Question

A car’s bumper is designed to withstand a 4 km/h collision with an immovable object without damaging 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 a bumper that collapses 0.205 m while bringing a 875 kg car to rest from an initial speed of 1.2 m/s, in Newtons.

Answer 1

Answer on Question 74312, Physics, Other

Question:

A car’s bumper is designed to withstand a $4 \, \text{km/h}$ collision with an immovable object without damaging 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 a bumper that collapses $0.205 \, \text{m}$ while bringing a $875 \, \text{kg}$ car to rest from an initial speed of $1.2 \, \text{m/s}$, in Newtons.

Solution:

We can find the average force in a bumper from the work-energy theorem (the change in the kinetic energy of the car is equal to the work done by the force $F$ over a distance $s$ to stop the car):

$$W = K E _ {f} - K E _ {i} = F s,$$ $$\frac {1}{2} m v _ {f} ^ {2} - \frac {1}{2} m v _ {i} ^ {2} = F s,$$ $$F = \frac {\frac {1}{2} m v _ {f} ^ {2} - \frac {1}{2} m v _ {i} ^ {2}}{s} = \frac {\frac {1}{2} \cdot 8 7 5 k g \cdot \left(0 \frac {m}{s}\right) ^ {2} - \frac {1}{2} \cdot 8 7 5 k g \cdot \left(1 . 2 \frac {m}{s}\right) ^ {2}}{0 . 2 0 5 m} =$$

The sign minus indicates that the car slows down. The magnitude of the average force in a bumper is $3073N$.

Answer:

$$F = 3 0 7 3 N.$$

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