# TURNING ON A PIVOT worksheet (ANSWER)

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

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
Clockwise  Moment = F x D
= 10N  x  4.5m
= 45Nm

b)      State the size of the anticlockwise moment
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