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Re: [Phys-l] Statics conundrum



Bob L,
If you include the L in the first term of your 2nd equilib. eq., it's
easy to see that your 3 eqs. are not linearly independent: the 2nd and
3rd equations added together give L times the first eq. In 2-D there
are only 2 independent equilibrium equations. Any others you write down
will represent a linear combination of the first two you write down.
Jeff

-----Original Message-----
From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of LaMontagne, Bob
Sent: Sunday, March 14, 2010 10:33 PM
To: Bob Sciamanda; Forum for Physics Educators
Subject: Re: [Phys-l] Statics conundrum

OK - What am I missing here?

F1 and F2 are applied at the ends.

F3 is applied, say, L/4 from the left end.

F1+F2+F3=mg where m is the mass of the rigid bar.

Moments from right end
F1 + F3*3L/4 - mgL/2 = 0

Moments from left end
F3*L/4+F2*L-mgL/2 = 0

Solve to get F1=mg/4, F3=mg/3, and F2=5mg/12

Why are you restricting the solution to only one moment equation?

Bob at PC

________________________________________
From: phys-l-bounces@carnot.physics.buffalo.edu [phys-l-
bounces@carnot.physics.buffalo.edu] On Behalf Of Bob Sciamanda
[treborsci@verizon.net]
Sent: Sunday, March 14, 2010 5:02 PM
To: phys-l@carnot.physics.buffalo.edu
Subject: [Phys-l] Statics conundrum

Here is a common elementary statics problem:

A perfectly rigid and uniform beam of given weight and length (W and
L)
is suported by two men, exerting upward vertical forces F1 and F2, one
at each end of the bar. Determine F1 and F2 in terms of W and L.

This is easily solved by imposing translational and rotational
equilibrium:
F1 + F2 = W
W*L/2 = F2*L => F2 = W/2 and F1 = W/2 (independent of L)

One can even add other given loads at given positions on the bar, and
the problem is still easily solved.

*****************
But a curious student might uncover the following conundrum:
If one adds a third man exerting a third upward force F3 at a given
location (say L/4 from one end), The two equilibrium equations are
insufficient to solve for the values of the three unknons, F1 F2 and
F3.

The three man experiment can be performed and the forces measured
(even
with added loads on the beam). They ARE physically determined.
How does one analytically predict this result?

Please discuss. Is it the perfect rigidity which must be relaxed? Why?
How explain this to the curious student? (and to me)

Bob Sciamanda
Physics, Edinboro Univ of PA (Em)
treborsci@verizon.net
http://mysite.verizon.net/res12merh/



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