Finding spring constant of bumper

In summary, the cars have elastic bumpers that behave like ideal springs up to a certain point and permanently deform beyond that. To find the effective spring constant, we need to consider the kinetic energy of the car and set it equal to the spring potential energy, using the formula PEs=1/2kx^2. This will give us the correct value for the spring constant, which is needed to absorb the car's kinetic energy during a collision.
  • #1
mohamud3917
11
0
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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  • #2
You need to consider energy, not force.
 
  • #3
energy? i am really confused, can you please give me a step by step

thanks
 
  • #4
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?
 
  • #5
PEs=1/2kx2

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

PEs=83.888

so what is next
 
  • #6
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.
 
  • #7
ok so how do i find the potential energy of the spring, is it mgh?
 
  • #8
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.
 

FAQ: Finding spring constant of bumper

What is a bumper spring constant and why is it important?

The bumper spring constant, also known as the spring rate, is a measure of the stiffness of the spring used in a bumper system. It determines how much force is required to compress the spring and how much resistance the spring will provide against external forces. Knowing the spring constant is important for designing and optimizing bumper systems for different applications.

How do you calculate the spring constant of a bumper?

The spring constant can be calculated by dividing the force applied to the bumper by the displacement of the spring. This can be done by measuring the force required to compress the spring to a certain distance or by analyzing the spring's properties and dimensions. It is important to note that the spring constant may vary depending on the material and design of the spring.

What factors can affect the spring constant of a bumper?

The spring constant of a bumper can be affected by various factors such as the material used for the spring, its dimensions, and the number of coils in the spring. Other factors include the type and amount of force applied to the bumper, the temperature, and the condition of the spring (e.g. wear and tear).

How does the spring constant impact the performance of a bumper?

The spring constant plays a crucial role in the performance of a bumper. A higher spring constant means a stiffer spring, which can provide more resistance and absorb more force. This can result in better protection for the vehicle and its passengers. On the other hand, a lower spring constant can make the bumper more flexible and absorb less force, which may be more suitable for certain applications such as off-roading.

Can the spring constant of a bumper be changed?

Yes, the spring constant of a bumper can be changed by altering the properties and dimensions of the spring. For example, using a different material or increasing the number of coils can increase the spring constant. Additionally, the spring constant can also be adjusted by changing the preload or the initial compression of the spring.

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