Force To Hold Horzontally?

[Danton]

I can hold a 4 foot long, 2x4 in. piece of wood one inch from the top vertically pretty easily with my thumb and index finger. Yet when I try to hold it horizontally with the same fingers at the same spot I can't produce no where near enough force. If it is vertically the force to hold it would be weight which I guess to be about 8 lbs. How would I find the force needed to hold it horizontally? Is there more force because the gravity is pulling down over a longer area? 

[exchemist]

I can hold a 4 foot long, 2x4 in. piece of wood one inch from the top vertically pretty easily with my thumb and index finger. Yet when I try to hold it horizontally with the same fingers at the same spot I can't produce no where near enough force. If it is vertically the force to hold it would be weight which I guess to be about 8 lbs. How would I find the force needed to hold it horizontally? Is there more force because the gravity is pulling down over a longer area? 

The problem in your second scenario is that because the centre of gravity, where the weight acts, and your fingers are not aligned, this creates a turning effect. You are unable to counteract this turning effect, due to the moment produced by the force of the weight. The moment of a force is determined by the magnitude of the force multiplied by the distance from the axis of rotation (your fingers).  

 

More here: https://en.wikipedia.org/wiki/Moment_(physics)

 

It's a form of leverage, basically. If you have 8lb wt acting at distance of 2ft, the moment is 16ft-lb wt. If you try to hold it horizontal by grasping with your hand, which is say, 4 in across incl thumb, i.e. 1/3 ft, you need a force of 16 / 1/3 = 16 x 3 = 48lb wt to do it.

[Danton]

The problem in your second scenario is that because the centre of gravity, where the weight acts, and your fingers are not aligned, this creates a turning effect. You are unable to counteract this turning effect, due to the moment produced by the force of the weight. The moment of a force is determined by the magnitude of the force multiplied by the distance from the axis of rotation (your fingers).  

 

More here: https://en.wikipedia.org/wiki/Moment_(physics)

 

It's a form of leverage, basically. If you have 8lb wt acting at distance of 2ft, the moment is 16ft-lb wt. If you try to hold it horizontal by grasping with your hand, which is say, 4 in across incl thumb, i.e. 1/3 ft, you need a force of 16 / 1/3 = 16 x 3 = 48lb wt to do it.

 I'm not entirely clear on is the denominator for the force calculation. If the length for the hand is set and the position is varied the force will vary but the force calculation does not. If the force was applied over the entire length of the board it would require a force of 4 lbs which is less than weight of the board. Is there some factor of area?

[exchemist]

 I'm not entirely clear on is the denominator for the force calculation. If the length for the hand is set and the position is varied the force will vary but the force calculation does not. If the force was applied over the entire length of the board it would require a force of 4 lbs which is less than weight of the board. Is there some factor of area?

No. Let's think of your thumb as the fulcrum of the lever formed by the piece of wood. Assume your thumb is 4in, i.e. 1/3ft, from the end and your little finger is what has to counteract the turning effect.  You have the centre of gravity in the middle, 2ft from either end, so that is where the weight acts.

 

I was previously slightly in error saying the moment due to the weight is 8lb wt x 2ft, since it is strictly 8 lb ft x 1 2/3 ft (i.e. 5/3ft) , because your thumb is 4in inward from the end. The force your little finger needs to apply has to generate the same moment, but with only an "arm" (i.e. leverage length) of 1/3 ft, instead of 5/3ft.

 

So if we call the force required F, then since the moments must be equal to avoid rotation, we have that F x 1/3 = 8 x 5/3. Or, F = 8 x 5/3 x 3 = 40lb wt. (It has come down a little, now that I have allowed for your thumb not being on the end). The force on your thumb, however, acting as the fulcrum, would be the sum of both downward forces, i.e. 8 lb wt + 40 lb wt = 48lb wt.  

 

If you used both hands, a distance of 1ft apart, to keep it horizontal, then again taking the inboard hand as the fulcrum of the lever, you would have F x 1 = 8 x 1 (the new distance of the CG from the fulcrum is now only 1ft), and so a force of 8lb applied by the outer hand would do. The inner, fulcrum, hand would again experience the sum of the two downward forces, so 8 + 8 = 16lb wt.  

 

And the limiting case is if the inner hand is 2ft from the end i.e. at the CG itself, when the force required by the outer hand becomes zero and the force experienced by the inner hand is just 8lb wt.   

 

Does it make sense now? 

[eodnhoj7]

I can hold a 4 foot long, 2x4 in. piece of wood one inch from the top vertically pretty easily with my thumb and index finger. Yet when I try to hold it horizontally with the same fingers at the same spot I can't produce no where near enough force. If it is vertically the force to hold it would be weight which I guess to be about 8 lbs. How would I find the force needed to hold it horizontally? Is there more force because the gravity is pulling down over a longer area? 

The application of force is an application of movement towards stability with the stability found in the "center".  This act of "centering" is an act of reflecting structural stability through symmetry. 

 

Take for example if you hold the 2x4 in the "center", it will balance itself perfectly as you will manifest a third "point" from which the dual points (as beginning and end) are able to structure themselves.  Think of it like a geometric problem:

 

1) If you have dual points (beginning and end) what you are observing is a polarity between forces where one is trying to overcome the other.  In this respect it is more subject to instability.

 

2) If you have a third point, which results as a synthesis of the beginning and end points, this third synthetic point as "center" enables "stability" through "medianality".  Think of this way all objects that are structurally stable have a "center" point.  This center point inevitably as a "qualitative numerical aspect" (not to be confused with quantitative) as being "odd" with this "odd" being a form of "center" as unity.  All odd numbers, as structural points, are simply even numbers with "1" added as a median. 

 

3)  As to holding it at one end (either the beginning or end) the force due to the assymetry involved will grow exponentiality as the length between the two points begins and ends.  Considering the 2x4 would fall, the majority of the force would have to be applied at the top finger with the bottom simply having enough to stabilize.  It breaks partially down to a question of biomechanics and the joint/muscular structure of the hand (for the majority of people) cannot apply enough force due to its inherent structural density. 

 

Now if you place the end on a table and press you hand down with you body weight the object will hold.  In these respects you have 3 points of centering.  The top end you are pressing down on as the first, maintaining a symmetry with the bottom stable center as the 2nd in turns stabilizes through the third points as the end "floating". 

[exchemist]

The application of force is an application of movement towards stability with the stability found in the "center".  This act of "centering" is an act of reflecting structural stability through symmetry. 

 

Take for example if you hold the 2x4 in the "center", it will balance itself perfectly as you will manifest a third "point" from which the dual points (as beginning and end) are able to structure themselves.  Think of it like a geometric problem:

 

1) If you have dual points (beginning and end) what you are observing is a polarity between forces where one is trying to overcome the other.  In this respect it is more subject to instability.

 

2) If you have a third point, which results as a synthesis of the beginning and end points, this third synthetic point as "center" enables "stability" through "medianality".  Think of this way all objects that are structurally stable have a "center" point.  This center point inevitably as a "qualitative numerical aspect" (not to be confused with quantitative) as being "odd" with this "odd" being a form of "center" as unity.  All odd numbers, as structural points, are simply even numbers with "1" added as a median. 

 

3)  As to holding it at one end (either the beginning or end) the force due to the assymetry involved will grow exponentiality as the length between the two points begins and ends.  Considering the 2x4 would fall, the majority of the force would have to be applied at the top finger with the bottom simply having enough to stabilize.  It breaks partially down to a question of biomechanics and the joint/muscular structure of the hand (for the majority of people) cannot apply enough force due to its inherent structural density. 

 

Now if you place the end on a table and press you hand down with you body weight the object will hold.  In these respects you have 3 points of centering.  The top end you are pressing down on as the first, maintaining a symmetry with the bottom stable center as the 2nd in turns stabilizes through the third points as the end "floating". 

What a load of utterly unhelpful and meaningless bilge. 

Edited October 18, 2017 by exchemist

[eodnhoj7]

Well I will make the post simpler then.

 

The beginning of the board and the end, when held from one end, become inherently less stable because you have two points (beginning and end) inevitably trying to counteract eachother through gravity.  There is no mediation to enable a form of stability.

 

Take for example the same experiment where one nails in one end of the board to the wall.  Using one nail rarely works as the board will be pulled down by gravity at the seperate end.  Add in a third centering point as a second nail near the first and the stability increases.

[exchemist]

Well I will make the post simpler then.

 

The beginning of the board and the end, when held from one end, become inherently less stable because you have two points (beginning and end) inevitably trying to counteract eachother through gravity.  There is no mediation to enable a form of stability.

 

Take for example the same experiment where one nails in one end of the board to the wall.  Using one nail rarely works as the board will be pulled down by gravity at the seperate end.  Add in a third centering point as a second nail near the first and the stability increases.

That's a lot better, certainly, though I still cannot see how it addresses the question that was being asked.  But maybe Danton will comment.  

[eodnhoj7]

That's a lot better, certainly, though I still cannot see how it addresses the question that was being asked.  But maybe Danton will comment.  

The nature of physics, while rooted in math as a form of definition, also is rooted in geometry.  By geometry, I mean simply the study of spatial properties nothing more.  In this respect, the nature of observing "centers" or the "reflection of points as centers" is inherently unavoidable. 

 

Physics has quantitative truths to it, but is simultaneously has qualitative truths (ie the nature of "centers" or "points" of balance reflecting eachother to form stability.

[exchemist]

The nature of physics, while rooted in math as a form of definition, also is rooted in geometry.  By geometry, I mean simply the study of spatial properties nothing more.  In this respect, the nature of observing "centers" or the "reflection of points as centers" is inherently unavoidable. 

 

Physics has quantitative truths to it, but is simultaneously has qualitative truths (ie the nature of "centers" or "points" of balance reflecting eachother to form stability.

Unfortunately this horseh1t does not help you work out how to find the force needed to hold the piece of wood horizontally, which is the question that was asked.  

[eodnhoj7]

Physics has quantitative truths to it, but it simultaneously has qualitative truths.  In this respect the force applied does not always require quantitative measures, qualitative works also.  Gravity does not always have to counteract gravity. 

 

Just a different perspective, that is all.

[Danton]

No. Let's think of your thumb as the fulcrum of the lever formed by the piece of wood. Assume your thumb is 4in, i.e. 1/3ft, from the end and your little finger is what has to counteract the turning effect.  You have the centre of gravity in the middle, 2ft from either end, so that is where the weight acts.

 

I was previously slightly in error saying the moment due to the weight is 8lb wt x 2ft, since it is strictly 8 lb ft x 1 2/3 ft (i.e. 5/3ft) , because your thumb is 4in inward from the end. The force your little finger needs to apply has to generate the same moment, but with only an "arm" (i.e. leverage length) of 1/3 ft, instead of 5/3ft.

 

So if we call the force required F, then since the moments must be equal to avoid rotation, we have that F x 1/3 = 8 x 5/3. Or, F = 8 x 5/3 x 3 = 40lb wt. (It has come down a little, now that I have allowed for your thumb not being on the end). The force on your thumb, however, acting as the fulcrum, would be the sum of both downward forces, i.e. 8 lb wt + 40 lb wt = 48lb wt.  

 

If you used both hands, a distance of 1ft apart, to keep it horizontal, then again taking the inboard hand as the fulcrum of the lever, you would have F x 1 = 8 x 1 (the new distance of the CG from the fulcrum is now only 1ft), and so a force of 8lb applied by the outer hand would do. The inner, fulcrum, hand would again experience the sum of the two downward forces, so 8 + 8 = 16lb wt.  

 

And the limiting case is if the inner hand is 2ft from the end i.e. at the CG itself, when the force required by the outer hand becomes zero and the force experienced by the inner hand is just 8lb wt.   

 

Does it make sense now? 

I'm still confused. I just got a book on that deals with this topic, so I'm going to brush up and follow up once I have better understanding.  

[pzkpfw]

I'm still confused. I just got a book on that deals with this topic, so I'm going to brush up and follow up once I have better understanding.  

 

Leverage.

 

Hold a pound of butter in your hand. It's easy.

 

Hold a 1 yard stick (assume the stick weighs nothing) with the pound of butter at the other end from your hand, you may have trouble holding it.

 

Try again with a 10 yard (even if itself weightless) stick and you'll have even more trouble.

 

It's about the distance of the weight from your point of holding. Torque.

 

Same reason a 2 foot crowbar is more use than a 2 inch crowbar.

[exchemist]

I'm still confused. I just got a book on that deals with this topic, so I'm going to brush up and follow up once I have better understanding.  

Good idea.

 

It's just leverage, as pzkpfw points out. Double the length of lever and you double the turning effect (torque) of a force of given magnitude. Halve the length of the lever and you halve it. In your case you have the long end with a leverage of 1 2/3 ft, i.e. measured from your thumb to the centre of gravity of the piece of wood. And the short end with a leverage of only 4 inches, i.e. 1/3ft (the distance between your thumb and little finger, i.e. width of your hand.)  

Edited October 20, 2017 by exchemist