Meter stick Challenge

Challenge: find the mass of a meter stick using only a meter stick and a 100g (.1kg) lead weight.

Finding the Torque of the left side of the meter stick:

First you must balance the stick on a table. My meter stick balanced at 25cm, and the center of gravity would be the middle of the stick which is 50cm. There is then 25 cm between where the stick meets the table and where the stick reaches center gravity.

Next it is important to know that:

            TORQUE= (FORCE) (LEVER ARM)

In this case you know that the force on the left of the ruler (where the weight is) is (.1kg)(9.8). The 9.8 represents gravity. 

             TORQUE= (.1kg)(9.8)(lever arm)

As mentioned before we already know what the lever arm is. The lever arm is the distance between the weight and the table, which is 25cm. 

              TORQUE= (.98N)(25cm)

So...

TORQUE= 24.5Ncm

This picture shows the lever arms, where the center of gravity is, and where the force is.

Finding the Torque of the right side of the stick:

First it is important to know that the torque on the left side is the exact same torque as the right side. 

Once you know that you use the same equation:

       TORQUE= (FORCE)(LEVER ARM)

The torque is 24.5

        24.5= (FORCE)(LEVER ARM)

We also know the lever arm. It is 25 cm, because the distance from the place the stick touches the table and the center of gravity.

         24.5=(FORCE)(25cm)

Then you solve for force

         FORCE=.98

Solving for the mass: 

Now you have the torque (which is the same on both sides of the stick) and you have the force, you must solve for the mass.

To solve for the mass you use the equation:

        w=mg

We know the weight because we used it before. The weight is (gravity)(the weight), so .98

        .98=mg

We also know that gravity is always 9.8

        .98=9.8m

Then you just solve for m

         m=100g

The mass of the meter stick is 100g 

We were able to figure out the mass of the meter stick by calculating the torque and then plugging it in to find the force which we then used to find the mass. The only way that this stick could balance on the table is if the torque's are both equal. We got .1 kg as our calculation which was very close to the actual mass which is .117 kg.