A car's bumper is designed to withstand a 6.84-km/h (1.9-m/s) collision with an immovable object without damage to the body of the car. The bumper cushions the shock by absorbing the force over a distance. Calculate the magnitude of the average force on a bumper that collapses 0.270 m while bringing a 820-kg car to rest from an initial speed of 1.9 m/s.
To calculate the magnitude of the average force on the bumper, you can use the work-energy principle. The work-energy principle states that the work done on an object is equal to the change in its kinetic energy. In this case, the initial kinetic energy of the car is converted into work done on the bumper to collapse it.
First, let's find the initial kinetic energy of the car:
Kinetic energy (KE) = (1/2) * mass * velocity^2
KE = (1/2) * 820 kg * (1.9 m/s)^2
Next, let's find the final kinetic energy of the car:
Since the car comes to rest, the final kinetic energy is zero.
The work done on the bumper is equal to the change in kinetic energy:
Work (W) = Final kinetic energy - Initial kinetic energy
W = 0 - [(1/2) * 820 kg * (1.9 m/s)^2]
Now, we know that work is equal to force times distance:
W = Force * distance
Force = W / distance
Force = [(1/2) * 820 kg * (1.9 m/s)^2] / 0.270 m
Now, we can calculate the magnitude of the average force on the bumper:
Force = [(1/2) * 820 kg * (1.9 m/s)^2] / 0.270 m