Final answer:
To find the magnitude of the average force on a car's bumper in the stated scenario, use the work-energy principle. Calculate the initial kinetic energy with the mass and speed of the car, then find the work done (which equals the initial kinetic energy) by stopping the car. Divide this work by the distance the bumper collapses to get the average force.
Step-by-step explanation:
The student has asked how to calculate the magnitude of the average force on a car's bumper that collapses 0.240 m while bringing an 830 kg car to rest from an initial speed of 1.3 m/s. To solve this problem, we can use the work-energy principle. The work done by the force in stopping the car is equal to the change in kinetic energy of the car.
The kinetic energy (KE) of the car before the impact is given by KE = ½ * m * v^2, where m is the mass of the car (830 kg) and v is the speed (1.3 m/s). After the impact, the kinetic energy is zero because the car comes to rest. The average force (F) can be found by dividing the work (change in kinetic energy) by the distance over which the force is applied (0.240 m).
- Initial KE = ½ * 830 kg * (1.3 m/s)^2
- Work done (W) = Change in KE = Initial KE
- Average Force (F) = W / distance
By plugging in the values and calculating, we obtain the magnitude of the average force.