Pushing spring from both sides - Find the spring constant

In summary, the spring constant k for a spring that is being pushed from both sides and contracted from 0.5[m] to 0.4[m] with a force of 3[N] on each side is 30. The constant is defined as the force applied divided by the total change in length of the spring. If the force is only applied on one side, the other side will provide an equal and opposite force. The constant is not defined by half the compression, but by the total compression.
  • #1
Pishard
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Homework Statement


A spring relaxed length is 0.5[m]. It is being pushed from both sides, and contracted to 0.4[m]. The force the spring is applying outwards is 3[N] on each side. What is the spring constant k?

Homework Equations

The Attempt at a Solution



I attempted drawing a force diagram, and then getting the equations out of it, but I got that the constant is 60 (6=0.1k - because total of force is 3+3=6[N]), although I know it is 30, but I can't get it right using the diagram and equations. What am I doing wrong?

Thanks!
 
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  • #2
Pishard said:

Homework Statement


A spring relaxed length is 0.5[m]. It is being pushed from both sides, and contracted to 0.4[m]. The force the spring is applying outwards is 3[N] on each side. What is the spring constant k?

Homework Equations

The Attempt at a Solution



I attempted drawing a force diagram, and then getting the equations out of it, but I got that the constant is 60 (6=0.1k - because total of force is 3+3=6[N]), although I know it is 30, but I can't get it right using the diagram and equations. What am I doing wrong?

Thanks!

Could you compress a spring by applying a force only on one side?
 
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  • #3
PeroK said:
Could you compress a spring by applying a force only on one side?

True, I have to apply force on both sides. So in the equation F=-kx, the x meaning the total change of spring length.
Thanks!
 
  • #4
Pishard said:
True, I have to apply force on both sides. But I am still confused, how do I know that the change in length on one side isn't half of the total, in this case half of 0.1[m]? Why it's 3=k*(0.1), and not 3=k*(0.05)?

That's just the way a spring constant is defined. If you apply a force ##F## to both sides and it compresses by ##x##, then the constant is defined to be ##k = F/x##.

If you put one end of the spring against a wall and apply a force to the other end, then the wall will provide an equal and opposite force.

In any case, the spring constant is defined by the force at one end and the total compression (not by half the compression).
 
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  • #5
Thank you! I got it now
 

1. What is the purpose of finding the spring constant?

The spring constant is a measure of how stiff or stretchy a spring is. It is an important quantity in physics and engineering, as it helps us understand the behavior of springs in different situations.

2. How do you find the spring constant?

The most common method is to use Hooke's Law, which states that the force exerted by a spring is directly proportional to its displacement from equilibrium. By measuring the force and displacement of a spring, we can calculate its spring constant using the equation k = F/x, where k is the spring constant, F is the force applied, and x is the displacement.

3. Can the spring constant change?

Yes, the spring constant can change depending on factors such as the material, length, and thickness of the spring. It can also be affected by external factors like temperature and stress.

4. Is the spring constant the same for all types of springs?

No, the spring constant varies depending on the type of spring. For example, a metal spring will have a different spring constant than a rubber band. The spring constant also changes if the spring is stretched or compressed beyond its elastic limit.

5. What are some real-life applications of knowing the spring constant?

The spring constant is used in various fields, including engineering, physics, and medicine. It helps in designing and analyzing structures such as bridges and buildings, as well as in understanding the behavior of biological tissues and materials. It is also used in designing and improving mechanical devices like springs in car suspensions or pogo sticks.

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