A car has a crumple zone that is 0.80 m (80 cm) long. In this car, the distance from the dummy to the steering wheel is 0.50 m. The car has a mass of 1,600 kg and the dummy has a mass of 75 kg. At the time of the crash, the car has a speed of 18 m/s. Based on the work-energy theorem, what is the smallest possible force that the dummy could experience during the crash?
–9.35 kN
–18.7 kN
–23.2 kN
–199 kN
The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy. In this case, we can use the work done on the car to calculate the force experienced by the dummy during the crash.
The work done on the car is equal to the change in its kinetic energy. The initial kinetic energy of the car is:
KE_initial = 0.5 * m_car * v_initial^2
KE_initial = 0.5 * 1600 kg * (18 m/s)^2
KE_initial = 259,200 J
The final kinetic energy of the car is zero because it comes to a stop. The work done on the car is then equal to the initial kinetic energy:
Work = KE_initial
Work = 259,200 J
This work is done over a distance equal to the crumple zone length. The force experienced by the dummy is equal to the work done on the car divided by the distance from the dummy to the steering wheel:
Force = Work / distance
Force = 259,200 J / 0.50 m
Force = 518,400 N
Force = 518.4 kN
Therefore, the smallest possible force that the dummy could experience during the crash is 518.4 kN. None of the given options match this calculation.