The Mass of a Meter Stick

Mass of a meter stick without a scale: explanation and process 

part 1-Step 1 and 2:  


Step 1-Demo

A) In step A, we were supposed to evaluate what would happen when the meter stick is not balanced on the edge of the table and has a torque. Because it is off balance, I knew that the center of gravity will not be centered above the base of support, causing it be off balance and have a torque.

In this picture, the center of gravity is hanging off of the table. So, the ruler will rotate clockwise. The ruler's center of gravity is not over the base of support, so there is a lever arm. Torque depends on lever arm and force SO there will be a torque, causing the system to be off balanced. 

( torque= force x lever arm) 

B) In step B, we are supposed to evaluate the system when it is completely balanced. If something is balanced, there is no lever arm or torque because the center of gravity should be exactly above the base of support. 

In this picture, the center of gravity is directly above the table (basis of support). This means that there is no torque or lever arm causing it to be completely balanced.

C) 

(I GOT THIS PICTURE FROM CATHERINE)

Catherine took this picture in class of the 100g weight that is added to the end of the meter stick. Obviously, putting a 100g weight will certainly change the center of gravity/mass. This will force the meter stick to have a new point of center of gravity in order to balance the new 100g weight. However, because the system is not falling, and a new center of gravity has been found, the system is balanced. This means that the clockwise and counterclockwise torques are equal. (torque=force x lever arm)

Step 2- Planning

Wyatt and I approached finding the total mass by deciding to find the torque of the system. Because of this, we needed to use the equation torque=force x lever arm  
We also used the equation of counter clockwise and clockwise torques
counterclockwise torque = clockwise torque
f x la (before)= f x la (after)
finally we used the equation of weight to be able to calculate the force.
weight=gravity x mass

Aside from equations, we also needed to find the lever arms of each side of the center of gravity in order to fill out the angular momentum equation.

(also Catherine's pictures)

We planned to measure each lever arm in order to fill out the angular momentum equation.

Step 3-Process

When we finished planning equations and measurements, we eventually began calculating. We began by calculating the force of the weight in order to start filling out the equation of f x la (before)=f x la (after)

weight=mass x gravity

weight=.1kg x 9.8

weight=.98N 

.98N x la (before)= f x la (after)

After this, we measured the lever arms. The calculation of the side with the weight was relatively simple as we just needed to measure from the table (the center of gravity).

we measured it to be 29.5 meters

.98 x 29.5 (before)= f x la (after)

Then, we measured the lever arm of the other side. This was slightly tricky because we needed to measure from the center of mass of the ruler (excluding the extra 100g weight). This meant measuring from the exact middle of the ruler (50). We then were able to calculate the lever arm. 

We measured it to be 20.5

.98 x 29.5= f x 20.5

We then realized that we simply needed to solve for f. Through doing the math and converting to kilograms, we ended with the number .1439 kilograms, only .01 off of the actual weight. 

Step 4-Final Drawing!