Question

A car’s bumper is designed to withstand a 4.0-km/h (1.1-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 on a bumper that collapses 0.200 m while bringing a 900-kg car to rest from an initial speed of 1.1 m/s.

Answer 1

Answer:

The force bumper at 0.200m

F=2722.5 N

Explanation:

Using the energy theorem of work

$W=K_{f}- K_{i}$

W=ΔK

W=F*d

ΔK=$\frac{1}{2}*m*v_{f} ^{2} -\frac{1}{2}*m*v_{i} ^{2}$

$v_{i} =0$

ΔK=F*d=$\frac{1}{2}*m*v_{f} ^{2} -\frac{1}{2}*m*v_{i} ^{2}$

$F*d=\frac{1}{2}*m*0 ^{2}- \frac{1}{2}*m*v_{i} ^{2}\\F*d=-\frac{1}{2}*m*v_{i} ^{2}=\frac{1}{2}*900kg*(1.1\frac{m}{s})^{2}\\F*d=544.5\frac{kg*m}{s^{2}}\\ F=\frac{544.5\frac{kg*m}{s^{2}}}{0.2m} \\F=2722.5 N$