We found the mass of a meter stick without using a scale!

The goal of this lab was to find the mass of a meter stick with our new knowledge of torque, a meter stick and a 100g lead weight.

First we did a demo with a meter stick unbalanced on the edge of a table with a torque. In order to make sure that we understood how to label the parts of torque (force and lever arm) we made diagrams.

The first diagram just showed the unbalanced meter stick.

The next diagram had a meter stick balanced, showing the relationship between center of gravity and the edge of the table. The center of gravity can never be over the base of support so there is only one lever arm in this situation. It is important to remember that the lever arm only stretches between the axis of rotation and where the force is applied.

When the 100g mass is added to the meter stick, the lever arm in the counterclockwise torque extends from the axis of rotation to the end of the meter stick only because that is where the force from the 100g lead mass is applied. However, on the clockwise side, the lever arm stretches from the axis of rotation to the center of gravity of the entire meter stick because that is where the force of gravity is applied. On the meter stick, the center of gravity is the 50cm mark and will always be the 50cm mark.

Plan:

Our plan to use our knowledge from unit 4 was as follows.

1. Find the center of gravity of the counter-clockwise side (with the mass) by finding the centimeter mark on which it is balanced on the edge of the table.
2. Measure the lever arms on each side.
3. Use the lever arms and the force of gravity (9.8N) to find the clockwise and counter-clockwise torques.
4. Use w=mg to find the mass.

It took us a couple of tries to figure out exactly what numbers to plug in, but when we figured it out, this is what it looked like:

• Counter-clockwise lever arm: the distance from the center of gravity to the 100g lead weight
• 24.8cm
• Clockwise lever arm: center of gravity - the counter-clockwise lever arm
• 25.2cm
• Force on the counter-clockwise side: force of gravity / 100g
• 0.98N
• Force on the clockwise side: unknown

Our equation to set the counter-clockwise and clockwise torques equal to each other ended up looking like this:

Then we multiplied it out to find:

 

 



We then divided each side by 25.2 in order to isolate the force and found that:

 

We know that force is equal to mass x gravity so we divided by the force of gravity to find the mass:

However since we were looking for the mass of the meter stick in grams, we had to divide the mass in kilograms by 1000 and found that: