ibwm said:
Homework Statement
Hi, the aim of this experiment is the investigate the relationship between the centripetal force acting on an object moving in a circle of constant radius and its frequency of revolution. For the experiment, there is a rubber stopper attached to fishing line, that is passed through a glass tube, and an alligator clip is used to keep the radius constant. Hanging on the fishing line are slotted masses, which are altered in order to alter the weight force, and in turn alter the centripetal force supplied by tension.
I have to amend a diagram to include the real rotation of the stopper and draw labelled vectors representing the forces acting on the rubber stopper whilst it is orbiting. I have tried to draw this diagram, but I am unsure as to whether it is correct, and have hence come here in seek of verification.
Homework Equations
Nil.
The Attempt at a Solution
The ideal diagram looks like this,
http://img140.imageshack.us/img140/2706/idealdiagram.png
Whilst the amended one looks like this,
http://img338.imageshack.us/img338/6104/amendeddiagram.png
But with the use of vector addition, I am unsure as to how this produces the tension resultant vector. Shouldn't there be a horizontal force too? If so, what is it? Please help.
Thank you in advance.
In the real situation, the Tension and the Weight force combine to make the horizontal Centripetal force.
In the ideal situation, the centripetal force is Tension, while the radius of rotation is L, the length of fishing line out the top of the tube.
In the second, real situation, where the stopper string is "drooping" at angle θ the horizontal, the Centripetal Force is only Tcosθ. However, the radius of the actual circle followed is only Lcosθ and when you finally get the relationship you will see that it is not surprising that those two cosθ factors effectivel compensate for each other / cancel out.
It is thus entirely reasonable to ignore the droop.
For those posters unfamiliar with the experiment, the slotted masses are added before each trial. In earlier editions of this experiment was performed with steel washers of a fixed, but undetermined mass, so the relation was derived in terms of F, 2F, 3F, 4F loads, rather than xx grams.
Once the weights are added, the tube is held above your head [not vertically, your heand operates at aboiut 45 degrees - you have to be able to see your hand holding the glass tube.
WHile holding the hanging weights, you begin spinning the stopper. As you do it you can feel the masses being supported by the tension in the fishing line - the same tension that supplies the centripetal force to the stopper.
When you experience approximate balance, you release the masses and try for balance.
If you rotate too fast, the stopper moves out / the masses move up.
If you rotate too slowly, the stopper moves in / the masses move down.
Get the speed just right and the masses stay in position - and a constant radius is maintained.
The paper clip is there so you can judge the balance situation. You usually try to maintain the paperclip at a chosen distance below the tube - perhaps 1 cm.
It is surprisingly easy to achieve balance after only a few minutes of trialling.
Your partner uses a stop watch to time, say, 10 rotations so that you can then calculate the Period - and thus frequency if you would like.
