Locating the Center of Gravity: The Dance of Normal and Frictional ForcesNuri Balta

Citation: The Physics Teacher 50, 456 (2012); doi: 10.1119/1.4758140 View online: http://dx.doi.org/10.1119/1.4758140 View Table of Contents: http://scitation.aip.org/content/aapt/journal/tpt/50/8?ver=pdfcov Published by the American Association of Physics Teachers Articles you may be interested in Getting the Swing of Surface Gravity Phys. Teach. 50, 232 (2012); 10.1119/1.3694077 Resource Letter PTG-1: Precision Tests of Gravity Am. J. Phys. 78, 1240 (2010); 10.1119/1.3481700 Inductively Modeling Parallel, Normal, and Frictional Forces Phys. Teach. 43, 107 (2005); 10.1119/1.1855748 The Pendulum, Gravity, and that Number “9.8” Phys. Teach. 42, 14 (2004); 10.1119/1.1639961 Demonstration of independent motion of two objects influenced by gravity and Newtonian friction Am. J. Phys. 66, 644 (1998); 10.1119/1.18926

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456 The Physics Teacher ◆ Vol. 50, NoVember 2012 DOI: 10.1119/1.4758140

meet at the center again. They usually argue that the oily fin-ger will move more than the other one. They are especially surprised to watch the demo when the oily finger is initially placed at the center. It is instructive to repeat the demonstra-tion using a pencil and a wooden rod instead of fingers to show that the demo works when the coefficients of friction of the supports are different. It is also worth doing the demon-stration by placing the stick on a finger and a pencil.

Demonstration with one end of the stick loaded

Afterwards, vary the conditions by loading the stick some-where. Depending on the mass of the stick, hang an appro-priate object on one end of the stick, as shown in Fig. 2, and perform the above demonstrations again. Students are now confident to guess that regardless of the starting position of the hands, the fingers will come together at the center of grav-ity of the system. It is instructive to hang the stick, or support it from below, at the point where the fingers meet up to show that there is no net torque acting on the system.

Then take a pole or a stick of irregular shape and find its center of mass with this method; you can easily hold up the pole with only one finger as long as it can withstand the en-tire weight of the pole. This can also be done with a bat or a broom.

Locating the Center of Gravity: The Dance of Normal and Frictional ForcesNuri Balta, Middle East Technical University, Ankara, Turkey

Teaching physics concepts with the basic materials that are around us is one of the beauties of physics. Without expensive lab materials and long experi-

ments, many physics concepts can be taught to students using simple tools. Demonstrations with these tools can be presented as discrepant events that surprise, amaze, or puzzle students. Greenslade1 has excellently described 14 things we can do with a stick, one of which is the “stick on two fingers.” In this paper I describe some variations of the “stick on two fingers” demonstration.

A meterstick on two fingers Hold a uniform stick or metal pipe horizontally between

your extended forefingers such that palms face each other as shown in Fig. 1(a). Ask students where the fingers will meet if you push them toward each other. Most students predict that they will meet at the center of the stick. Now, move your fin-gers underneath the stick and confirm that your students are right. The fingers will slip and slide along the stick, coming to-gether at the center of mass. I usually ask, “Is anyone surprised at what happened?” The general answer is no. Then I say, “It is time for amazement,” and I place my forefingers so that one end of the stick sticks out further than the other end, as shown in Fig. 1(b). The next question is: “If I slowly bring my fingers together, will they again meet at the center of the stick?” Most, if not all, of the students erroneously say no. Then I conduct the demonstration and my fingers meet at the center of the stick. Many observers do not give up and claim that I purpose-fully move my hands such that they end up at the center. So I let a volunteer repeat the demonstration and he/she usually ends with a smile! Many other students also try and all have fun with it; they even start doing it with their pencils or pens.

Demonstration with one oily finger Now, oil one of your fingers and ask students what will

change if you repeat the above demo. Since oil decreases the friction, it is hard for students to predict that the hands will

Fig. 1. (a) Fingers are at equal distances from the ends. (b) Left-hand finger sticks out the end of the stick.

Fig. 2. One of the ends of the stick is loaded.

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The Physics Teacher ◆ Vol. 50, NoVember 2012 457

Oscillation of a stick on two shaftsThis version can either be designed by or discussed with

students. Have two small motors with parallel shafts side by side (see Fig. 6). Place a small plank across the two shafts at equal distances to the ends of the shafts. The shafts are now turned at opposite directions by the running motors. The question to observers is: “What will happen to the plank?” It is not difficult for students to conclude that it will stay in equilibrium. However, repeat the experiment by placing the plank at unequal distances from the ends of shafts and ask students’ opinions. If you have gifted students, you are lucky to hear this answer: the plank will oscillate.

ConclusionThe above demonstrations with simple materials (general-

ly only a stick) illustrate many physics concepts such as center of mass, torque, frictional force, and normal force.

Reference1. Thomas B. Greenslade, “Fourteen things you can do with a

stick,” Phys. Teach. 39, 106–107 (Feb. 2001).

Nuri Balta is a physics teacher and head of the physics department at Private Samanyolu Cemal Sasmaz College in Ankara-Turkey. He has taught high school physics courses in Kazakhstan (7 years) and Uzbekistan (one year). As an experienced teacher (18 years) he guides physics teachers for effective teaching methods and he is currently pre-paring gifted students for International Physics Olympiads. In addition, he is a doctoral student in physics education at Middle East Technical University in Ankara.nuribalta@yahoo.com

Demonstration when the stick is inclined

The above exercises were done with the stick horizontal. Now, let’s try something a little bit different—explore the situ-ation with the stick inclined, where one end is higher than the other (Fig. 3). Unfortunately, although students comprehend what has happened previously, this time they again generally misapprehend and believe that the fingers will not come to-gether at the center of mass.

Demonstration when one of the supports is fixed

Until now, we have found the center of gravity with both supports moving and the stick stationary. Next, fix one of the supports as shown in Fig. 4 and move only one finger. When you conduct this demonstration, sometimes only your hand will move and sometimes the stick will move together with your hand.

A plate on three fingers

Take a large dinner, or other flat, plate with objects on it, perhaps even a glass of water (Fig. 5), and use three fingers spread wide to support it. Slowly bring the fingers together, making sure that your fingers are dry. Support the point where your fingers meet up with only one finger to indicate the center of mass of the three-dimensional system. If you use a wooden plate, you can drive a nail at the center of mass of the system and hang all the weight from this point to show the center of mass of a three-dimensional system.

Fig. 3. Left hand is a bit higher than the right hand.

Fig. 4. One of the supports is fixed.

Fig. 5. A wooden plate on three fingers.

B

B

Fig. 6. Oscillation of a stick on two shafts. Top view of the design of the demonstration with two motors.

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