Verifying the Relationship Between Force and Displacement in a Spring Experiment

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Discussion Overview

The discussion revolves around verifying the relationship between force and displacement in a spring experiment, focusing on the calculation of the spring constant using the formula K = -F/x. Participants explore the implications of force, displacement, and the conditions under which Hooke's Law applies, as well as the nuances of equilibrium in the system.

Discussion Character

  • Exploratory
  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant questions whether the net force on the spring can be expressed as 9.8 times the mass, suggesting that in equilibrium, the net force is zero and the relevant force is the weight of the mass.
  • Another participant agrees with the calculation of the spring constant but advises removing the negative sign, stating that the spring constant is unsigned.
  • A different participant emphasizes the importance of drawing a free body diagram for clarity in such problems.
  • One participant raises concerns about the validity of using the relationship F = kx, noting that it should be verified through experimentation with different masses, as real springs may not always obey this linear relationship due to deformation.
  • There is a mention of the sinusoidal variation of force when the mass is bouncing, indicating that the force changes dynamically rather than being constant.

Areas of Agreement / Disagreement

Participants express differing views on the interpretation of net force in the context of equilibrium and the application of Hooke's Law. There is no consensus on the conditions under which the relationship F = kx holds true, with some emphasizing the need for verification through experimentation.

Contextual Notes

Participants note that the relationship F = kx assumes a linear behavior of the spring, which may not hold if the spring is deformed or if the experimental conditions vary. The discussion highlights the importance of context in applying theoretical principles.

Who May Find This Useful

This discussion may be useful for students and educators in physics, particularly those involved in experimental physics or studying the principles of mechanics and elasticity in springs.

oneplusone
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Suppose I hang a spring vertically from a table. I attach a mass on it. Am I correct in saying that the net force on the spring is 9.8*mass ?

If I note the displacement, can I calculate the spring constant by using:

K = -F/x = -g*mass / displacement ?

Thanks,
 
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oneplusone said:
If I note the displacement, can I calculate the spring constant by using:

K = -F/x = -g*mass / displacement ?
Yes, but lose the minus sign. (The spring constant is unsigned.)
 
... though the displacement and the force will be signed, it is usually easier to work in magnitudes.
The standard approach to these kinds of problems is to, 1st, draw a free body diagram.
I'd encourage anyone to get into the habit.
 
oneplusone said:
Suppose I hang a spring vertically from a table. I attach a mass on it. Am I correct in saying that the net force on the spring is 9.8*mass ?

If I note the displacement, can I calculate the spring constant by using:

K = -F/x = -g*mass / displacement ?

Thanks,
I don't think you can mean "net force". If the system is in equilibrium (When the spring is supporting a stationary mass), the net force is zero. It is the force, due to the mass (weight) that is mg, which will also be the tension, in equilibrium. When it's bouncing, the force will have a sinusiodal variation (SHM), from zero, through mg, to 2mg and back.
 
oneplusone said:
Suppose I hang a spring vertically from a table. I attach a mass on it. Am I correct in saying that the net force on the spring is 9.8*mass ?

If I note the displacement, can I calculate the spring constant by using:

K = -F/x = -g*mass / displacement ?

Thanks,

In addition to what has been said, there is another factor that needs to be mentioned here, and this is a common mistake that I see students make in intro physics labs. How do you know that the relationship F = kx works for that spring? Because not knowing the context of the question (i.e. is this simply a textbook question, or you are actually doing this and testing it out, etc.?), it is hard to know what can assumed to be correct.

Remember, F=kx explicitly implies that there is a linear relationship between F and x. While this may be true in "usual" case of springs being used in many lab courses, it is part of the practice to do this for a series of different masses to VERIFY that this relationship works and thus, F = kx can be used. It is not uncommon to find a spring that has been deformed slightly, and where F = kx no longer works! Thus, using that relationship is invalid.

Incidentally, I gave a similar scenario in our last PF Trivia/Quiz in relation to Ohm's Law.

Zz.
 

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