How Do You Calculate the Swing Angle in a Conical Pendulum?

[ImStuck1]

Conical pendulum question help!?

Homework Statement

By resolving forces horizontally and vertically and using Newtons second law, find an expression for the angle swung out. You must use calculus where needed. Use this analysis to answer questions 1-3
Q1: Will a child swing at a greater angle than a heavy adult?
2: Will people on the inside swing out at the same angle?
3: Will empty chairs be a problem?
The context is of a chair-o-plane ride
I'm very stuck and need some help please!
solution
Honestly I have no clue, I have inklings for each question, like I know there is a formula that would probably give me question one if I assume the weight of the child/adult but I've been looking for two hours and I can't find anything on the internet!

 

[voko]

Start by writing down the forces acting an a chair.

 

[ImStuck1]

There is force pushing the chair up from the ground and one pushing it down (I guess gravity). What next? :)

 

[voko]

What is this force that is "pushing the chair up"?

Draw it! A chair is attached to the carousel with a chain. What forces could possibly act on a chair in this arrangement?

 

[ImStuck1]

We learned that the force is simply called lift. I don't know of that is the correct term or not.
i've got it in front of me, at a stand still its those two forces but when you turn the chair o plane there is third force pushing it out, right?

 

[voko]

Lift is usually considered for things with an "aerodynamic" shape, such as a wing of an airplane. The lift of a typical chair would be negligible (although one could imagine a specially designed aerodynamic chair generating some serious lift).

What about the tension of the chain? Is it a force?

 

[ImStuck1]

Yeah I guess it is, if we assume that the thing isn't stretchy is it always the same force?
Then the weight of the object its another force?

 

[voko]

Everything is stretchy to an extent. The chain is designed to be stretchy enough to hold the flying chair.

So now you have two forces. Note they are at an angle to one another. What is the resultant force acting on the chair?

 

[ImStuck1]

Don't we have three forces? Gravity, lift and tension? Possibly four with weight?

 

[voko]

Gravity = weight. For lift, we have no data in the problem. Of course, we could make some conclusions on the effect of lift on the system even without data from general principles, but I think it will be easier for you to understand first what happens when lift = 0.

 

[ImStuck1]

So we have tension and weight/gravity. Is the resulting force pushing the chair away from the centre of the spinning?

 

[voko]

That's for you to answer, "by resolving forces horizontally and vertically". I cannot do the entire assignment for you :)

 

[ImStuck1]

Ahh I think I get it, when you make the weight bigger the angle increases? But there would be a point when it doesn't increase any moreand starts to decrease. I think I understand that part now! You've been such a great help!

 

[voko]

I suggest, at this stage, you really should write the equations down. Then you can make conclusions.

By the way, what angle are you measuring? From the vertical or from the horizontal? Both are valid approaches, but you need to choose one and stick with it.

 

[ImStuck1]

from the vertical.
So I guess if I do two different tests, one with a person at 40kgs and one at 80kgs where the tension is the same can you find it the angle?

 

[voko]

You do not need any tests. You need to write the equations connecting the forces, in vertical and horizontal projections, just like the problem requires.