Simple Harmonic Motion (F=-kx) - Help

[ProgressNation]

Simple Harmonic Motion (F=-kx) -- Help!

Hello Ladies & Gentlemen please answer my question:

Q: The formula for Hooke's LAW is Felastic=-kx , so, the "X" is always negative? And the "F" is always negative? I know the "K" is always should be positive but please explain to me because I'm confused which to put negative and which to put positive; I want to understand!

I'm waiting for an answer ASAP!
Thank you!

 

[Averki]

Consider a spring with one end fixed to a wall and the other end connected to a block. If you were to pull the block in the positive x-direction, in which direction would the spring force act? If you were instead to push the block in the negative x-direction, in which direction would the spring force act?

 

[ProgressNation]

Consider a spring with one end fixed to a wall and the other end connected to a block. If you were to pull the block in the positive x-direction, in which direction would the spring force act? If you were instead to push the block in the negative x-direction, in which direction would the spring force act?

If I pulled the block in the positive x-direction, the Spring Force will act in the negative Direction so the force will be negative. And if was pulling the block in the negative x-direction, the Spring force will act on the opposite direction (the positive direction) so the force will be positive. Am I right?

But the problem is that the question doesn't say to you that if the block was pulled either right or left direction like this question:
If a mass of 0.55 KG attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium position, what is the spring constant?

If you notice there is no force in this question so it's Fg=mg
And so on...
So this question only says "stretches the spring 2.0 cm from it's original equilibrium position", it doesn't say it's either right,left,north,south.
So please answer and Thanks for helping!

 

[Averki]

If I pulled the block in the positive x-direction, the Spring Force will act in the negative Direction so the force will be negative. And if was pulling the block in the negative x-direction, the Spring force will act on the opposite direction (the positive direction) so the force will be positive. Am I right?

Exactly! The spring will always oppose the applied force, in this case being your pulling / pushing the block.

But the problem is that the question doesn't say to you that if the block was pulled either right or left direction like this question:
If a mass of 0.55 KG attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium position, what is the spring constant?

If you notice there is no force in this question so it's Fg=mg
And so on...
So this question only says "stretches the spring 2.0 cm from it's original equilibrium position", it doesn't say it's either right,left,north,south.
So please answer and Thanks for helping!

While it is true that the problem does not explicitly specify the direction of the stretching, it is implied. If this spring is vertical, presumably with one end of the spring fixed to, say, a ceiling and the other end attached to the 0.55kg block, logically, which direction would the applied force, in this case the force of gravity, stretch the spring?

 

[sophiecentaur]

If I pulled the block in the positive x-direction, the Spring Force will act in the negative Direction so the force will be negative. And if was pulling the block in the negative x-direction, the Spring force will act on the opposite direction (the positive direction) so the force will be positive. Am I right?

But the problem is that the question doesn't say to you that if the block was pulled either right or left direction like this question:
If a mass of 0.55 KG attached to a vertical spring stretches the spring 2.0 cm from its original equilibrium position, what is the spring constant?

If you notice there is no force in this question so it's Fg=mg
And so on...
So this question only says "stretches the spring 2.0 cm from it's original equilibrium position", it doesn't say it's either right,left,north,south.
So please answer and Thanks for helping!

This is a correct way of describing what happens - but it took a lot of words. However, a half dozen symbols plus the all-important minus sign describe it better because you can often solve things once they have been put into a mathematical equation. The minus sign just tells you the force is a 'restoring force' - in a direction which is against the displacement. You need to have the confidence to go into the Maths and believe what comes out. (There are times when you do need to give the mathematical answer a credidbility test, though because it can throw up unreal answers).

The oscillation of a mass on a spring is not affected, in principle, by whether the spring is pre-stressed by the mass hanging down, being pushed up or not under gravity at all as long as the force displacement law is not distorted by extra influences - like the spring coils starting to touch each other.