Balancing Forces: Calculating Center of Mass and Support Distance

[Miri]

Homework Statement

A 20g rubber is lying on the end of a 30cm long 30g ruler. Determine how far from the rubber you have to support the ruler with your finger to keep the system balanced.

Homework Equations

I know that I have to calculate the forces which act downwards: the rubber: 20*10^-3kg * 9.81m/s^2 and the ruler: 30*10^-3 * 9.81m/s^2 and then I don't know what to do...Do I have to add them to get the force which is acting upwards? Or how do I get the distance from the rubber to my finger? The solution is 9.0cm.

 

[LowlyPion]

Homework Statement

A 20g rubber is lying on the end of a 30cm long 30g ruler. Determine how far from the rubber you have to support the ruler with your finger to keep the system balanced.

Homework Equations

I know that I have to calculate the forces which act downwards: the rubber: 20*10^-3kg * 9.81m/s^2 and the ruler: 30*10^-3 * 9.81m/s^2 and then I don't know what to do...Do I have to add them to get the force which is acting upwards? Or how do I get the distance from the rubber to my finger? The solution is 9.0cm.

Consider the length away that the center of mass of just the ruler alone will need to be from your finger to balance the rubber?

The moment of the cener of mass will need to counteract the moment of the rubber to be in balance.

 

[Miri]

So you mean that the force which is pointing downwards (the one from the ruler) has to be equal to zero when you subtracted the force of the rubber? I don't really get what you mean? Can you help me with giving me a formula which relates those two forces so that I can find out the distance. Isn't there a force pointing upwards in this whole system? The one which you could calculate by adding the masses of the objects...?

 

[LowlyPion]

So you mean that the force which is pointing downwards (the one from the ruler) has to be equal to zero when you subtracted the force of the rubber? I don't really get what you mean? Can you help me with giving me a formula which relates those two forces so that I can find out the distance. Isn't there a force pointing upwards in this whole system? The one which you could calculate by adding the masses of the objects...?

There is only one force pointing upward ... the finger.

There are 2 forces pointing downward. The center of mass of the rubber. The center of mass of the ruler.

When the center of mass of the combined system is over the finger pushing up, the system is in balance.

Generally speaking the ∑(Cm*m)/∑m is the center of mass of the system.

 

[Miri]

So what exactly does this mean? :∑(Cm*m)/∑m, can you give me another formula? When the two forces which are pointing downward are added, then you should get the force which is pointing upward, so the force of your finger. But like I calculated it, it doesn't work...

 

[Miri]

Can somebody help me? I have my matura exams next week :S Thanks and have a nice weekend

 

[LowlyPion]

So what exactly does this mean? :∑(Cm*m)/∑m, can you give me another formula? When the two forces which are pointing downward are added, then you should get the force which is pointing upward, so the force of your finger. But like I calculated it, it doesn't work...

It means the sum of the weighted locations of the centers of mass of a system divided by the total mass is where the center of mass of the system is. (Or think of it as the weighted average of the the individual centers of mass give the center of mass for the system.)

Armed with that you can use the center of mass at the ruler and the center of mass of the rubber and determine the center of mass. And that is where you want to use your finger to balance the two.