Finding spring constant of bumper

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Homework Help Overview

The discussion revolves around determining the effective spring constant of a car bumper, which behaves like an ideal spring under certain conditions. The scenario involves a car with a specified mass colliding with a solid wall, and the problem includes details about the elastic limit of the bumper material.

Discussion Character

  • Conceptual clarification, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between kinetic energy and spring potential energy, questioning the correct method to find the spring constant. There is confusion regarding the application of formulas and the relevance of gravitational potential energy.

Discussion Status

The discussion is ongoing, with participants attempting to clarify the correct approach to relate kinetic energy to spring potential energy. Some guidance has been provided regarding the appropriate formulas, but there is still uncertainty about the calculations and the next steps.

Contextual Notes

Participants are navigating the constraints of the problem, including the misunderstanding of how to apply the spring potential energy formula and the distinction between different types of energy. There is an emphasis on the need to correctly interpret the scenario involving the car's collision.

mohamud3917
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Today's cars have elastic bumpers that are designed to compress and rebound without any physical damage at speeds below about 5 mi/h (8 km/h). The material of the bumpers behaves essentially as an ideal spring up to that point but permanently deforms beyond that. If the compression corresponding to the elastic limit for a particular bumper is 1.6 cm, what must be the effective spring constant of the bumper material, assuming the car has a mass of 1070 kg and is tested by ramming into a solid wall

when i tried the k=mg/x
i got k=(1070kg)(9.8)/(0.016m)
so k=655375n/m

but it says its wrong
 
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You need to consider energy, not force.
 
energy? i am really confused, can you please give me a step by step

thanks
 
What you did was find the spring constant needed to stretch 1.6cm if the car where hung from such a spring. But that's not what's going on here. The car has kinetic energy, which must be absorbed by the spring.

How do you find the spring potential energy of a compressed spring?
 
PEs=1/2kx2

PEs=1/2(655375n/m)(0.0162m)

PEs=83.888

so what is next
 
mohamud3917 said:
PEs=1/2kx2
This is the right formula for spring PE. Good!

PEs=1/2(655375n/m)(0.0162m)
This is incorrect. Remember you are solving for the spring constant. (Your calculation from your first post was wrong--otherwise you'd be done.)

You need to set the initial KE equal to the spring PE and solve for the spring constant.
 
ok so how do i find the potential energy of the spring, is it mgh?
 
mohamud3917 said:
ok so how do i find the potential energy of the spring, is it mgh?
mgh is gravitational PE, which is not relevant here. You gave the correct expression for spring PE in post #5.
 

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