Question

A car's bumper is designed to withstand a 7.20 km/h (2.0 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 (in N) on a bumper that collapses 0.195 m while bringing a 830 kg car to rest from an initial speed of 2.0 m/s.

Answer 1

8512 N

Step-by-step explanation:

From the work energy theorem we know that: The net work done on a particle equals the change in the particles kinetic energy:

Where:

-W is the work done by the force.

- F is the force actin on the.

- d is the distance travelled.

- m is the mass of the car.

-
`v_(f), v_(i)` are the final and the initial velocity of the car

`K_(f), K_(i)` are the final and the kinetic energy of the car.

Givens:
`m=830 \mathrm{~kg}, v_(i)=2 \mathrm{~m} / \mathrm{s}, v_(f)=0 \mathrm{~km} / \mathrm{h}, d=0.195 \mathrm{~m}`

Plugging known information to get:

`F \cdot d &=(1)/(2) m v_(f)^(2)-(1)/(2) m v_(i)^(2) \\ F &=((1)/(2) m v_(f)^(2)-(1)/(2) m v_(i)^(2))/(d) \\ &=(0-(1)/(2) * 830 * 2^(2))/(0.195) \\ &=8.512 * 10^(3) \\ F &=8.512 * 10^(3) \mathrm{~N}`