# A 2kg rock is suspended by a massless string from one end of a 1m measuring stick.

1. Dec 12, 2012

### Lo.Lee.Ta.

"A 2kg rock is suspended by a massless string from one end of a 1m measuring stick."

1. "A 2kg rock is suspended by a massless string from one end of a 1m measuring stick. What is the mass of the measuring stick if it is balanced as shown below."
______________
|___|___|___|___|
M....^
.....^^
....^^^

Okay, this is not a very good drawing of the situation... But I am trying to show a meter stick on a fulcrum (^) and the 2kg mass is the M.

So the M is at the very end, at the 0m mark.

The fulcrum is at the .25m mark.

I need to figure out the mass of the meter stick...

2. I didn't really know there was a formula to working these sorts of problems at first, so I just though a reasonable answer would be 4 kg... 3kg on each side of the fulcrum is balanced...?

But this is not right... The answer is 2kg for the meter stick.

How am I supposed to figure this out???

I know the formula for the center of mass is: [x1(m1) + x2(m2) +...]/(m1 + m2 +...)
But I don't think this formula will help me because the "balance beam" is not massless.

Thank you!!! :)

Last edited: Dec 12, 2012
2. Dec 12, 2012

### Lo.Lee.Ta.

Re: "A 2kg rock is suspended by a massless string from one end of a 1m measuring stic

Oh, wait a second!

I just went on one website after researching this problem forever, and MAY have found the answer...
Is this right???

In (m1)(x1) + (m2)(x2) +.../(m1) + (m2)...,

The m's stand for the distance away from the fulcrum?
And we always say the middle of the beam is where the mass of the beam is located?
That's why we put the weight of the beam at m2?

*f stands for fulcrum

m1--f---m2--m3--m4
|___|___|___|___|
M....^

So it's:
(m2)(x2) + (m3)(x3) + (m4)(x4) = (m1)(x1)
(.25m)(weight of beam) + (.5)(0) + (.75)(0) = (2)(.25)
So weight of beam = 2kg

Is this how it is solved?

3. Dec 12, 2012

### haruspex

Re: "A 2kg rock is suspended by a massless string from one end of a 1m measuring stic

It's not clear to me what those equations are saying or how you arrive at them.
Is it one equation or two? If two, the first seems wrong.
Look like you're breaking the mass of the beam into four equal sections, but for the distance to the mass centre of each section you've written the distance to the far point of the section.