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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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