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Mechanical Leverage

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  Mechanical Leverage Boris <nospam@nospam.invalid> - 2017-07-21 20:48 +0000
    Re: Mechanical Leverage Double-A <double-a3@hush.com> - 2017-07-21 13:56 -0700
      Re: Mechanical Leverage Boris <nospam@nospam.invalid> - 2017-07-21 20:53 +0000
    Re: Mechanical Leverage "F. Russell" <fr@random.info> - 2017-07-21 22:16 +0000
      Re: Mechanical Leverage Boris <nospam@nospam.invalid> - 2017-07-22 15:43 +0000
        Re: Mechanical Leverage "F. Russell" <fr@random.info> - 2017-07-22 17:22 +0000
        Re: Mechanical Leverage "F. Russell" <fr@random.info> - 2017-07-22 23:59 +0000
    Re: Mechanical Leverage "F. Russell" <fr@random.info> - 2017-07-23 00:07 +0000
      Re: Mechanical Leverage James McGinn <jimmcginn9@gmail.com> - 2017-07-22 17:24 -0700

#641712 — Mechanical Leverage

Physics was my favorite subject in college, but not my major.

Many observations in mechanical and optical physics either make (intuitive)
sense to me, or I've never needed a deeper understanding of the priciples 
at work, except...

I have no intuitive sense, but do want a deeper understaning of why it is 
that a lever and a fulcrum work the way they do.  What physical principal 
is it that lets me move the earth if I had a place to stand and a long 
emough lever, let alone raise my heavier brother on the other end of a see-
saw, if I am far enough from the fulcrum?

TIA

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#641714

On Friday, July 21, 2017 at 1:52:57 PM UTC-7, Boris wrote:
> Physics was my favorite subject in college, but not my major.
> 
> Many observations in mechanical and optical physics either make (intuitive)
> sense to me, or I've never needed a deeper understanding of the priciples 
> at work, except...
> 
> I have no intuitive sense, but do want a deeper understaning of why it is 
> that a lever and a fulcrum work the way they do.  What physical principal 
> is it that lets me move the earth if I had a place to stand and a long 
> emough lever, let alone raise my heavier brother on the other end of a see-
> saw, if I am far enough from the fulcrum?
> 
> TIA


Archimedes was too optimistic.

Double-A

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#641715

Double-A <double-a3@hush.com> wrote in
news:5e44f40c-8627-4cb7-b971-99b5d72fc004@googlegroups.com: 

> On Friday, July 21, 2017 at 1:52:57 PM UTC-7, Boris wrote:
>> Physics was my favorite subject in college, but not my major.
>> 
>> Many observations in mechanical and optical physics either make
>> (intuitive) sense to me, or I've never needed a deeper understanding
>> of the priciples at work, except...
>> 
>> I have no intuitive sense, but do want a deeper understaning of why
>> it is that a lever and a fulcrum work the way they do.  What physical
>> principal is it that lets me move the earth if I had a place to stand
>> and a long emough lever, let alone raise my heavier brother on the
>> other end of a see- saw, if I am far enough from the fulcrum?
>> 
>> TIA
> 
> 
> Archimedes was too optimistic.

I think he had a sense of humor.
> 
> Double-A
> 
> 

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#641735

On Fri, 21 Jul 2017 20:48:56 +0000, Boris wrote:

> 
> I have no intuitive sense, but do want a deeper understaning of why it is 
> that a lever and a fulcrum work the way they do.
>

Energy = Force * Displacement

An one end of the lever there is a small force but a large
displacement.

At the other end of the lever there is a large force but
a small displacement.

But the energy at both ends is the same (see equation above).

Thus, a small force is able to generate a larger force but
only if that larger force acts through a smaller displacement.

This basic idea applies not only to a lever but also to
the hydraulics lift that one sees at auto mechanic shops.

Does this help?  If not, ask again.

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#641823

"F. Russell" <fr@random.info> wrote in
news:oktuf80r4a@news3.newsguy.com: 

> On Fri, 21 Jul 2017 20:48:56 +0000, Boris wrote:
> 
>> 
>> I have no intuitive sense, but do want a deeper understaning of why
>> it is that a lever and a fulcrum work the way they do.
>>
> 
> Energy = Force * Displacement

Hmmm...I've never seen that formula.  That would be E = mass x 
acceleration x distance moved.

I understand the "E" and the "F", and I see how the distance moved 
applies to the hydraulic lift example, and in the see-saw example, the 
distance moved by each person on the see-saw is the same, so the 
equation balances.
> 
> An one end of the lever there is a small force but a large
> displacement.
> 
> At the other end of the lever there is a large force but
> a small displacement.
> 
> But the energy at both ends is the same (see equation above).
> 
> Thus, a small force is able to generate a larger force but
> only if that larger force acts through a smaller displacement.
> 
> This basic idea applies not only to a lever but also to
> the hydraulics lift that one sees at auto mechanic shops.
> 
> Does this help?  If not, ask again.
> 

I am wondering why, in the see-saw example (or wheelbarrow, etc), the 
distance from the fulcrum is important.  I am not necessarily looking 
for a formula, but that may help.  I am looking for an intuitive reason 
as to why this is true.

I don't know the formula (but I would understand it) that causes a wing 
shaped object to rise when moveing forward with enough speed.  But I do 
have an intuitive sense of how lift is created by the air moving faster 
over the top of a wing than under the bottom of a wing.

What is it about the distance from the fulcrum that is so important?

> 

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#641834

On Sat, 22 Jul 2017 15:43:58 +0000, Boris wrote:

> 
> Hmmm...I've never seen that formula.  That would be E = mass x 
> acceleration x distance moved.
> 

That's correct, although the term "work" is usually used with
this equation rather that "energy," but work is the same as
energy.

This equation demonstrates intuitively that the same amount
of work can be achieved in different ways. 

> 
> What is it about the distance from the fulcrum that is so important?
> 

The above equation does not strictly apply to the lever.  Because
we are essentially rotating about a fixed point, the fulcrum, 
rather than moving things in a straight line, the ideas of "angular
momentum" and "torque" come into play.  This may be a little less
intuitive because now, instead of linear distance, we are rotating
things through angular distance about an axis.

The new, but totally equivalent, equation is now:

Work (energy) = Torque * angular displacement

In the case of the lever, the angular displacement is just s/d,
where d is the lever arm (distance to fulcrum) and s is the
circular arc length.

But Torque = Force * d, so the equation reduces to:

Work = Force * d * angular displacement = Force * s

Thus, we see that the two equations are identical.

The problem may be see how the concept of torque arises,
but this requires elementary vector analysis and may not
be that intuitive.

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#641888

On Sat, 22 Jul 2017 15:43:58 +0000, Boris wrote:

> 
> What is it about the distance from the fulcrum that is so important?
> 

Think about transforming the lever into an equivalent machine.

Consider two wheels on the same shaft.  One wheel has a large radius
and the other wheel has a much smaller radius.

By winding ropes around each wheel, we can use the large wheel
to lift a very heavy load that is attached to the smaller wheel.

See this image:

https://s14.postimg.org/wzukfdxtd/wheellever.jpg

Is this a lever?

The same equation, W = F*s, can be applied here to understand
how a small force can easily lift a very heavy load.

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#641889

On Fri, 21 Jul 2017 20:48:56 +0000, Boris wrote:

>
> lets me move the earth if I had a place to stand and a long 
> emough lever
>

Actually, this cannot be done.  Archimedes failed to understand
the science of materials.  No lever of any great length would
be stiff enough to implement this otherwise sound principle.

Even a hardened steel rod just a few dozen meters in length
would bend considerably.  Longer rods would behave like cooked
spaghetti.

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#641891

On Saturday, July 22, 2017 at 5:08:24 PM UTC-7, F. Russell wrote:
> On Fri, 21 Jul 2017 20:48:56 +0000, Boris wrote:
> 
> >
> > lets me move the earth if I had a place to stand and a long 
> > emough lever
> >
> 
> Actually, this cannot be done.  Archimedes failed to understand
> the science of materials.  No lever of any great length would
> be stiff enough to implement this otherwise sound principle.
> 
> Even a hardened steel rod just a few dozen meters in length
> would bend considerably.  Longer rods would behave like cooked
> spaghetti.

Well, yes, of course. Archimedes knew this too.  He was talking figuratively. 

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