Finding the Mass of a Meter Stick without using a Scale

Goal of assignment: Find the mass of a meter stick using only a meter stick and a 100g lead weight. 

Our reminders: 

a.) convert g to Kg 

b.) Use 9.8 when converting mass to weight 

Step 1- Demo 

A.) The meter stock is not balanced on the edge of the table and has a torque. Below is a picture of the meter stick with labels such as the force and lever arm that cause the torque.

B.) Now the meter stick is balanced on the edge of the table. What do you now know about the relationship between the edge of the table and the center of gravity? Refer to the picture below for answer. 

Answer: The edge of the table is where the center of gravity is, when the meter stick is balanced.

C.) Now see how the balance point changes when the 100g mass is added to the end of the meter stick. Refer to the picture below to see the forces and lever arms that are causing the clockwise and counterclockwise torques. (Hint: has the center of mass of the meter stick itself changed just because we added the mass to the end?)

Step 2- Planning 

In this section I will list:

A.) the equations used

B.) measurements taken

C.) reasoning behind my choices

A.) Equations

- Torque= F x Lever Arm (Torque= Force x Lever Arm)

- w=m x g (Weight= Mass x Gravity)

B.) Measurements taken

- Length of the lever arms
- weight of the added weight

C.)  Reasoning behind my choices

I choose the equation, w=mg, because I need to convert the weight of the added weight. That will let me know how much force is acting on the meter stick besides gravity. I need to have the equation,
Torque= F x Lever arm, because I need to find out the force of the side where the weight will not be placed. I need to find the length of the lever arms because I need that to figure out the torque. Finally, I need the weight of the added weight because I need to know how much force is acting on the side where the weight will be placed.

Step 3- Trying our plan out 

In this section, I will list out the steps we took.


1.) Plugged the weight of the added weight, after we converted it from grams to kilograms, into the equations w=mg. Remember 9.8 is the measure of the force of gravity!

- w= (1kg)(9.8)

- w= 0.98


2.) Found the center of gravity/ center of mass

- 50cm

3.) Measured the lever arms

    - Lever arm 1: 30.8 cm

   - Lever arm 2: 19.2 cm

4.) Plugged the lever arm with the added weight into the equation: Torque= F x Lever Arm (write out torquer and lever arm)

    - Torque= (0.98) x (30.8)

    - Torque= 30.18

5.) Since, we knew that the counter clockwise and clockwise torques are equal, we then knew to set the torque of the added weight equal to the side of the stick without the added weight multiplied by the unknown force.

6.) We then had to convert the new known force to mass.

 

7.) Once we got the mass, we had to convert the kilograms into grams. 

Results 

After getting our educated guess, we weighed the meter stick. The meter stick was 147.6g. We were off by 13.6 grams. Overall successful, but not as successful as I would've liked our experiment to be. 

See below for a picture of our final! Make note that it is balanced because the center of gravity is inside the base of support, which is the table. As pointed out before, the edge of the table is where the center of gravity is.