Monday, January 20, 2014

Meter Stick Experiment

In this lab, our goal was to find the mass of a meter stick using only the meter stick and a 100g lead weight.

The purple dot on the ruler shown above is the center of gravity (or mass).  The ruler above is balanced on the table because it's center of gravity is directly above the base of support (the table).  Therefore, there is no lever arm and no torque to make the ruler rotate at all.

This illustration shows a ruler with a lever arm.  In reality, this ruler would rotate counterclockwise.  Since the ruler's center of gravity is not over a base of support, there is a lever arm (shown in green).

As we know, torque depends on two factors:
Torque = Lever arm * Force

In class, we added a force to the left end of the ruler by adding a 100g weight. 
For the ruler to be balanced, the center of gravity of the ruler must be moved back to increase the lever arm.


Force * Lever arm   =  Force * Lever Arm

TO FIND METER STICK'S MASS
-First, you must find the weight of the 100g weight because that is the force.  You use the w=mg equation, using 9.8 as g and .1 as the mass (because it is 100g but in kilograms).  Therefore, the force from the weight is .98 N.
-Next, to find the lever arms of both sides, you measure the distance from the weight to the table:
-Then, we found the other lever arm by measuring from the point on the table to the center of mass of the ruler:

We measured both these lengths and got these results:
                Lever Arm 1: 24.5
                Lever Arm 2: 25.5


We then entered these measurements into the toque equation like so:
Torquecounter clockwise = Torqueclockwise
Force * Lever Arm = Force * Lever Arm
.98 * LA1 = w * LA2
(.98)(24.5) = w(25.5)
w = .94 N
To then convert this to grams, we plug it back into the w=mg equation, and get .096 kg, which converts to 96 grams.

We then weighed the meter stick and got 95.7 grams
Therefore, we were only .3 grams off!



Here's how to explain this lab on a quiz or test:







1 comment:

  1. Wow... Your blog is so thorough. I really like it. Your post on the meterstick is superb. How did you even have time for this? What? It was easy to follow and you made everything super neat. I think I might have actually learned a better way to solve the problem. Thanks.

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