TURNING ON A PIVOT worksheet (ANSWER)

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