What is the Relationship Between Restoring Force and Angle in a Pendulum?

  • Thread starter Thread starter mancity
  • Start date Start date
  • Tags Tags
    Pendulum
AI Thread Summary
The discussion centers on the relationship between restoring force and angle in a pendulum, with a focus on the correctness of answer choice (IV). Participants express confusion over the definitions of restoring force and its direction, noting that it points toward the rest point but may not always align with the pendulum's path. The consensus suggests that both answer choices (III) and (IV) can be correct, particularly under the small angle approximation, which simplifies the relationship between angle and restoring force. The ambiguity in the question's wording is highlighted, indicating that it lacks clarity regarding the forces involved. Ultimately, the correct answers are identified as (III) and (IV) when considering these factors.
mancity
Messages
26
Reaction score
2
Homework Statement
Which of the following is true regarding the restoring force on a pendulum?

I. The force is constant and dependent on the mass of the pendulum bob.

II. The force is always in the same direction.

III. The force is proportional to the distance from the rest point.

IV. The force is always directed toward the rest point.
Relevant Equations
n/a (conceptual problem)
I put the answer as (IV) but that happens to be wrong (or maybe it was only one of the multiple correct answers). Here is my reasoning:
I. the force is dependent on mass, but isn't always constant.
II. It's not always in the same direction, it points towards the rest point. Consider a point at top/ almost near the bottom. they won't be in the same direction
III. I believe it is proportional to the angle, not the distance.
IV. I'm pretty sure this is true, as intuitively that's what a restoring force does
Can someone help me as to why this answer of (IV) is wrong, and help guide me towards the correct answer(s)? Thanks
 
Physics news on Phys.org
Please, see:
https://courses.lumenlearning.com/suny-physics/chapter/16-4-the-simple-pendulum/

https://en.wikipedia.org/wiki/Pendulum

Figure_17_04_01a.jpg


200px-PenduloTmg.gif

200px-Oscillating_pendulum.gif
 
mancity said:
Homework Statement: Which of the following is true regarding the restoring force on a pendulum?

I. The force is constant and dependent on the mass of the pendulum bob.

II. The force is always in the same direction.

III. The force is proportional to the distance from the rest point.

IV. The force is always directed toward the rest point.
Relevant Equations: n/a (conceptual problem)

I put the answer as (IV) but that happens to be wrong (or maybe it was only one of the multiple correct answers). Here is my reasoning:
I. the force is dependent on mass, but isn't always constant.
II. It's not always in the same direction, it points towards the rest point. Consider a point at top/ almost near the bottom. they won't be in the same direction
III. I believe it is proportional to the angle, not the distance.
IV. I'm pretty sure this is true, as intuitively that's what a restoring force does
Can someone help me as to why this answer of (IV) is wrong, and help guide me towards the correct answer(s)? Thanks
It's a poorly thought out question.

First, which force, the net force, gravity, the tension, or some component of one of those? I would say "the restoring force" could mean the component of the net force directed along the path of travel.

Next, is one supposed to consider that the path of the bob is an arc?
To get true SHM, we need to consider only a vanishingly small arc of swing so that we can approximate it as linear. That makes III and IV both true.
Treating it as the arc it really is, there is some ambiguity in "towards the rest point". That could mean directly towards it, or in that direction along the path of travel which leads to to the rest point. Combining my interpretation of restoring force with that latter interpretation of direction makes your answer defensible; III is not.
 
  • Like
Likes mancity and Chestermiller
So, per my understanding, would the correct answer then be III & IV? (because that is indeed an answer choice. all other answer selections only have one, i.e. I, or II, or III, or IV).

Because I believe III only holds for small angles (in which we can approximate theta=sin(theta)), which would make that statement true.
 
mancity said:
So, per my understanding, would the correct answer then be III & IV? (because that is indeed an answer choice. all other answer selections only have one, i.e. I, or II, or III, or IV).

Because I believe III only holds for small angles (in which we can approximate theta=sin(theta)), which would make that statement true.
As I wrote, depending on interpretation, IV also only holds for small angles, so III and IV is a reasonable answer.
 
haruspex said:
First, which force, the net force, gravity, the tension, or some component of one of those? I would say "the restoring force" could mean the component of the net force directed along the path of travel.
I think it's worse than that. The equation that one normally writes for the hanging mass involves a restoring torque, ##\tau=-mgL\sin\theta##, not a restoring force. The small angle approximation appears not to be an issue because "small angles" is not mentioned as a premise to the choices.
 
Last edited:
kuruman said:
I think it's worse than that. The equation that one normally writes for the hanging mass involves a restoring torque, ##\tau=-mgL\sin\theta##, not a restoring force.
True, but it can be expressed in terms of force on, and acceleration and displacement of, the bob. That could be either treating it as a straight horizontal line (small angle approximation) or displacement etc. around a curved path.
kuruman said:
The small angle approximation appears not to be an issue because "small angles" is not mentioned as a premise to the choices.
We agree the question is shoddy, so small angles could have been the intent.
 
The correct answer as given by the system is III & IV. I believe small angles were indeed the intent for this problem.
 

Similar threads

Back
Top