Springs Equilibrium Length Question

In summary, the equilibrium length of a spring with a force constant of 260N/m is 0.25m. To hold the spring at twice its equilibrium length of 0.5m, a force of 130N is required according to Hookes Law.
  • #1
grenier11
1
0

Homework Statement



The equilibrium length of a certain spring with a force constant of K = 260N/m is 0.25m

What is the magnitude of the force that is required to hold this spring at twice its equilibrium length?

Homework Equations



Hookes Law F=Kx

The Attempt at a Solution



260 N/m = F/.25
twice the length is .50m so 260 N/m * .50 = 130
 
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  • #2
Here's a picture:

http://solomon.physics.sc.edu/~tedeschi/demo/explain/images/hooks7.jpg

The equilibirium, original, X=0 point in this case is where X=0.25m. You're looking to extend the spring to 0.5m in length - that's an extension of 0.25m. So I think the correct figure should be 260 * 0.25 = 65N
 
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  • #3
N

I can confirm that your calculations are correct. According to Hooke's Law, the force required to hold a spring at a certain length is directly proportional to the displacement from its equilibrium length. Therefore, at twice the equilibrium length, the force required would be twice the original force. In this case, the force required would be 130N, as you have correctly calculated.
 

Related to Springs Equilibrium Length Question

What is the "Springs Equilibrium Length Question"?

The "Springs Equilibrium Length Question" is a concept in physics that refers to the length at which a spring is in a state of equilibrium, or balance. This is when the spring is not stretched or compressed and exerts no force on an object attached to it.

What factors affect the equilibrium length of a spring?

The equilibrium length of a spring is affected by the material of the spring, the thickness of the wire, and the number of coils. It is also influenced by external factors such as temperature and weight of the object attached to the spring.

How is the equilibrium length of a spring calculated?

The equilibrium length of a spring can be calculated using Hooke's Law, which states that the force exerted by a spring is directly proportional to the distance it is stretched or compressed from its equilibrium length. The equation is F = kx, where F is the force, k is the spring constant, and x is the distance from equilibrium length.

Can the equilibrium length of a spring change?

Yes, the equilibrium length of a spring can change due to various factors such as temperature, weight of the object attached, and the amount of force applied to the spring. These changes can also affect the spring constant, resulting in a new equilibrium length.

Why is understanding equilibrium length important in science?

Understanding equilibrium length is important in science because it helps us understand the behavior of springs and other elastic materials. It also allows us to accurately predict how much force is needed to stretch or compress a spring to a certain length, which has practical applications in various fields such as engineering and design.

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