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## Homework Statement

A moving car has 40,000 J of kinetic energy while moving at a speed of 7.0 m/s. A spring-loaded automobile bumper compresses 0.30 m when the car hits a wall and stops. What can you learn about the bumper’s spring using this information? Answer quantitatively and list the assumptions that you made.

[itex]KE = 40,000 J[/itex]

[itex]v_i = 7.0 m/s[/itex]

[itex]v_f = 0 m/s[/itex]

[itex]\vec s = 0.30 m[/itex]

## Homework Equations

[itex]KE = Elastic PE = \frac {1}{2} k {\vec s}^2 \Rightarrow k = \frac {2KE}{{\vec s}^2}[/itex]

## The Attempt at a Solution

[itex]k = \frac {2(40,000 J)}{(0.30 m)^2} = 888888.88 N/m \sim 8.9x10^5 N/m[/itex]

I learned that the bumper's spring has a constant of 8.9x10^5 N/m. I assumed that energy wasn't lost from the point when the car had 40,000 J of KE to when it impacted the wall, i.e. the energy was perfectly conserved.

Thank-you