Question

To test the resiliency of its bumper during low-speed collisions, a 3 010-kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 6.00 106 N/m and compresses 3.26 cm as the car is brought to rest. What was the speed of the car before impact, assuming no mechanical energy is transformed or transferred away during impact with the wall? m/s

Answer 1

1.45549 m/s

Step-by-step explanation:

m = Mass of car = 3010 kg

v = Velocity of car

k = Spring constant =
`6* 10^6\ N/m`

x = Displacement of spring = 3.26 cm

As the energy of the system is conserved

`(1)/(2)mv^2=(1)/(2)kx^2\\\Rightarrow v=\sqrt{(kx^2)/(m)}\\\Rightarrow v=\sqrt{(6* 10^6* 0.0326^2)/(3010)}\\\Rightarrow v=1.45549\ m/s`

The speed of the car before impact is 1.45549 m/s