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“We must trust to nothing but facts: These are presented to us by Nature, and cannot deceive. We ought, in every instance, to submit our reasoning to the test of experiment, and never to search for truth but by the natural road of experiment and observation.” ― Antoine Lavoisier, Elements of Chemistry

Saturday, 29 November 2014

TURNING ON A PIVOT worksheet (ANSWER)

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1. Calculate the moment of this force. Show your working.  



 ANSWER:
Moment = F x D
               = 100N  x  0.3m
               = 30Nm

2.   This system is balanced
 a)      Calculate the size of the clockwise moment
Clockwise moment    = (20N x 3m)  +  (25N x (3m + 1m))
                                    = 60 Nm  + 100 Nm
                                    = 160 Nm

b)      State the size of the anticlockwise moment
Anti-clockwise moment        = X N  x 2m
                                                = 2X m

c)      Calculate the size of force X
      Clockwise moment    =  Anti-clockwise moment
                 160 Nm      =  2X m
                        160 : 2 = X
                                     80 = X


3.  A pivoted uniform bar is in equilibrium under the action of the forces shown.
 What is the magnitude of the force F?
Anti -Clockwise moment  =  Clockwise moment
      10N  x  4m                    =  (F x 2m) + (6N x (2m+2m))
                              40 Nm   =  2F m + 24 Nm
              40 Nm – 24 Nm    = 2F m
                        16 Nm         = 2F m
                     16 Nm : 2 m              = F
                              8 N      = F


4.   A uniform beam AB of mass 20kg and length 3m rests in equilibrium in a horizontal position. The beam is supported by a single pivot at C and a particle of mass 6kg is attached at B.

       Calculate the distance AC.
Assume:    AC is X meter, so CB is (3 – X) meter
Anti -Clockwise moment  =  Clockwise moment
      20 kg  x  X                    =  6 kg  x  (3 – X)
                  20X                    = 18 – 6X
                  20X + 6X           = 18
                              26X        = 18
                                  X        = 18 : 26
                                  X        = 0.69 meter



5.    a uniform metre rule, freely pivoted at a point 20 cm from end P.

The rule is kept horizontal by means of a 120g mass suspended 5.0 cm from end P. Use the principle of moments to help you determine the mass of the metre rule.
Anti -Clockwise moment  =  Clockwise moment
            120 x 15                        =  MASS x 30
                        1800                 = MASS x 30
                        1800 : 30          = MASS

                        60 gram            = MASS


6.   Look at this example of a balanced system

      a)      Calculate the size of the clockwise moment
ANSWER:
Clockwise  Moment = F x D
                                    = 10N  x  4.5m
                                     = 45Nm

b)      State the size of the anticlockwise moment
ANSWER:
Anti-clockwise  Moment       = F x D
                                                = 15N  x  Xm
                                                = 15XNm


c)      Calculate the distance x.         
Clockwise moment      = Anti-clockwise moment
                10N  x  4.5m =  15N  x  Xm
                          45 Nm = 15X Nm
                                  X = 45 : 15
                                  X = 3 m
       

                         

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