Understanding the Relationship Between a Compressed Spring and Attached Wall

[jbriggs444]

Even this doesn't say anything about the spring applying equal and opposite forces at both ends.

Springs are not the only things that apply equal and opposite forces at both ends. So do ropes, gloves, shoes and bathroom scales. As long as the thing in the middle either has negligible mass or negligible acceleration then this is a consequence of Newton's second law: F = ma. If the spring is not accelerating (a is approximately zero) and has a small mass (m is approximately zero), it follows that the net force on it must be approximately zero. That means that the force on the one end is approximately equal and opposite to the force on the other. This fact is sufficiently basic that it is not mentioned in articles describing springs.

 

[russ_watters]

Even this doesn't say anything about the spring applying equal and opposite forces at both ends.

Maybe its assumed to be too obvious to state explicitly. Like tension in a string or compression of a rod: there is only one force, so there is no need to say that it acts in both directions. That would be redundant. IE:

When a coil spring is compressed or stretched slightly from rest, the force it exerts is approximately proportional to its change in length (this approximation breaks down for larger deflections).

"The force it exerts" means there is only one force.

 

[andyrk]

Yeah. So maybe the book I have does the same thing. But I think this should have been stated to make things clear from the very beginning.

 

[russ_watters]

Yeah. So maybe the book I have does the same thing. But I think this should have been stated to make things clear from the very beginning.

I disagree. What you are suggesting means teaching all of physics from scratch every time one wants to introduce a new concept. A one-semester, first physics class would only cover two weeks of material if that were how it was done (and later classes could cover nothing new because by the time they finished their review, the semester would be over!)! It is entirely reasonable - indeed essential - that people build on more basic concepts when learning new concepts.

 

[Dale]

Yeah. So maybe the book I have does the same thing. But I think this should have been stated to make things clear from the very beginning.

Were Newton's laws not stated clearly from the beginning? Newton's laws do not stop simply because you are learning about springs. Everything that you have asked about in this thread comes from the spring law and Newton's laws.

 

[andyrk]

Were Newton's laws not stated clearly from the beginning? Newton's laws do not stop simply because you are learning about springs. Everything that you have asked about in this thread comes from the spring law and Newton's laws.

How will you explain both hands experiencing the same force with Newton's Laws?

 

[russ_watters]

How will you explain both hands experiencing the same force with Newton's Laws?

It's Newton's 1st and 3rd laws:

1st Law: When viewed in an inertial reference frame, an object either remains at rest or continues to move at a constant velocity, unless acted upon by an external force.

3rd Law: When one body exerts a force on a second body, the second body simultaneously exerts a force equal in magnitude and opposite in direction on the first body.

https://en.wikipedia.org/wiki/Newton's_laws_of_motion

 

[andyrk]

Yeah. So what I am saying is, what makes the forces on the two hands equal? If they weren't the spring would accelerate and not extend or compress. But why can't it compress/extend while still having unequal forces at both the ends?

 

[russ_watters]

Yeah. So what I am saying is, what makes the forces on the two hands equal? If they weren't the spring would accelerate and not extend or compress. But why can't it compress/extend while still having unequal forces at both the ends?

If the spring is in the act of compressing or extending, the forces can be unequal. Chestermiller said that in post #23.

 

[Qwertywerty]

Let us suppose F_net on spring is not zero . Mass of ideal spring equals zero .

So using F_net = m*a , if m =0 , a will become infinite . This is not possible .

 

[olivermsun]

Yeah. So what I am saying is, what makes the forces on the two hands equal? If they weren't the spring would accelerate and not extend or compress. But why can't it compress/extend while still having unequal forces at both the ends?

As several posters have alluded to earlier, if the whole system (hands + spring) isn't accelerating, then the forces on the two hands have to be equal just by virtue of the fact that the spring isn't accelerating, hence the net force on the spring must be zero.

Anyway, if the system is allowed to accelerate to the side, then consider this: the force it takes to compress the spring increases with compression (Hooke's Law: f = -kx), i.e., no matter what amount of force you imagine pushing with to compress the spring, the spring will compress to the point where its springiness is sufficient to resist further compression. At that point, the spring will be transmitting all the force to the other side and you'll be pushing one hand with the other.

 

[A.T.]

Yeah. So what I am saying is, what makes the forces on the two hands equal? If they weren't the spring would accelerate and not extend or compress.

If the extension/compression is asymmetrical, then the center of mass can be accelerating.

 

[Drakkith]

Yeah. So what I am saying is, what makes the forces on the two hands equal? If they weren't the spring would accelerate and not extend or compress. But why can't it compress/extend while still having unequal forces at both the ends?

The force exerted on the spring by your left hand is equal and opposite to the force exerted on your left hand by the spring. This is exactly in accordance with Newton's laws.
The force exerted on the spring by your right hand is equal and opposite to the force exerted on your right hand by the spring. Again, this is exactly in accordance with Newton's laws.

Now, the force exerted by your left hand on the spring does not have to be equal to the force exerted by your right hand on the spring. If the two forces exerted on the spring are NOT equal, then the spring will accelerate, along with one of your hands. Indeed, for a small amount of time between the static and the non-static, but non-accelerating situations, the forces are unequal. Thus, one of your hands along with the spring accelerates. Now, when I say that the spring accelerates, I mean that the center of mass of the spring accelerates and the entire spring begins to compress.

Now, after this acceleration is over, you could reduce whichever force is doing the accelerating so that both your hand and the center of mass of the spring are now moving, but not accelerating. During this steady-velocity phase (remember, the spring's center of mass is moving) the forces exerted by each hand on the spring are equal to each other. Because the spring force increases as you compress it, this requires a steady increase in force applied by your hands to balance out the spring force according to the spring equation.

 

[andyrk]

Everyone has written such complicated replies. I was simply saying that if the spring is mass-less, then unequal forces at its two ends can never lead to any compression/expansion of the spring. Why is this true?

 

[Drakkith]

Everyone has written such complicated replies.

Because science is complicated. Even the basics science are MUCH more complicated than many people think.

I was simply saying that if the spring is mass-less, then unequal forces at its two ends can never lead to any compression/expansion of the spring. Why is this true?

It's not true. I don't know why you think it is.
Edit: Standby on that. Lemme read Chester's post on the last page again.
Edit 2: After checking, I'm fairly certain what I said is correct.

 

[andyrk]

Because science is complicated. Even the basics science are MUCH more complicated than many people think.

Also I was just thinking, does science come naturally to those who are good at it? Like I have been doing this for the past 3 years now and I don't enjoy doing this much and have to put a lot of effort to get things clear. But that's not the case with everyone right? Ofcourse I have gotten better, but after a LOT of effort.

It's not true. I don't know why you think it is.

Intuition.

 

[Drakkith]

Also I was just thinking, does science come naturally to those who are good at it?

I certainly true that science concepts are easier to grasp for some than it is for others. But so what? So is everything.

Like I have been doing this for the past 3 years now and I don't enjoy doing this much and have to put a lot of effort to get things clear. But that's not the case with everyone right? Ofcourse I have gotten better, but after a LOT of effort.

What have you been doing for the past 3 years? Have you been going to classes to learn science, or just read about things online, or what?

Intuition.

Your intuition is wrong. If you apply a force of 100 Newtons to the left end of a massless spring with a spring constant of 100, the force on the right side of the spring, which is anchored to the wall, starts at zero and reaches -100 Newtons once the left end of the spring has moved 1 meter. This is in accordance with the spring equation F = -kx.

 

[andyrk]

I think its problematic for me because it isn't as flexible as maths/programming. I am programmer/mathematician by field of study. Physics doesn't have that much creative potential in it.

 

[Drakkith]

I'm not sure I agree. Every programming language has certain rules that MUST be obeyed, else you can't use the language. As does math. I think the difference is that those rules are MUCH easier to learn and apply than the rules of science are (at least the programming rules are). Once you learn the rules, then you have a near infinite way of applying them.

If you haven't learned the most basic rules of physics, such as Newton's laws, which includes how to use them, then of course you're going to have trouble when you try to get into the details of more advanced topics.

 

[andyrk]

Correct. My bad.

 

[sophiecentaur]

So just applying a force on one end doesn't mean that the spring would extend or compress?

Of course not. If you apply a force to just one end, the spring will move off in the direction of the force and, if it is an ideal, massless spring, it will not compress at all. Things would be more complicated due to the distributed mass of a real spring. But - one thing at a time, I advise.

If I take a spring in my hand and stretch it a length x more than its original length, with both my hands. Now, do both my hands experience an inward force F=−kxF = -kx?

Yes. And the work done would be divided between the two hands, which would 'share' the displacement.

 

[Dale]

if the spring is mass-less, then unequal forces at its two ends can never lead to any compression/expansion of the spring. Why is this true?

Anything massless must have a net force of 0, otherwise it would have infinite acceleration per Newton's 2nd law. Is that clear?

 

[sophiecentaur]

I think its problematic for me because it isn't as flexible as maths/programming. I am programmer/mathematician by field of study. Physics doesn't have that much creative potential in it.

If you think Maths and Programming are "flexible" then try doing the wrong operation in Maths or Programming at any time and you will find you get the wrong answer out. It strikes me that you are trying to approach Physics (in nearly all of your recent threads), expecting it to be 'flexible' and you are just getting upset because it is, in fact, a discipline and not just a bit of chatty fun.
As for "creative potential", the advances that have been made in Physics over the centuries demonstrate a lot of creative potential from leading edge Physicists. But, in addition to their creative potential, they have been prepared to learn the basics with hard personal effort and self discipline. If you want to use your own personal creative potential in a less demanding study, there are many other fields that can give satisfaction with less personal intellectual input.
Physics is Hard.

 

[andyrk]

Anything massless must have a net force of 0, otherwise it would have infinite acceleration per Newton's 2nd law. Is that clear?

Yes. That much is clear.

 

[Dale]

Yes. That much is clear.

So the net force on the spring must be zero, and therefore the forces on either side of the spring must be equal and opposite. Otherwise they would not sum to zero.

Edit: thread closed. If you have further questions please show some effort working through the analysis first.