Concepts

Centre-of-gravity, dependence of friction on the normal force, balance of torques

Overview

A metre stick is supported on the two forefingers. The fingers are moved slowly together and end up at the centre-of-gravity of the stick.

Details

Equipment

• [1] Metre stick
• [1] 200-g weight
• [1] Plexiglas cylinder and a cork-covered piece of wood
• Optional: an 8-foot length of 2" x 2" and a 1-kg weight

Script

1. Place the metre stick on your forefingers with one finger at 0 cm and one at 100 cm.
2. Slowly move your fingers together. Your fingers will alternate between slipping and sliding along the stick and will come together at 50 cm, the centre-of-gravity.
3. Place a 200-g weight on one end of the metre stick.
4. Repeat steps 1 and 2. The centre-of-gravity has moved because of the weight and your fingers will come together on the side with the weight.
5. Repeat steps 1 through 4 using a plexiglass cylinder and a cork covered piece of wood instead of your fingers to show this works when the coefficients of friction of the supports are different.
6. (Optional) Repeat steps 1 through 4 above using an 8-foot length of 2" x 2" in place of the metre stick. Using a 1-kg weight on the end moves the centre-of-gravity to 70 cm from the end.

Here is a presentation of this demonstration by Julius Sumner Miller (Demonstrations in Physics pages 16 and 17):

Metre stick on two fingers

I. Support Symmetric 

A metre stick is supported horizontally on two fingers symmetrically placed. The fingers are pushed toward each other.

1. When at rest what force is supplied by each finger? 
2. When the fingers are pushed towards each other what forces now exist at each finger? 
3. What condition must be met for the fingers to experience identical motion? 
4. What now is the question to ask? And how is it answered? Why is this the answer? 
5. Suppose the fingers are replaced by two supports of enequal roughness, say an iron rod and a wooden stick or a rubber rod. What now? 
6. Can you conjure up a situation where, with symmetric supports to begin with, the supports will not meet in the middle? 
7. Suppose in all of this the metre stick is not uniform. What now will happen? Consider doing it with a baseball bat. 
8. Conjecture on what will happen if the fingers are moved away from each other.

II. Support Asymmetric 

The metre stick is supported as in I but the support is asymmetric. 

1. Consider each of the questions under I. 
   
2. The 'leading question', the principal inquiry, in this exercise is clearly this: In I the fingers (supports) meet in the middle. This is to be expected! In II the 'feeling' is that the stick will tip. But it does not! State in ordinary language for those unschooled in physics why it does not. 
3. At times in the experiment an observer claims that the fingers (supports) are not being moved or even pushed. Argue this away. 
4. These exercises were done with the stick horizontal. Explore the matter with the stick inclined somewhat, that is, one support a bit higher than the other. 
5. Suppose you make worse the conditions in both cases by loading the stick somewhere. What now obtains? 
6. Conjecture on the following: Two motors with long shafts reside side by side. Across the two shafts a plank or 2x4 is placed. The shafts are now turned by the running motors. What will happen to the plank?"

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