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In the absence of the forces P and Q, the force R would produce the same turning effect on the bar as do the forces P and Q jointly.

If the magnitude of R were not equal to the magnitude of W, the vector sum of the forces would not be zero, there would be a torque about any point on the barother than at the point C, and the bar would not be in equilibrium.

Exercise involving a bar supported at only one point

Tactile graphics

The file named Phy1110c1.svg contains a vector diagram that represents this scenario. All of the action occurs near the right end of the bar, so only theright end is shown in the image.

Figure 8 shows the mirror image that is contained in that file for the benefit of your assistant who will create the tactile graphicfor this exercise.

Figure 8 . Mirror image from the file named Phy1110c1.svg.
Missing image

Figure 9 shows a non-mirror-image version of the same image.

Figure 9 . Non-mirror-image version of the image from the file named Phy1110c1.svg.
Missing image

Figure 10 shows the key-value pairs that go with the image in the file named Phy1110c1.svg.

Figure 10 . Key-value pairs for the image in the file named Phy1110c1.svg.
m: P = 15 N n: File: Phy1110c1.svgo: B = 0 p: a = 1q: b = 2 r: C = 3s: W = -10 N t: A = 1u: Bar v: Q = -5 Nw: Exercise involving a bar supported at only one point

Unlike or antiparallel

It's time to modify your drawing to reflect a different scenario.

Make your bar 20 units in length. Draw a downward force labeled Q at the right end of the bar. Label this as point C on the bar.

Draw an upward force labeled P somewhere on the bar. Label the location of this point on the bar as A

In this case, we have two parallel forces, P and Q pulling in opposite directions but not in the same line of action. These forces are said to be unlike or antiparallel .

Add another downward force

Draw a downward force labeled W somewhere to the left of A. Label this point as B and consider it to be the horizontal origin. Directions to the right of Bare positive directions.

Label the horizontal distance from B to A as a. Label the horizontal distance from A to C as b.

What is required for equilibrium?

We can look at this scenario and tell that the forces labeled W and P, both of which point down, must be on opposite sides of the force labeled P.Otherwise, the bar will rotate in a clockwise direction.

The following two conditions must be true for the bar to be in equilibrium.

P + W + Q = 0, or

P = - (W + Q) (vector sum must be zero)

a*P + (a+b) * Q = 0 (moments around point B)

The plan

We will set values for all the variables in the twoconditions other than a and P and then solve for values of a and P that will result in the bar being in equilibrium .

  • Let W = -10
  • Let Q = -5
  • Let b = 2

The computations

Substituting these values into the two conditions and rearranging terms gives us:

P = -(W + Q), or

P = 15 , this is one of the answers

a*P +(a+2)*(-5) = 0, or

15*a -5*a -10 = 0, or

10*a = 10, or

a = 1 , this is the other answer

The answers

Therefore, for the values of W, Q, and b given above , P must be equal to 15 and a must be equal to 1 for the bar to be in equilibrium.

Questions & Answers

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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
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Brian Reply
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analytical skills graphene is prepared to kill any type viruses .
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
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Damian Reply
what king of growth are you checking .?
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Stoney Reply
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Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
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anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
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Praveena Reply
what does nano mean?
Anassong Reply
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how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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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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