# Balancing a mass using a balance beam

1. Jun 9, 2010

### louza8

1. The problem statement, all variables and given/known data

A rock is attached to the left end of a uniform meter stick that has the same mass as
the rock.
How far from the left end of the stick should the triangular object be placed so that
the combination of meter stick and rock is in balance?
a. 0.25 m.
b. between 0.25 m and 0.50 m.
c. 0.50 m.
d. more than 0.50 m.

2. Relevant equations
The only question similar to this that I have done is where the masses balance on each end of the ruler and the ruler applies zero torque as it is on the fullcrum. (length*mass=length*mass)

3. The attempt at a solution
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

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2. Jun 9, 2010

### rock.freak667

Just know that the force is weight, the acceleration cancels out to leave mass alone.

But in the position it is in, between the mass and the center of gravity of the stick, call the distance from the fulcrum to the left end 'x'.

Then sum torques about the fulcrum.

3. Jun 10, 2010

### louza8

little bit more help please, i'm still not following. exam tomorrow. sorry to be a bother.

4. Jun 10, 2010

### Physicsy

Just to point out, im still in secondary school so i may not be the most reliable person to answer this but i think the answer is b. between 0.25-0.5

5. Jun 10, 2010

### Physicsy

This is how i did it

1. I assigned both the ruler and rock with masses of 100 grams.
2. I then divided the ruler into 10 equal size pieces each 0.1m long and 10 grams in mass.
3. Then i placed the triangle at 0.25m inside the ruler.
4. Then i multipled each piece of ruler by its distance from the triangle, I also include the weight of the rock.
5. It came up with a moment of 2975 on the left side and a moment of 3225 on the right.
6. This is very close to an equalibruim, so all you have to do is move the triangle between 0.25-0.5 and you should have the answer.

I created an attachment with a diagram that show how i did it.

Hope this helps

#### Attached Files:

• ###### Balance ruler.jpg
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6. Jun 10, 2010

### rock.freak667

If the distance from the center of gravity of the ruler to the left end is 0.5 m and the distance from from the rock to the fulcrum is x. Then shouldn't the distance of the center of gravity of the ruler to the fulcrum be '0.5-x'?

Then just sum moments about the fulcrum

Moment about point = Force * perpendicular distance of the force from the point

7. Jun 10, 2010

### louza8

thanks to both of you guys :)