Optional Practical: Spinning stopper
Introduction
In this practical you are going to spin a rubber stopper on the end of a string. The string is passed through a tube and mass is attached to the other end (as in the diagram below), this will provide the tension in the string that will cause the stopper to move in a circle. Try swinging the stopper in a circle by holding the tube vertically, don't hold the string but allow the hanging mass to provide the tension. After a bit of practice you should be able to keep the frequency constant and the circle horizontal. If you try increasing the speed of the stopper you will notice that the string gets longer, it is the relationship between the Time period of the stopper and the length of the string that you will be investigating in this experiment.
Research question
How does the time period of the stopper depend upon the length of the string.
Independent variable: Length of string.
Dependent variable: Time period
Controlled variables: mass of stopper, mass hanging on string, method of spinning, friction in system, properties of string.
Theory
The centripetal force that causes the stopper to move in a circle is provided by the horizontal component of the tension and the Tension is equal to the weight of the hanging mass, W so we can write Mω2r = Wsinθ
We can see from the triangle made by the string in the diagram that sinθ = r/L substituting this gives:
Mω2r = Wr/L
so
Mω2 = W/L
Now ω is the angular velocity of the stopper this can be written in terms of the Time period, ω = 2π/T
Substituting this into the equation for centripetal Force gives:
M4π2/T2 = W/L
By varying the length and measuring the Time period use a graphical method to show that this relationship holds and find the mass of the stopper, M.