How Fast Can a Car Hit a Spring Bumper Without Damage?

[Smartgurl]

Homework Statement

A small truck is equipped with a rear bumper that has a spring constant of 8 x 10^5 N/m. The bumper can be compressed 15 cm without causing damage to the truck. What is the maximum velocity with which a solid 1000kg car can collide with the bumper without causing damage to the truck?[/B]

Homework Equations

Ek = 1/2 mv^2
El = 1/2 kx^2

The Attempt at a Solution

I made these two equations equal to each other and got the answer 4.2 m/s. The right answer is 34 m/s. I'm way off and not sure what I'm doing wrong

 

[Chestermiller]

Homework Statement

A small truck is equipped with a rear bumper that has a spring constant of 8 x 10^5 N/m. The bumper can be compressed 15 cm without causing damage to the truck. What is the maximum velocity with which a solid 1000kg car can collide with the bumper without causing damage to the truck?[/B]

Homework Equations

Ek = 1/2 mv^2
El = 1/2 kx^2

The Attempt at a Solution

I made these two equations equal to each other and got the answer 4.2 m/s. The right answer is 34 m/s. I'm way off and not sure what I'm doing wrong

Does 34 m/s seem like a reasonable speed at which damage would be avoided?

Chet

 

[Smartgurl]

Does 34 m/s seem like a reasonable speed at which damage would be avoided?

Chet

No now that I think about it that's not reasonable. Does that mean I'm actually doing it right?

 

[Chestermiller]

No now that I think about it that's not reasonable. Does that mean I'm actually doing it right?

4.2 m/s sounds much more like it, doesn't it?

Chet

 

[Smartgurl]

4.2 m/s sounds much more like it, doesn't it?

Chet

Yes it does! I guess it's one of those rare occasions when the textbook is wrong! Thanks! I'll definitely make sure the answer is reasonable next time