Bumpers on cars are not of much use in a collision. To see why, calculate the average force a bumper would have to exert if it brought a 1200 kg car (a so-called "compact" model) to a rest in 15 cm when the car had an initial speed of 2 m/s (about 4.5 mph). Bumpers are built with springs which compress to provide a stopping force without (hopefully) denting the metal
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For the force required, multiply the mass by the required decleration, a.
V = sqrt(2aX)
a = V^2/(2X) = 13.3 m/s^2
M a = ___ Newtons
To calculate the average force exerted by the bumper, we can use the principle of conservation of momentum.
Here's how we can approach this problem step by step:
1. Calculate the initial momentum of the car using the formula:
momentum = mass × velocity
The mass of the car is given as 1200 kg, and the initial velocity is 2 m/s.
Therefore, the initial momentum of the car is:
momentum_initial = 1200 kg × 2 m/s = 2400 kg⋅m/s
2. Calculate the final velocity of the car when it comes to rest. In this case, the final velocity is 0 m/s since the car comes to a stop.
3. Apply the conservation of momentum principle:
momentum_initial = momentum_final
2400 kg⋅m/s = 1200 kg × 0 m/s + bumper force × 0.15 m
Here, 0.15 m is the distance over which the bumper compresses.
4. Solve for the bumper force:
bumper force = (2400 kg⋅m/s) / 0.15 m
bumper force ≈ 16,000 N
So, the average force that the bumper would have to exert to bring the car to rest in 15 cm is approximately 16,000 Newtons.