Finding mass of a meter stick using torque

[khannon5]

Homework Statement

I did a lab and am trying to find the mass of a meter stick. Our fulcrum was at the 60cm mark at the meter stick. A 100 g mass was placed 30 cm away from the fulcrum on the shorter side. A 50 g mass was placed 43 cm away from the fulcrum on the longer side. How do I find the mass of the meter stick?

Homework Equations

Torque=rfsintheta

The Attempt at a Solution

Not sure how to calculate this

 

[Nathanael]

I assume when you placed the masses there, the meter stick was balanced? What does this say about the net torque? Is anything other than the 100g and 50g masses causing any torque?

 

[khannon5]

I assume when you placed the masses there, the meter stick was balanced? What does this say about the net torque? Is anything other than the 100g and 50g masses causing any torque?

The net torque is 0 and the meter stick causes torque. When I find try to calculate the torque of the meter stick i get 230 which would make the mass 230 g. The actual measured mass of the stick is 97 so this can't be right I don't know what I did wrong

 

[Nathanael]

I don't know what I did wrong

Okay, please show your work.

 

[khannon5]

Okay, please show your work.

 

[Nathanael]

Well firstly, the masses are in grams not kilograms! So the weight is not 980 and 490 Newtons, it is 0.98 and 0.49 Newtons. I would suggest not even calculating the weights, just call it 0.1g and 0.05g because the g ends up canceling so why not save a bit of effort.
(It is very often good to not plug in numbers till the end!)

Anyway, you wrote "980*0.4" and "490*0.33" and I have no idea where you got these numbers from...

What is the torque due to the 100g mass? What is the torque due to the 50g mass?

 

[khannon5]

Well firstly, the masses are in grams not kilograms! So the weight is not 980 and 490 Newtons, it is 0.98 and 0.49 Newtons. I would suggest not even calculating the weights, just call it 0.1g and 0.05g because the g ends up canceling so why not save a bit of effort.
(It is very often good to not plug in numbers till the end!)

Anyway, you wrote "980*0.4" and "490*0.33" and I have no idea where you got these numbers from...

What is the torque due to the 100g mass? What is the torque due to the 50g mass?

I got the .4m and .33m because those are the distances from the center of gravity of the meter stick.
The torque of the 100g would be .4m X .98 Newtons = .392 Nm.
The torque of the 50g would be .33m X .49 Newtons = .1617 Nm.
Right? Am I supposed to use the distances form fulcrum of the center of gravity?
If this is correct I would do .392Nm - .1617Nm = .2303Nm which would be the torque of the meter stick. And since it is .1 meters away from center of gravity wouldn't that make the meter stick .2303 kg?

 

[Nathanael]

Am I supposed to use the distances form fulcrum of the center of gravity?

You can take the torque about any point, but if you choose to take the torque about any point other than the fulcrum, then you will have to account for the torque due to the normal force from the fulcrum. You don't know what this normal force is, so you ought to take the torque about the fulcrum (that way the normal force has a distance zero and thus has zero torque).

And since it is .1 meters away from center of gravity wouldn't that make the meter stick .2303 kg?

And since what is 0.1 meters from the center of gravity...? Certainly that is not the distance that the force of gravity acts?

 

[khannon5]

You can take the torque about any point, but if you choose to take the torque about any point other than the fulcrum, then you will have to account for the torque due to the normal force from the fulcrum. You don't know what this normal force is, so you ought to take the torque about the fulcrum (that way the normal force has a distance zero and thus has zero torque).And since what is 0.1 meters from the center of gravity...? Certainly that is not the distance that the force of gravity acts?

The fulcrum is .1 m from the center of gravity so I'm not sure how to account for this and how to set up the equations

 

[Nathanael]

The fulcrum is .1 m from the center of gravity so I'm not sure how to account for this and how to set up the equations

There's no point in taking the torque about the center of gravity because the thing you're trying to solve for (gravity) causes zero torque! So there's no way to solve for it...

Like I said, you can take the torque about any point you want to. (There must be zero torque about every point!) So around what point should you take the torque?

 

[khannon5]

There's no point in taking the torque about the center of gravity because the thing you're trying to solve for (gravity) causes zero torque! So there's no way to solve for it...

Like I said, you can take the torque about any point you want to. (There must be zero torque about every point!) So around what point should you take the torque?

The fulcrum
So should I find the torque of each mass by doing .3m X .98N = .294Nm and .43m X .49N = .2107Nm? Then would I subtract those to find the torque of the fulcrum

 

[Nathanael]

And what do you get?

 

[khannon5]

And what do you get?

.0833Nm then how do I find the mass of the meter stick from this number

 

[Nathanael]

That is the torque due to gravity, right? Which equals...?

 

[khannon5]

That is the torque due to gravity, right? Which equals...?

I'm not sure what you mean. How would you go from .0833Nm to just grams if there's no m? What would the m be?

 

[Nathanael]

Forget about the 0.0833Nm... Does gravity cause a torque or not? What is the torque from gravity? Is it zero?

 

[khannon5]

Forget about the 0.0833Nm... Does gravity cause a torque or not? What is the torque from gravity? Is it zero?

Yes I'm not sure what to do next to get the mass of the meter stick

 

[Nathanael]

Yes I'm not sure what to do next to get the mass of the meter stick

Ok.. but what is the torque from gravity? Can you write an expression for it?

Write out your torque equation and include the torque from gravity, and set the net torque equal to zero.

 

[khannon5]

Ok.. but what is the torque from gravity? Can you write an expression for it?

Write out your torque equation and include the torque from gravity, and set the net torque equal to zero.

Would it be torque of mass 1 + torque of mass 2 + torque of gravity = 0

 

[Nathanael]

Would it be torque of mass 1 + torque of mass 2 + torque of gravity = 0

Yes. Now what is the value of these torques? Specifically, the torque from gravity... At what distance does the force of gravity act from the fulcrum?
Put it all into your torque equation.

 

[khannon5]

Yes. Now what is the value of these torques? Specifically, the torque from gravity... At what distance does the force of gravity act from the fulcrum?
Put it all into your torque equation.

Torque 1 = .294Nm
Torque 2 = .2107Nm
-.294 + .2107 + torque of gravity = 0
The force of gravity acts .1m away from the fulcrum

 

[Nathanael]

The force of gravity acts .1m away from the fulcrum

OK but can you put those words into the equation...? Call the mass of the meter stick "m"

 

[khannon5]

OK but can you put those words into the equation...? Call the mass of the meter stick "m"

I'm not sure how to put it in the equation..would it be torque of gravity / .1m?

 

[Nathanael]

I'm not sure how to put it in the equation..would it be torque of gravity / .1m?

Have you learned about gravity? What is the force of gravity?

 

[khannon5]

Have you learned about gravity? What is the force of gravity?

9.8 X mass
My teacher isn't very good so I'm usually left to try and figure everything out on my own

 

[Nathanael]

9.8 X mass

Can you now find the mass?

It's hard to tell when you're stuck. Please try to finish the problem or else make it clear where you are stuck so I can help you.

 

[khannon5]

Can you now find the mass?

It's hard to tell when you're stuck. Please try to finish the problem or else make it clear where you are stuck so I can help you.

I don't know where the fact that the fulcrum is .1m away from the center of gravity comes in and how to find the mass of the stick after finding the torque of gravity

 

[Nathanael]

I don't know where the fact that the fulcrum is .1m away from the center of gravity comes in

Where does the force of gravity act? What is the definition of torque?

 

[khannon5]

Where does the force of gravity act? What is the definition of torque?

The force of gravity acts on the whole thing but the center of gravity is in the center
Torque is a force that causes a rotational change to something

 

[Nathanael]

The force of gravity acts on the whole thing but the center of gravity is in the center

Right, gravity acts everywhere, but it effectively acts on the center of gravity. In other words, if you treat the full force of gravity acting only the center of gravity, then it will be the same as if you treat gravity as being spread across the object. So we can say the force of gravity (9.8 X mass) acts on the center of gravity.

Torque is a force that causes a rotational change to something

I mean the mathematical definition. How is torque defined with numbers? If you know a force, and you know the distance it acts, then what is the torque from that force?

Put this all together and take some time to try to solve the problem.

 

[khannon5]

Right, gravity acts everywhere, but it effectively acts on the center of gravity. In other words, if you treat the full force of gravity acting only the center of gravity, then it will be the same as if you treat gravity as being spread across the object. So we can say the force of gravity (9.8 X mass) acts on the center of gravity.I mean the mathematical definition. How is torque defined with numbers? If you know a force, and you know the distance it acts, then what is the torque from that force?

Put this all together and take some time to try to solve the problem.

Torque = rfsintheta but in this problem sintheta=1. I found the torque of gravity to be .0833 from that equation if that's cprrect? So I have .0833 = .1 X f. Solve for f and get f = .833 N. I divide this number by 9.8 to get

 

[khannon5]

.085 kg but this can't be right what am I doing wrong?

 

[Nathanael]

.085 kg but this can't be right what am I doing wrong?

Good. 85 grams. The actual weight was 97 grams? You're not doing anything wrong. You said it was a lab, right? So you actually measured these distances? That can account for the error.

Look at it like this... If the 50g mass was actually at 42.5 cm and the 100g mass was actually at 30.5 cm, then you would get an answer of 92.5 grams. (Not to mention if the fulcrum is not exactly at 60 cm! That's probably where the error really comes from!)

 

[khannon5]

Good. 85 grams. The actual weight was 97 grams? You're not doing anything wrong. You said it was a lab, right? So you actually measured these distances? That can account for the error.

Look at it like this... If the 50g mass was actually at 42.5 cm and the 100g mass was actually at 30.5 cm, then you would get an answer of 92.5 grams. (Not to mention if the fulcrum is not exactly at 60 cm! That's probably where the error really comes from!)

Ok thank you so much. I really appreciate your time