potential Energy.

SPE = 0.5kx²

k = gradient of the force x time graph.
Gradient = k = (16000-8000) / (0.2-0.1) = 80000 N/m

Now, SPE = 0.5 * 80000 * x² = KE = 900
x² = 0.0225
x = 0.15m

Therefore, maximum compression distance = 0.15m