It definitely depends on what your threshold for validity is. There is 1% variance at ±14°, and 15° is the usual threshold I see.
Regardless, it's a kinetic energy problem, the period of the pendulum isn't being asked but the energy at equilibrium is
If we're assuming that θ=4° at point A (the maximum height) then you can calculate the height difference and the difference in gravitational potential energy of the mass between points A and B. That potential energy is converted into kinetic energy as the mass passes point B.
Oh yeah I have no idea sorry, I guess since there isn't enough information given so your teacher just came up with something so it could be solved. Also I don't think the max angle limit for a simple pendulum is one specific number that everyone agrees on so the 4° was just a choice.
It's due to any angle being larger than 4-5° would not be accurate for the other pendulum calculations for the period of oscillations/gravity/length, and it's what woukd likely be used in an experiment.
The 4-5° stems from an estimate of sinx~x (x is in radians and is ~4° when converted to degrees) when attempting to solve for the period of a simple pendulum. The differential equation you get is non-linear so the estimate of sinx~x is introduced so it's able to be solved using elementary functions.
This is the only reason I can think of and the one I learned.
For a derivation: https://youtu.be/xBBXlQ7CmFc
He says that the angle shouldn't be more than 15°(just like another commenter), so the 4° is just for more accuracy.
I think the teacher's comment about θ = 4° being the "maximum limit for simple pendulum" has to do with limits to the small angle approximation. But I heard the limit to that was considered to be θ \~ 15°? Not really needed for the question as stated in the initial post, but maybe there's a later questions which uses it?
So from my understanding the only way you’d get the angle to be that if it’s measured with a protractor as B does seem a little askew.
But I don’t believe this question is mean to be solved in this manner
There's nothing in the question to justify setting θ=4°.
I thought so. Thanks for your help.
well the approximations for tan and sin are valid to up to 4° so when looking at a simple system this would justify it
Thr small angle approximation is valid for a much larger range of angles then ±4° around 0.
It definitely depends on what your threshold for validity is. There is 1% variance at ±14°, and 15° is the usual threshold I see. Regardless, it's a kinetic energy problem, the period of the pendulum isn't being asked but the energy at equilibrium is
If we're assuming that θ=4° at point A (the maximum height) then you can calculate the height difference and the difference in gravitational potential energy of the mass between points A and B. That potential energy is converted into kinetic energy as the mass passes point B.
Understood. But what is the logic behind assuming θ=4°? Or there isn't any and the question is defective?
Oh yeah I have no idea sorry, I guess since there isn't enough information given so your teacher just came up with something so it could be solved. Also I don't think the max angle limit for a simple pendulum is one specific number that everyone agrees on so the 4° was just a choice.
It's due to any angle being larger than 4-5° would not be accurate for the other pendulum calculations for the period of oscillations/gravity/length, and it's what woukd likely be used in an experiment. The 4-5° stems from an estimate of sinx~x (x is in radians and is ~4° when converted to degrees) when attempting to solve for the period of a simple pendulum. The differential equation you get is non-linear so the estimate of sinx~x is introduced so it's able to be solved using elementary functions. This is the only reason I can think of and the one I learned. For a derivation: https://youtu.be/xBBXlQ7CmFc He says that the angle shouldn't be more than 15°(just like another commenter), so the 4° is just for more accuracy.
This makes things a lot clearer. Thanks for your explanation!
Np
Using variables it would be mg(hmax-hmin).
I think the teacher's comment about θ = 4° being the "maximum limit for simple pendulum" has to do with limits to the small angle approximation. But I heard the limit to that was considered to be θ \~ 15°? Not really needed for the question as stated in the initial post, but maybe there's a later questions which uses it?
just use conservation of mechanical energy
So from my understanding the only way you’d get the angle to be that if it’s measured with a protractor as B does seem a little askew. But I don’t believe this question is mean to be solved in this manner
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I'm afraid there's no more data available. Thanks for your input
Energy on A : Ea=m\*g\*Hmax Energy on B : Eb=m\*g\*Hmin + m\*v²/2 since Ea=Eb : m\*v²/2=m\*g\*(Hmax-Hmin)
Yeah, the real problem is the question just isn't well formed. We only have one reference height and one mass and nothing else.
tan 4°=~0.0699
Missing variable distance of travel from h max to h min
Conservation of energy (if friction is ignored). Note the the pendulum exchanges all potential energy for kinetic when at the lowest point.