Final answer:
The magnitude of the average force on the bumper can be calculated using the work-energy principle, where work done is equal to the change in kinetic energy. The initial kinetic energy of the car is calculated, and then the force is found by dividing this energy by the collapse distance of the bumper (0.200 m).
Step-by-step explanation:
To calculate the magnitude of the average force on a bumper that collapses 0.200 m while bringing a 900-kg car to rest from an initial speed of 1.1 m/s, we can use the work-energy principle. The work done by the force is equal to the change in kinetic energy. We start with the formula for kinetic energy, KE = 0.5 * m * v^2, where 'm' is the mass and 'v' is the velocity of the car. The initial kinetic energy is KE_initial = 0.5 * 900 kg * (1.1 m/s)^2. The car comes to rest, so the final kinetic energy, KE_final, is 0. The work done (W) is the force (F) times the distance (d), thus W = F * d = KE_initial - KE_final.
When the car stops, all its kinetic energy is absorbed by the force of the bumper, so KE_final = 0 and W = KE_initial. Substituting into the equation with the given numbers gives W = 0.5 * 900 kg * (1.1 m/s)^2. The distance over which the force is applied is d = 0.200 m. Therefore, we can calculate the force as F = W/d.
Using these calculations, we can find the average force exerted by the bumper during the collision to be:
- Initial Kinetic Energy (KE_initial) = 0.5 * 900 kg * (1.1 m/s)^2
- Work Done (W) = KE_initial
- Average Force (F) = W/0.200 m
After the calculations, we'll have the magnitude of the average force that the bumper applied to stop the car over the 0.200 m collapse.