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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

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.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
for teaching engĺish at school how nano technology help us
Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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