Final answer:
To calculate the magnitude of the average force on the bumper, use the work-energy theorem by equating the work done to the car's change in kinetic energy. The work done (933.75 J) equals the force multiplied by the distance (0.210 m), resulting in 4446.4 N as the average force on the bumper.
Step-by-step explanation:
The student has asked how to calculate the magnitude of the average force on a car bumper that collapses 0.210 meters while bringing an 830 kg car to rest from an initial speed of 1.5 m/s. To solve this problem, we can use the work-energy theorem which states that the work done on an object is equal to its change in kinetic energy. In this case, the work done is the force multiplied by the distance over which the force is applied (W = Fd), and the change in kinetic energy is KE = 0.5mv^2, where m is the mass and v is the velocity of the car.
The initial kinetic energy of the car is:
KEi = 0.5 * 830 kg * (1.5 m/s)^2
which calculates to 933.75 J. Since the car comes to rest, the final kinetic energy is 0 J. The work done by the bumper is the difference in kinetic energy, hence the work done (W) is also 933.75 J.
Finally, we can find the magnitude of the average force by rearranging the work formula to F = W/d where d is the distance. Plugging in our values, we get:
F = 933.75 J / 0.210 m which calculates to approximately 4446.4 N.
The average force on the bumper is therefore 4446.4 N. To provide the correct option in the final answer, the magnitude of the average force on the bumper is 4446.4 N.