Students were asked to read 2.1 Seesaws in How Things Work, or Ch 11: Rotation in the Cartoon Guide to Physics and watch the following videos before class. I really enjoy Doc Schuster’s physics videos.
Before we started the lab, I had cut out some very weird shapes out of cardboard and asked the students to find the center of mass of the shapes. Most knew to try to balance the shape on a finger and the center of mass would be the spot above their finger when it was balanced. But some of the shapes didn’t work for this, like the one on the left in the photo below.
Another way to find the center of mass is to hang the object on a nail or tack and then let a string with a weight (plumb line) hang down as well. The center of mass of the object will fall on this line. If you do this from two points (2nd almost horizontal line was found by hanging the shape from the hole on the right), the center of mass can be found at the intersection of the two lines. For this oddball shape below we see the center of mass is not in the object at all, which is why it was impossible to balance it on a finger.
The lab for today was one I did before, but I think we got it to work a bit better this time. Students tied a rubber stopper to a string, fed the string through an acrylic straw and then tied a weight to the other end of the string. By holding on to the straw and letting the string slide through the straw, the students could make the stopper go in a circle of radius r, above their heads at constant speed, v (or at least that’s the goal). The weight on the end of the string is the centripetal force and is measured using a spring scale. For uniform circular motion Fc = mac = mv2/r.
We can rearrange that so v2 = macr. In this lab we measures the velocity of the rubber stopper being swung around at different values of the radius, r. To measure the speed of the stopper we need to know the distance traveled (d = 2 π r x 10) as it completes 10 revolutions and the time, t, it takes to travel that distance: v = d/t. Since its a bit difficult to measure the time of 10 revolutions, students did each measurement 3 times and used the average time to calculate speed. Once they had the speed, v, they found v2 and graphed it as a function of the radius, r. Data should form a line (y= mx + b, v2 = y, m(slope) =ac, x = r and b(y-intercept) = 0 ) with a slope equal to the centripetal acceleration. The value they get from their slope should be the same as Fc / m=ac when they plug in the force of the weights hanging on the string in Newtons and the mass of the stopper in kg (measured on a triple beam balance).
Since there were a lot of calculations in this lab, I encouraged the students to try using a spreadsheet on their tablets or smart phone. Most had never used a spreadsheet before so its a good learning experience. (I frequently get frustrated using Numbers to make graphs and found this website which explained a problem I always had.) Here’s a graph of one set of data and the best line drawn through the data points and the origin.
The slope of this graph is 53 m/s2 which is very close to the value of acceleration found by taking the known force and dividing by the mass of the stopper (54 m/s2).
This lab worked much better this time and I think using the acrylic straws instead of empty pens helped, as did using a larger centripetal force (0.7-1.0 N).