# Major trouble with a ball attached to a string on a pole...

## Homework Statement

A 0.5 kg mass is attached to a string that is 20 cm tall and anchored to a pole. There is an angle between the string and the pole.

1) What is the force of gravity on the mass in terms of the angle?
2) If the mass is pulled slightly to an angle of 5 degrees and if sin(theta) is congruent to theta, find an equation and its solution that best fits the case when at time = 0 the mass is held at 5 degrees. (If you are stuck, please consider the following two questions: a) What is the moment of inertia of the mass on the string in terms of mass and string length L? b) What is the expression for the angular acceleration I(omega) in terms of mass and string length L and d(theta)/dt when one notes that d(theta)/dt = omega?)
3) Will the mass oscillate if the mass is released after being pulled to 5 degrees?
4) If it oscillates, what is the angular frequency if the mass is 0.2 kg?
5) If it oscillates, does doubling the mass change the frequency, and if so how?
6) If it oscillates, does doubling the length of the string change the frequency, and if so how?

## Homework Equations

omega = 2(pi)(frequency)

## The Attempt at a Solution

1) The only one I could really answer. Fsin(theta), which is equal to mgsin(theta).
2) I don't know. I absolutely don't understand this. My teacher would only give me the answer (900 m) and told me I have to figure out the solution on my own. And I don't get it.
3) I think it could. It can go into simple harmonic motion, although it is eventually slowed by friction and air resistance. Plus, I don't think my teacher would have asked questions 4-6 if this wasn't yes.
4) omega
5)
6)

I am having an unbelievably hard time with this. This is an intro to physics class, and I can't believe my teacher would seriously give this when she did not go over the subject. I've been self-teaching, and I'm still not sure I got the topic 100%. I seriously need someone to guide me through this. Any and all help is appreciated!

Simon Bridge
Homework Helper
Not enough information.
Is the pole upright and the ball is swinging around the pole or more of a pendulum arrangement with the pole horizontal or what?
We should be able to draw a diagram from your description.

1. the force of gravity does not depend on the angle of the string - the net force probably does though.
2. how can the sine of an angle be "congruent to" the angle? You can have two angles that are congruent...
But can you answer a and b?
3. good reasoning.

I suspect some sort of pendulum arrangement - and you have recently done coursework on simple harmonic motion ... so that material should help you figure it out.

Not enough information.
Is the pole upright and the ball is swinging around the pole or more of a pendulum arrangement with the pole horizontal or what?
We should be able to draw a diagram from your description.

1. the force of gravity does not depend on the angle of the string - the net force probably does though.
2. how can the sine of an angle be "congruent to" the angle? You can have two angles that are congruent...
But can you answer a and b?
3. good reasoning.

I suspect some sort of pendulum arrangement - and you have recently done coursework on simple harmonic motion ... so that material should help you figure it out.

Hi, thank you for assisting me!

As for the diagram, the pole, according to my teacher, is upright and the ball is pulled to the right at a certain degree. So it should be swinging left and right in simple harmonic motion. Kind of like in the following picture, minus the measurements. 1) I just figured that the ball's acceleration is gravity, so F = mg. Then, because it asked for angle, I just used the one available in the question.
2) I honestly don't know what my teacher wants in this question. I don't know where to start or even go with this. I don't know how to solve A and B either, although I am familiar with both topics.
3) thank you

And it looks like I left the rest incomplete for some reason! Sorry, I must have not saved it right.

4) I absolutely don't know.
5) Yes. If the ball is heavier, it will have a lower frequency and a lighter ball a higher frequency.
6) The length of the string doesn't affect the frequency. It depends more on the angle and the mass of the ball.

haruspex
Homework Helper
Gold Member
2020 Award
1) I just figured that the ball's acceleration is gravity, so F = mg. Then, because it asked for angle, I just used the one available in the question.
Gravity is a force on it, and its magnitude will be mg, but g will not be its acceleration. The acceleration will come from the net force, so takes into account the tension in the string.
With regard to q2, I believe it should say sin(theta) approximates theta (because theta is small).

CWatters
Homework Helper
Gold Member
1) What is the force of gravity on the mass in terms of the angle?

Brinstar - Can I recommend you check and repost the questions if any are incorrect.

I may be wrong, but I think you should look over 5 and 6 again.

Okay, to clarify all the questions, I scanned the document and took a screenshot of the question. This is the original, and my teacher had everything rephrased in class the way I wrote it. So 2 and 3 were used as subsections to solve for 4 rather than being actual questions.

Gravity is a force on it, and its magnitude will be mg, but g will not be its acceleration. The acceleration will come from the net force, so takes into account the tension in the string.
With regard to q2, I believe it should say sin(theta) approximates theta (because theta is small).

Oh gosh, now I'm confused. I tried asking my teacher for more help, and she said the answer to 1 was mgsin(theta). I am very unsure of myself now.

And yeah, it's probably approximates. I thought it meant congruent, so that's my bad >.<

Brinstar - Can I recommend you check and repost the questions if any are incorrect.

I may be wrong, but I think you should look over 5 and 6 again.

Okie doke, I'll check it out again. I wouldn't be surprised if I goofed that up.

#### Attachments

haruspex
Homework Helper
Gold Member
2020 Award
Oh gosh, now I'm confused. I tried asking my teacher for more help, and she said the answer to 1 was mgsin(theta). I am very unsure of myself now.
The force of gravity is always going to be mg here. Your teacher should have asked for the net force. Can you see how to get her answer with that interpretation?
(And yes, that equals sign with a tilde above it means is approximately equal to.)

Simon Bridge
Homework Helper
I'm with haruspex here. I'd also ask what stops the ball from hitting the pole, but Im cheeky that way. ;)

You can see haruspex is correct if you draw a free body diagram... gravity mg points down and tension T points off to the right at angle ##\theta## to the vertical. (This is like those problems you've probably seen where something slides down a slope, only you get tension instead of a normal force.)

You are going to want something like ##\tau = I\alpha## ... take care to distinguish between the oscillator angular frequency and the instantanious angular velocity of the mass.

CWatters