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Simplifying, rearranging terms, and dividing both sides by 2 gives us:

P = 4*Q ( eq. a2 )

Two equations and two unknowns

Including eq. a1 , (repeated below) we now have two equations and two unknowns.

P + Q = W

Inserting the numeric value for W gives us

P + Q = 10, or

Q = 10 - P ( eq. a3 )

Substituting this value of Q into eq. a2 gives us

P = 4*(10 - P), or

P = 40 - 4*P, or

5*P = 40, or

P = 8

which is one of the answers that we are looking for.

Inserting the value for P into eq. a3 gives us

Q = 10 - 8, or

Q = 2

which is the other answer that we are looking for.

A more general case of the trapeze bar

Let's pick another point, label it X, and compute the moments about that point. Those moments must also sum to zero for the bar to be in equilibrium.(The moments computed about any point on the bar must sum to zero for the bar to be in equilibrium.)

The moments about X produced by the three forces are:

  • P: (X-A)*(P)
  • W: (X-C)*(W)
  • Q: (X-B)*(Q)

Let X = 5

Substituting for X gives us:

(5)*(P) - (3)*(10) + (-5)*(Q) = 0

Simplifying, rearranging terms, and diving both sides by 5 gives us:

P - Q - 6 = 0, or

P = Q + 6 ( eq. a4 )

Now we can use this equation along with eq.a1 to solve for Q.

P + Q = 10, from eq.a1 , or

Q = 10 - P

Substituting this value for Q in eq. a4 gives us,

P = 10 - P + 6

Simplifying and dividing both sides by 2 gives us,

P = 8 , which is the same answer as before (which it should be)

Substitution of P back into eq. a1 gives us,

Q = 2

Apply theweight at different locations on the trapeze

If you solve for P and Q for any location of the weight between the ropes, you will find that the values for the upward forces at each end of the bar areinversely proportional to the distance from the weight to that end of the bar.

For example, for equilibrium, using the dimension symbols established for your drawing earlier:

a*P = b*Q

Dividing both sides by a gives:

P = (b/a)*Q

Weight is centered

If b/a = 1 (weight is centered), then:

P = Q meaning that both upward forces are equal.

Weight towards the left end

If b/a = 4 (weight at 2), then:

P = 4*Q meaning that most of the force is being exerted by the rope on the left end.

Weight toward the right

If b/a = 1/4 (weight at 8), then

P = Q/4 meaning that most of the force is being exerted by the rope on the right end.

Weight at the right end

If b/a = 0 (weight at 10, right end of the bar)

P = 0 meaning that all of the force is being exerted by the rope on the right end of the bar.

Because P + Q = W, we conclude that Q = W

The bar is essentially eliminated

The scenario where b/a = 0 essentially eliminates the bar from consideration. The weight is hanging directly on the rope on the right end of the bar and theweightless bar and the other rope are simply floating in the air.

Hypothetical replacement by a single upward force

If we were to draw an imaginary force labeled R pointing directly up from the point C where R is equal to P + Q, we could imagine the forces P and Q as beingreplaced by R. In that case, R would be the resultant of P and Q and would be equal in magnitude and opposite in direction to the downward force W.

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
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Source:  OpenStax, Accessible physics concepts for blind students. OpenStax CNX. Oct 02, 2015 Download for free at https://legacy.cnx.org/content/col11294/1.36
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