Central Force Particle Lab

Central Force Particle
Paradigm Lab

Patrick Daisley
Joel E. Ferris High School, Spokane, Washington.

June 2009. This apparatus is outdated. When time allows I may update this page.
You can, however, get the general idea here.

This page roughly outlines my solution to the inadequacies of the Central Force Particle (uniform circular motion) lab.
After having my classes perform the old "string and glass tube" lab over several years I felt, as I think many others do, that the data collected by the students was of limited value. The challenge was to find a way of collecting data reliable and accurate enough to uncover the nature of the Central Force Particle model.
My solution involves using a box fan as a rotating platform while controlling the period of rotation with a variable voltage power supply. The period is measured with a photogate and the centripetal force is measured with a force probe. The radius of the motion is also easily changed and measured. I have used this apparatus for two years now and my students have achieved excellent results. Below are photographs of the setup with descriptions and information. Also included are some graphs of actual student data collected during this lab.
If you have any questions email me at physics@daisley.net. Comments and suggestions are always welcome.

This is an overview showing the apparatus.
A force probe is suspended above the center of the fan with lab stands and is connected to a CBL. A clear plastic tube is attached to the fan with screws and tape. A small mass on a string is inside the tube and is connected to the force probe. A photogate sits in one corner. A small flag is attached to one of the fan blades and passes through the photogate once per rotation. The photogate is connected to a computer via a ULI.

Both a CBL and ULI are needed because the software (LoggerPro) can not handle input from both the photogate (digital) and force probe (analog) at the same time. I have had conversations with David Vernier about this and believe that a future version of LoggerPro (or something similar) may be able to do this.
UPDATE I do not know but perhaps this is now possible using LoggerPro 3 and Labpro interfaces. (I sill have ULI's).

The plastic tube was purchased at Home Depot and is apparently used to protect fluorescent light bulbs. It is rigid but cuts easily with scissors. A hole is cut in the top and a pulley is attached as shown (I used Knex).
The tube is then attached to the fan using a screw (the ones that held the fan cover on) and tape. The pulley is aligned so that one edge is above the center or rotation for the fan. A small mass is attached to a string and placed in the tube so that the string wraps around the pulley. The ball bearing acts as a counter weight on the other end of the tube.

The other end of the string is attached to the force probe suspended above the fan. A fishing "spinner" is connected in line so that the string won't wind up as the fan rotates. (Note: some sewing machine oil on the spinner proved very useful.)
It is important to line the force probe up with the center of the fan to reduce variations in the force measurements. A CBL, TI-83+ and Vernier's Physics application was used with the force probe. The 60 force readings taken over 3 seconds were averaged.

A variable voltage power supply was used to vary the speed at which the fan turned. The 3 position switch on the fan was set to "medium" and the power supply was set to 0-15V AC. This kept the fan from spinning too fast.
I believe that a control mechanism could be built using a dimmer switch, electric outlet, receptacle box and cord with a plug in place of the power supply. Another teacher in my building built such a device to vary the brightness of light bulbs. It has the advantage of being cheaper than the power supply.

By raising and lowering the height of the cross bar holding the force probe, the radius of the path the mass follows can be varied. The radius itself is measured the old fashioned way.

I have found that the students have an easier time varying the period and measuring the force than they do varying the radius. The setup takes a little getting used to and this is a good place to start.
The kids vary the speed at which the fan rotates and measure the period by looking at a period-time graph displayed on the computer using LoggerPro, or other similar software. When a constant period is reached, as shown by the graph, the force is measured with the force probe and CBL. Again, it is necessary to take many force readings and average them. Vernier's physics application for the TI-83+ will draw a regression line on the force-time graph. The slope is near zero and the intercept is a good value for the centripetal force. It is easy to collect 15-20 data points this way.

Once they have collcted data for changing period they are familar enough with the setup that the changing radius collection goes smoother, and faster. Decreasing the radius is by far the best way to go. If the students are careful they won't have to re-string the pulley each time they change the radius. By raising the cross bar the mass is pulled in a few centimeters. The kids can then measure the distance from the center of rotation to the center of the mass with a ruler, as shown above. When the power is turned back on they will need to adjust the rotation of the fan using the power supply to maintain the same constant period. Many students think that if the voltage reading on the power supply isn't changed then the period remains constant. This is a common source of error. A quick demo using a solid wood wheel and a hollow metal wheel of the same mass and diameter can help them see that they don't behave the same when the mass distribution is different. When they have the necessary period again they can collect the force data as before.
When finished collecting data I had my students graph it using Graphical Analysis. One group's actual data from this year is shown below.
Plan on spending several days on this lab. I needed to show my students how to use the CBL's and they needed a day to figure out how to work well together as a group with this equipment.

The graph shown to the left is the student graph for force verses radius at a constant period. It shows that the force is proportional to the radius of the circular path.
The graph lower left shows the relationship between the force and period at a constant radius. The graph below is the linearized graph of force verses period and shows the that the force is proportional to the inverse square of the period.
These graphs are typical of the results most student groups achieve. Naturally some get better results, some not as good. In general, I have been very pleased with the results of this lab. No more glass tubes and stoppers for me!

This page roughly outlines my solution to the inadequacies of the Central Force Particle (uniform circular motion) lab. After having my classes perform the old "string and glass tube" lab over several years I felt, as I think many others do, that the data collected by the students was of limited value. The challenge was to find a way of collecting data reliable and accurate enough to uncover the nature of the Central Force Particle model.		My solution involves using a box fan as a rotating platform while controlling the period of rotation with a variable voltage power supply. The period is measured with a photogate and the centripetal force is measured with a force probe. The radius of the motion is also easily changed and measured. I have used this apparatus for two years now and my students have achieved excellent results. Below are photographs of the setup with descriptions and information. Also included are some graphs of actual student data collected during this lab. If you have any questions email me at physics@daisley.net. Comments and suggestions are always welcome.