Moments - Balancing a weighted meter stick

[alexmahone]

Moments -- Balancing a weighted meter stick

A meter stick is found to balance at the 49.2cm mark when placed on a fulcrum. When a 46.0g mass is attached at the 14.7cm mark, the fulcrum must be moved to the 38.7cm mark for balance. What is the mass of the meter stick?

I know I have to use moments but I don't know where to start. Any help would be appreciated.

 

[berkeman]

A meter stick is found to balance at the 49.2cm mark when placed on a fulcrum. When a 46.0g mass is attached at the 14.7cm mark, the fulcrum must be moved to the 38.7cm mark for balance. What is the mass of the meter stick?

I know I have to use moments but I don't know where to start. Any help would be appreciated.

Draw FBDs for the two situations, and show the torques about the fulcrum. When the stick is balanced, what must the sum of the torques be?

(BTW, I will add some more descriptive words to your thread title -- 1-word titles are not generally allowed in the technical PF forums.)

 

[alexmahone]

Draw FBDs for the two situations, and show the torques about the fulcrum. When the stick is balanced, what must the sum of the torques be?

(BTW, I will add some more descriptive words to your thread title -- 1-word titles are not generally allowed in the technical PF forums.)

Thanks. Once I drew the FBDs, I got the answer. :D

 

[berkeman]

Sweet!

 

[Nickie]

Based on the given information, we can use the principle of moments to determine the mass of the meter stick. The principle of moments states that the sum of the clockwise moments is equal to the sum of the counterclockwise moments.

First, let's define our variables. Let m be the mass of the meter stick, d1 be the distance from the fulcrum to the 49.2cm mark, d2 be the distance from the fulcrum to the 14.7cm mark, and d3 be the distance from the fulcrum to the 38.7cm mark.

Now, we can set up the equation using the principle of moments:

Clockwise moment = Counterclockwise moment

m x g x d1 = (46.0g x g x d2) + (m x g x d3)

Since we are looking for the mass of the meter stick, we can rearrange the equation to solve for m:

m = (46.0g x g x d2) / (d1 - d3)

Plugging in the given values, we get:

m = (46.0g x 9.8m/s^2 x 14.7cm) / (49.2cm - 38.7cm)

m = 784.44g / 10.5cm

m = 74.71g

Therefore, the mass of the meter stick is approximately 74.71g.