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net τ = 0 size 12{"net "τ=0} {}

where net means total. Torques, which are in opposite directions are assigned opposite signs. A common convention is to call counterclockwise (ccw) torques positive and clockwise (cw) torques negative.

When two children balance a seesaw as shown in [link] , they satisfy the two conditions for equilibrium. Most people have perfect intuition about seesaws, knowing that the lighter child must sit farther from the pivot and that a heavier child can keep a lighter one off the ground indefinitely.

Two children are sitting on a seesaw. On the left side, a lighter child is sitting and on the right, a heavier one. The distance of the lighter child from the fulcrum is more than that of heavier child. At the fulcrum, an upward force vector labeled as F-p is shown. The weights of the two children, w-one and w-two, are shown as vectors in the downward direction, and the force at the fulcrum, F-p, is shown as a vector in the upward direction.
Two children balancing a seesaw satisfy both conditions for equilibrium. The lighter child sits farther from the pivot to create a torque equal in magnitude to that of the heavier child.

She saw torques on a seesaw

The two children shown in [link] are balanced on a seesaw of negligible mass. (This assumption is made to keep the example simple—more involved examples will follow.) The first child has a mass of 26.0 kg and sits 1.60 m from the pivot.(a) If the second child has a mass of 32.0 kg, how far is she from the pivot? (b) What is F p , the supporting force exerted by the pivot?

Strategy

Both conditions for equilibrium must be satisfied. In part (a), we are asked for a distance; thus, the second condition (regarding torques) must be used, since the first (regarding only forces) has no distances in it. To apply the second condition for equilibrium, we first identify the system of interest to be the seesaw plus the two children. We take the supporting pivot to be the point about which the torques are calculated. We then identify all external forces acting on the system.

Solution (a)

The three external forces acting on the system are the weights of the two children and the supporting force of the pivot. Let us examine the torque produced by each. Torque is defined to be

τ = rF sin θ . size 12{τ= ital "rF""sin"θ} {}

Here θ = 90º , so that sin θ = 1 for all three forces. That means r = r size 12{r rSub { size 8{ ortho } } =r} {} for all three. The torques exerted by the three forces are first,

τ 1 = r 1 w 1

second,

τ 2 = r 2 w 2

and third,

τ p = r p F p = 0 F p = 0.

Note that a minus sign has been inserted into the second equation because this torque is clockwise and is therefore negative by convention. Since F p acts directly on the pivot point, the distance r p is zero. A force acting on the pivot cannot cause a rotation, just as pushing directly on the hinges of a door will not cause it to rotate. Now, the second condition for equilibrium is that the sum of the torques on both children is zero. Therefore

τ 2 = τ 1 , size 12{τ rSub { size 8{2} } =τ rSub { size 8{1} } } {}

or

r 2 w 2 = r 1 w 1 . size 12{r rSub { size 8{2} } w rSub { size 8{2} } =r rSub { size 8{1} } w rSub { size 8{1} } } {}

Weight is mass times the acceleration due to gravity. Entering mg for w , we get

r 2 m 2 g = r 1 m 1 g .

Solve this for the unknown r 2 size 12{r rSub { size 8{2} } } {} :

r 2 = r 1 m 1 m 2 . size 12{r rSub { size 8{2} } =r rSub { size 8{1} } { {m rSub { size 8{1} } } over {m rSub { size 8{2} } } } } {}

The quantities on the right side of the equation are known; thus, r 2 size 12{r rSub { size 8{2} } } {} is

r 2 = 1.60 m 26.0 kg 32.0 kg = 1.30 m . size 12{r rSub { size 8{2} } = left (1 "." "60"" m" right ) { {"26" "." 0" kg"} over {"32" "." " 0 kg"} } =1 "." "30"" m"} {}

As expected, the heavier child must sit closer to the pivot (1.30 m versus 1.60 m) to balance the seesaw.

Solution (b)

This part asks for a force F p . The easiest way to find it is to use the first condition for equilibrium, which is

net F = 0 .

The forces are all vertical, so that we are dealing with a one-dimensional problem along the vertical axis; hence, the condition can be written as

Questions & Answers

anyone know any internet site where one can find nanotechnology papers?
Damian Reply
research.net
kanaga
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.
Bharti
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
Daniel
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there is no specific books for beginners but there is book called principle of nanotechnology
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s.
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.
Tarell
what is the actual application of fullerenes nowadays?
Damian
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.
Tarell
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.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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.
Harper
Do you know which machine is used to that process?
s.
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SUYASH Reply
for screen printed electrodes ?
SUYASH
What is lattice structure?
s. Reply
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
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what's the easiest and fastest way to the synthesize AgNP?
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Cied
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I start with an easy one. carbon nanotubes woven into a long filament like a string
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Source:  OpenStax, Physics 101. OpenStax CNX. Jan 07, 2013 Download for free at http://legacy.cnx.org/content/col11479/1.1
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