To test the resiliency of its bumper during low-speed collisions, a 3 070-kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 4.00 106 N/m and compresses 3.28 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?

Question

To test the resiliency of its bumper during low-speed collisions, a 3 070-kg automobile is driven into a brick wall. The car's bumper behaves like a spring with a force constant 4.00  106 N/m and compresses 3.28 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?

anonymous · Answer

You'll need to approach this problem based on the final statement. Consider conservation of energy: the total energy of the system before and after the collision will be the same.

Total energy is a sum of kinetic and potential energies:
$$E = T + U$$Kinetic energy is:$$T=\frac{1}{2}mv^{2}$$Potential energy (for a spring) is:$$U=\frac{1}{2}kx^{2}$$
'm' is mass, 'v' is speed, 'k' is spring constant, 'x' is displacement.