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

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SUMMARY

The maximum velocity at which a solid 1000 kg car can collide with a truck's rear bumper, equipped with a spring constant of 8 x 105 N/m and a compression limit of 15 cm, is 34 m/s without causing damage. The kinetic energy equation (Ek = 1/2 mv2) and the elastic potential energy equation (El = 1/2 kx2) were used to derive this result. Initial calculations incorrectly suggested a maximum velocity of 4.2 m/s, highlighting the importance of verifying answers against reasonable expectations.

PREREQUISITES
  • Understanding of kinetic energy (Ek = 1/2 mv2)
  • Knowledge of elastic potential energy (El = 1/2 kx2)
  • Familiarity with spring constants and their implications in physics
  • Basic principles of collision dynamics
NEXT STEPS
  • Study the principles of energy conservation in collisions
  • Learn about the mechanics of springs and their applications in automotive safety
  • Explore advanced topics in dynamics, including impulse and momentum
  • Investigate real-world case studies of vehicle collisions and bumper designs
USEFUL FOR

Physics students, automotive engineers, safety analysts, and anyone interested in vehicle dynamics and collision safety mechanisms.

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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