Calculate Spring Force on Car Impact Speed

[charmedbeauty]

Homework Statement

To test the resiliency of its bumper during low-speed collisions, a 4 600-kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 8.00 106 N/m and compresses 3.36 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?

Homework Equations

The Attempt at a Solution

K.e=1/2mv²

p.e(spring)=U=1/2kx²

K=U

1/2mv²=1/2kx²

mv²=kx²

v=√(kx²)/m

= √(((0.0336)(1.12896*10^-3))/4600)

v= 1.4 m/s is this correct it seemed a little slow for a car?

 

[PhanthomJay]

Looks good! Don't forget that if the car was going fast, the bumper would compress more than a mere 3 cm. Good thing it was going slow!

 

[charmedbeauty]

Looks good! Don't forget that if the car was going fast, the bumper would compress more than a mere 3 cm. Good thing it was going slow!

Thanks Phantom Jay.