How masses are added together on a lever

[gallimaufry]

lets say we have a balance with these masses attached:
1) 11g mass at 7cm to the left of the fulcrum
2) 32g mass at 16cm to the left of the fulcrum
3) 11g mass at 7cm to the right of the fulcrum
4) 32g mass at 16 cm to the right of the fulcrum

This balance should be balanced right now because we have the same weights on each side. Let's say i wanted to combine the masses on the right so that i have one mass on the right balancing out the 2 masses on the left, How would i figure out what the mass is and the distance it should be at. I added a picture of the original balance to give you a visual, and another picture to show you what I want it to look like. In the picture the before and after should both be balanced, I just don't know what should go in the after picture. Thanks for the help.

 

[tiny-tim]

Welcome to PF!

lets say we have a balance with these masses attached:
1) 11g mass at 7cm to the left of the fulcrum
2) 32g mass at 16cm to the left of the fulcrum
3) 11g mass at 7cm to the right of the fulcrum
4) 32g mass at 16 cm to the right of the fulcrum
…
Lets say i wanted to combine the masses on the right so that i have one mass on the right balancing out the 2 masses on the left, How would i figure out what the mass is and the distance it should be at.
…
I just don't know what should go in the after picture.

Hi gallimaufry! Welcome to PF!

Just use moments about the fulcrum …

on the after picture, mark the ? distance as L, and the ? mass as M …

what moment do you get (on the right-hand side), and what moment was there in the before picture?

(you should find that L can be anything, so long as you're allowed to choose the right M )

 

[astrokreng]

I would like to explain how masses are added together on a lever and how to calculate the mass and distance needed to balance the lever in this scenario.

Firstly, it is important to understand that a lever works based on the principle of moments, which states that for a body to be in equilibrium, the sum of clockwise moments must be equal to the sum of counterclockwise moments. In other words, the product of the mass and its distance from the fulcrum on one side must be equal to the product of the mass and its distance from the fulcrum on the other side.

In this scenario, the balance is already in equilibrium, as the sum of the clockwise moments (11g x 7cm + 32g x 16cm = 397gcm) is equal to the sum of the counterclockwise moments (11g x 7cm + 32g x 16cm = 397gcm).

To combine the masses on the right side, we need to determine the mass and distance needed to balance the lever. This can be done by setting up an equation:

(11g x 7cm + 32g x 16cm) = (xg x dcm)

Where x is the mass we need to add on the right side and d is the distance it needs to be placed from the fulcrum.

Solving for x, we get:

x = (11g x 7cm + 32g x 16cm) / d

Now, we need to determine the distance d. This can be done by rearranging the equation:

d = (11g x 7cm + 32g x 16cm) / x

We can choose any value for x, as long as it balances the lever. In this case, let's choose x = 11g.

Substituting the values, we get:

d = (11g x 7cm + 32g x 16cm) / 11g = 25.09 cm

Therefore, to balance the lever, we need to add a mass of 11g at a distance of 25.09 cm from the fulcrum on the right side. This will result in a clockwise moment of 11g x 25.09cm = 276.99 gcm, which is equal to the counterclockwise moment