Balancing Mass: Solving for Bar Length

[IhasSwag]

Homework Statement

The bar has a mass of 3 grams/cm. When a mass of 15 grams is hung on the left side, the system is balanced. Calculate the length of the bar.

Homework Equations

F₁*r₁ = F₂*r₂

The Attempt at a Solution

I thought that the moment on the left should be equal to the moment at the right, so it should be
m_left * g * r_left = m_right* g *r_right

But apparently it should be that the moment of the mass on the left side is equal to the moment of the whole bar.
Can someone explain why this is?

 

[giokrutoi]

what is the mass of the right side

 

[IhasSwag]

the bar is 15cm on the right side. The mass is 3 grams / cm. So 45 grams.

 

[giokrutoi]

the center of mass on bar where is it ?

 

[giokrutoi]

the bar is 15cm on the right side. The mass is 3 grams / cm. So 45 grams.

and length is not 15
it is 15 + x

 

[IhasSwag]

isn't the center of mass exactly in the middle?

 

[giokrutoi]

isn't the center of mass exactly in the middle?

yes an it is in 15 + x /2

 

[giokrutoi]

so what is distance from center of mass to the thing that balances the bar

 

[IhasSwag]

I really don't know

 

[giokrutoi]

look on the picture the center of mass is exactly in the middle and i am asking you to tell what is distance between the center and the big black thing that is holing the bar

 

[IhasSwag]

is it: 15 - (15+x)/2 ?

 

[giokrutoi]

no but you were close (15 + x ) / 2 - x
edit : x doesn't belong to 2

 

[IhasSwag]

I see now that it is (15 + x ) / 2 - x

 

[giokrutoi]

if you got it than what can you say about forces

 

[IhasSwag]

They cancel out at the center of mass?

 

[giokrutoi]

nope what do you think is holding 15 grams from not falling

 

[IhasSwag]

The mass of the bar on the right side?

 

[giokrutoi]

what do you mean under mass on the right side do you say that it is smaller that hole mass of bar

 

[IhasSwag]

I meant the mass of the bar on the right side of the center of mass

 

[giokrutoi]

that is not correct in center of mall is localized hole mass so it fully acts on the "holder"

 

[giokrutoi]

mass of bar times distance from center of mass to "holder" equals to hung mass times distance from that mass to "holder" that is your equation