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

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Homework Help Overview

The discussion revolves around a physics problem involving a small truck's spring bumper, specifically focusing on the maximum velocity at which a car can collide with the bumper without causing damage. The subject area includes concepts from mechanics, particularly energy conservation and spring dynamics.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between kinetic energy and elastic potential energy, attempting to equate the two to find the maximum collision speed. There is uncertainty regarding the correctness of their calculations, with one participant questioning the reasonableness of the derived speeds.

Discussion Status

The discussion reflects a mix of interpretations regarding the calculated speeds, with participants expressing doubt about the higher value of 34 m/s and favoring the lower value of 4.2 m/s. There is no explicit consensus, but participants are engaging in a productive examination of their reasoning and assumptions.

Contextual Notes

Participants are grappling with the implications of their calculations and the reasonableness of the results, indicating a potential misunderstanding of the problem setup or the physics involved.

Smartgurl
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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
 
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Smartgurl said:

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
 
Chestermiller said:
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?
 
Smartgurl said:
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
 
Chestermiller said:
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
 

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