# Moments - Balancing a weighted meter stick

• alexmahone
In summary, the conversation discusses the use of moments to determine the mass of a meter stick. The stick is found to balance at the 49.2cm mark on a fulcrum, but when a 46.0g mass is attached at the 14.7cm mark, the fulcrum must be moved to the 38.7cm mark for balance. By drawing free body diagrams and considering the torques, it is possible to determine the mass of the 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.

alexmahone said:
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.)

berkeman said:
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

Sweet!

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.

## What is a moment and how is it related to balancing a weighted meter stick?

A moment is a measure of the tendency of a force to cause an object to rotate about a specific point or axis. In the context of balancing a weighted meter stick, it refers to the force exerted by the weights on either side of the stick and their distance from the balancing point.

## How do you calculate the moment of a force?

The moment of a force is calculated by multiplying the magnitude of the force by the distance from the point of rotation to the point at which the force is applied. This can be represented by the equation M = F*d, where M is the moment, F is the force, and d is the distance.

## What is the principle of moments?

The principle of moments states that for an object to be in rotational equilibrium, the sum of the clockwise moments must be equal to the sum of the counterclockwise moments.

## How can you balance a weighted meter stick using moments?

To balance a weighted meter stick, you can adjust the position of the weights on either side of the stick until the clockwise and counterclockwise moments are equal. This can be achieved by changing the distance of the weights from the balancing point or by changing the weights themselves.

## What factors can affect the balance of a weighted meter stick?

The balance of a weighted meter stick can be affected by the weight and position of the weights, the length and weight of the stick, and the surface on which it is balanced. Friction and air resistance may also play a role in the balance of the stick.

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