Hooke's law = negative spring constant?

In summary: The current conversation is a lot more advanced.In summary, the conversation discussed a graph showing the relationship between force and displacement in a linear function. The point (0.5 metres, 140 Newtons) was identified as an obvious point for the gradient. The conversation also touched on Hooke's law, which states that F=-kx. It was determined that the spring constant cannot be negative, and the potential energy of the spring was discussed in relation to the work done and the area bound by the line and the x-axis. The conversation also mentioned the importance of considering direction when using Hooke's law to calculate the spring constant.
  • #1
scolaiw
8
0
A graph shows the Force of a spring (y axis) against Displacement (x axis) in a linear function. An obvious point for the gradient is the point (0.5 metres, 140 Newtons). What is the spring constant and how much energy is stored in the spring when it is compressed by 0.5 metres?

Hope the description helps.

Hooke's law states: F=-kx

Therefore: 140=-0.5k
Therefore: k=-40/0.5=-80 (But I thought spring constant cannot be negative?)
Also, no idea how to work out energy stored.

Any help will be appreciated! Thanks
 
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  • #2
scolaiw said:
A graph shows the Force of a spring (y axis) against Displacement (x axis) in a linear function. An obvious point for the gradient is the point (0.5 metres, 140 Newtons). What is the spring constant and how much energy is stored in the spring when it is compressed by 0.5 metres?

Hope the description helps.

Hooke's law states: F=-kx

Therefore: 140=-0.5k
Therefore: k=-40/0.5=-80 (But I thought spring constant cannot be negative?)
Also, no idea how to work out energy stored.

Any help will be appreciated! Thanks
Welcome to physics forums.

Don't forget that displacement, is a vector quantity - i.e. direction matters. In the usual set up, a spring is compressed when x < 0 (i.e. its length decreases). Therefore, if your spring is compressed by 0.5 meters, then x = -0.5.

How is potential energy related to the force (in general)?
 
  • #3
Thanks for the welcome!

I see about displacement. (Forgot displacement is a vector quantity - sad face)

About the potential energy, is potential energy the same as the work done? So in this case, the area bound by the line and the x-axis from 0 to 0.5 metres?
 
  • #4
This is one of those Newton's third law issues. If you are talking about the force you exert on the spring to stretch it a distance x, then the force is positive when the displacement is positive, and the force is negative when the displacement is negative. If you are talking about the force that the spring exerts on you when you stretch it a distance x, then the force is negative when the displacement is positive, and the force is positive when the displacement is negative.
 
  • #5
Mathematics is a tool used by Physicist. We are not bound by it. It does help us to predict what should be the case. Hooke's law describes the relationship between the restoring force of the spring, as experienced by the agent stretching the spring, and the change in length of the spring. The negative sign in this law serves to indicate that the direction of the restoring force and the change in length is in opposite directions. The spring constant is therefore positive - no sense in having a negative constant! If you want to use Hooke's law to calculate the constant you need to take the directions into account.
 
  • #6
Realize that this thread is years old.
 

1. What is Hooke's law?

Hooke's law is a principle in physics that describes the relationship between the force applied to an elastic object and the resulting deformation or displacement of that object. It states that the force is directly proportional to the displacement, as long as the object remains within its elastic limit.

2. What is a negative spring constant?

A negative spring constant is a value that indicates the stiffness or rigidity of a spring. It is a negative value because it represents the force that is exerted in the opposite direction of the displacement, as predicted by Hooke's law.

3. How is Hooke's law related to springs?

Hooke's law is most commonly associated with springs because it was first discovered and described by Robert Hooke while studying the behavior of springs. However, it can be applied to any elastic object, such as rubber bands, trampolines, and even human tissues.

4. What is the significance of a negative spring constant?

A negative spring constant indicates that the force applied to an object will result in a displacement in the opposite direction, as predicted by Hooke's law. This is important because it allows us to calculate and predict the behavior of elastic objects when a force is applied.

5. Can the negative spring constant ever be positive?

No, the negative spring constant will always be a negative value because it represents the direction of the force exerted on the object. A positive value would indicate that the force and displacement are in the same direction, which is not in accordance with Hooke's law.

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