Leverage and weight positioning

[Pinon1977]

This is probably kind of a simple question but it is one that I have questioned for quite some time. Please see the drawing. Does the position of the 100lbs effect the MA or leverage in this simple lever system?

 

[Nugatory]

What do you think and why?

 

[Pinon1977]

My first thought: the 100lbs would be exerting 100 ftlbs of pressure at the union of these two pieces of square tubing (assuming that the shorter piece if tubing (at 30 degrees) is 1 foot in overall length). Of course that only tells me the leverage at that point. So in that sense, I would have to say yes, 100lbs located in such a manner would produce 1000lbs of leverage. My second thought: the leverage would only be whatever the distance is from the 100lbs to the fulcrum point. So if the 100lbs is 8 feet from the fulcrum, it would yield 800lbs.

That's where I'm at right now. And both hypothesis are completely different in their outcome. Ha ha.

 

[hsdrop]

let me ask you something about your drawing
Do you think it would make a difference if the 100lb was fixed above or below the end of the lever??
outside of hitting the ground faster when on the bottom

 

[sophiecentaur]

. . . . also, would the situation be any different (ignoring the mass of the lever) if a large rectangular plate had been used instead of the angled tubes? These theoretical questions always assume perfect rigidity and (usually but not always) massless levers. If we at least start with that assumption, we can apply the simple principle of moments to the load, the fulcrum and the resulting torque. If you start with the torque about the joint of the two tubes and then relate it to the torque about the fulcrum, you are doing it the hard way - but you will still get the same answer.
If you want to include the masses of the tubes, you can add add the moments, taken about the fulcrum and you will get a different answer as you vary that angle and the various lengths. But the torque just due to the 100lbs will be the same if it's the same point in space (perhaps using two lengths of string, instead of a tube).

fixed above or below the end of the lever

If that affects where the 100lbs is, in space, you could get a change in torque - just follow the rules about taking moments. Have you done any searching about this?

 

[Pinon1977]

let me ask you something about your drawing
Do you think it would make a difference if the 100lb was fixed above or below the end of the lever??
outside of hitting the ground faster when on the bottom

There was be some amount of negligible torque differences between top and bottom, but nothing worth noting. Other than that, no I don't believe it would matter. Why do you ask, good sir? Is this a rhetorical question? Ha ha.

 

[Pinon1977]

. . . . also, would the situation be any different (ignoring the mass of the lever) if a large rectangular plate had been used instead of the angled tubes? These theoretical questions always assume perfect rigidity and (usually but not always) massless levers. If we at least start with that assumption, we can apply the simple principle of moments to the load, the fulcrum and the resulting torque. If you start with the torque about the joint of the two tubes and then relate it to the torque about the fulcrum, you are doing it the hard way - but you will still get the same answer.
If you want to include the masses of the tubes, you can add add the moments, taken about the fulcrum and you will get a different answer as you vary that angle and the various lengths. But the torque just due to the 100lbs will be the same if it's the same point in space (perhaps using two lengths of string, instead of a tube).

If that affects where the 100lbs is, in space, you could get a change in torque - just follow the rules about taking moments. Have you done any searching about this?

No I haven't done any researching on taking moments. I have calculated MOI and all things rotational.

 

[sophiecentaur]

I have calculated MOI and all things rotational.

So you understand about Second Moments? And the First Moment is even less complicated. Look up "principle of Moments". or "turning effect" Its basics are taught to school kids of around 14 years of age and it's extended in A level maths to 2 dimensional situations.

 

[Khashishi]

A good way to see if your reasoning makes sense is to consider extreme cases. One extreme case is to change the angle from 30 degrees to 0 degrees and make the length of the short piece 10ft. What do you suppose will happen then?