Maximum extension of the spring

[Jahnavi]

Homework Statement

Ans) F/k

Homework Equations

The Attempt at a Solution

Consider only figure a) .

I believe the given answer is wrong . The maximum extension should be 2F/k . F/k is the extension in the spring in the equilibrium position . Maximum extension should be double of that .

Work energy theorem also gives maximum extension to be 2F/k .

But the answer given is F/k .The book answers are mostly correct .

Is book answer correct ?

 

[BvU]

F/k is the extension in the spring in the equilibrium position . Maximum extension should be double of that

How do you come to that conclusion ?

 

[BvU]

Work energy theorem also gives maximum extension to be 2F/k

SAme question: how do you calculate that ?

I do agree that the question is phrased a bit unclear -- in this case, they refer to the static situation, not the dynamic situation you would get when a mass hangs from an unstretched spring and is left to drop suddenly.

 

[Doc Al]

Consider this: In (a), what force does the wall exert on the spring? Now compare that to (b).

 

[Jahnavi]

Consider this: In (a), what force does the wall exert on the spring? Now compare that to (b).

I am considering only figure a) .Please ignore fig b) .

Is the book answer F/k correct for figure a) ?

 

[BvU]

Yes

 

[Jahnavi]

Yes

When the block is in equilibrium then F=kx .This gives x=F/k . But the question is asking for maximum extension .

in this case, they refer to the static situation, not the dynamic situation you would get when a mass hangs from an unstretched spring and is left to drop suddenly.

How can there be a static situation in this problem ? Please consider only figure a) .The block will perform SHM .

I am assuming a constant force F .

 

[Doc Al]

I am considering only figure a) .Please ignore fig b) .

Don't do that. If you understand how the two figures compare, you'll understand why they both have the same answer.

Is the book answer F/k correct for figure a) ?

Yes.

 

[Doc Al]

How can there be a static situation in this problem ? Please consider only figure a) .The block will perform SHM .

I'm interpreting this as a static case. Everything shown at the equilibrium position. (As BvU said, the problem statement is a bit unclear.)

(What textbook is this from?)

 

[Jahnavi]

I'm interpreting this as a static case. Everything shown at the equilibrium position.

What sense does it make to ask for "maximum extension" if this is a static case ?

I am interpreting this as if the spring is initially in the unstretched position and then a constant force F starts to act .

 

[Doc Al]

What sense does it make to ask for "maximum extension" if this is a static case .

Poorly worded, I will admit. (What's the complete problem with all parts?)

I am interpreting this as if the spring is initially in the unstretched position and then a constant force F starts to act .

I interpret them as two situations where the masses are held in equilibrium by the applied force. (I assume they will then remove the applied forces and SHM will ensue.)

Would you at least agree that if you assumed that interpretation the book answer makes sense?

 

[Jahnavi]

I interpret them as two situations where the masses are held in equilibrium by the applied force. (I assume they will then remove the applied forces and SHM will ensue.)

That's exactly what part b) of the question asks . Now I see your point .

Would you at least agree that if you assumed that interpretation the book answer makes sense?

Only if "maximum" word is removed from the question .The question should simply ask about the extension when the block is held in place by a force F .

Do you agree ?

 

[Doc Al]

That's exactly what part b) of the question asks . Now I see your point .

Good.

Only if "maximum" word is removed from the question .The question should simply ask about the extension when the block is held in place by a force F .

Do you agree ?

I agree with you. Sloppy wording in part (a), but that's why you need to sometimes read (b) to make sense of (a).

 

[Jahnavi]

Consider this: In (a), what force does the wall exert on the spring? Now compare that to (b).

I find this interesting that the two figures are equivalent as far as the extension in the spring is concerned (same extension ) , but they have different time periods of oscillation .Time period of a) being √2 times that of b) .

 

[Doc Al]

I find this interesting that the two figures are equivalent as far as the extension in the spring is concerned (same extension ) , but they have different time periods of oscillation .Time period of a) being √2 times that of b) .

Yes, it is interesting. The simplest way (at least for me) is to think of where the stationary point is for SHM. In (a) it's at the end of the spring, but in (b) it's at the middle.

 

[Jahnavi]

Thanks !

 

[BvU]

That's exactly what part b) of the question asks . Now I see your point .

So do us all a favor and state the FULL problem statement at a future occasion. Saves helpers guesswork -- guesswork that came out right in this case but can cause a lot of confudsion in others.