Final answer:
The magnitude of the average force exerted on the bumper that collapses 0.205 m while stopping a 975-kg car from a speed of 1.4 m/s is approximately 4661 Newtons. This is found using the work-energy theorem which relates the work done on the car to its change in kinetic energy.
Step-by-step explanation:
To calculate the magnitude of the average force on the bumper that collapses 0.205 m while bringing a 975-kg car to rest from 1.4 m/s, we use the work-energy theorem. This theorem states that the work done on an object equals the change in its kinetic energy. In this case, the work done on the car by the bumper is the force times the distance over which it acts (Work = Force × Distance).
The change in kinetic energy (ΔKE) of the car is equal to its final kinetic energy minus its initial kinetic energy. Because the car comes to rest, its final kinetic energy is zero, and its initial kinetic energy is ½× mass × speed^2 (KE_initial = ½ × 975 kg × (1.4 m/s)^2).
The complete calculation entails finding the initial kinetic energy and setting it equal to the work done by the bumper. The work done by the bumper is equal to the force on the bumper multiplied by 0.205 m. By setting the work equal to the change in kinetic energy, we can solve for the average force on the bumper. The calculation follows these steps:
- Calculate the initial kinetic energy: KE_initial = ½ × 975 kg × (1.4 m/s)^2
- Set Work = ΔKE
- Solve for the force: Force = ΔKE / 0.205 m
Plugging in the values, we obtain:
KE_initial = ½ × 975 kg × (1.4 m/s)^2 = 955.5 J
Force = 955.5 J / 0.205 m = 4661 N
Therefore, the magnitude of the average force exerted on the bumper is approximately 4661 Newtons.