Final answer:
The magnitude of the average force on a bumper that collapses 0.200 m while bringing a 900-kg car to rest from an initial speed of 1.12 m/s is calculated to be 2,822.4 N using the work-energy principle, none of the provided options (A: 900 N, B: 1800 N, C: 3600 N, D: 7200 N) exactly match but Option B is closest.
Step-by-step explanation:
To calculate the magnitude of the average force on a bumper that collapses 0.200 m while bringing a 900-kg car to rest from an initial speed of 1.12 m/s, we use the work-energy principle, which states that work done is equal to the change in kinetic energy. The initial kinetic energy (KE) of the car can be calculated using the formula KE = ½mv², where m is the mass of the car, and v is the initial velocity. Since the car comes to rest, its final kinetic energy is 0.
The work done by the force is also equal to the force multiplied by the distance over which it is applied. So, the equation for work done (W) by the force (F) becomes W = F × d, where d is the distance over which the force is applied. Since work done is equal to the change in kinetic energy, we have: ½mv² = F × d.
Plugging in the values, we get:
½ × 900 kg × (1.12 m/s)² = F × 0.200 m.
F = (½ × 900 kg × (1.12 m/s)²) / 0.200 m = 2,822.4 N.
None of the provided options (A: 900 N, B: 1800 N, C: 3600 N, D: 7200 N) exactly match the calculated value of 2,822.4 N, but Option B is the closest to the correct result. Therefore, the correct average force magnitude rounded to the closest available option is 2,800 N or Option B: 1800 N if we are to choose from the provided options.