Moments and Levers The turning effect or effect or moment moment of of a force is dependent on both the size of the force and how far it is applied from the pivot pivot or or fulcrum fulcrum..
Moment of Force = Force x Perpendicular Perpendicular distance from fulcrum Units = ewton metres !m ! m""
#.$. $ate %& %& % force !F" is acting on the gate at the edge.
$ate '& % force !F" is acting on the gate at the centre.
(n a"&
Moment of force about ) = * x +m = ,*m
(n b"&
Moment of force about ) = * x ,.*m = -.*m
This shows that the turning effect of F is greater in a" than in b". This therefore agrees agrees with the fact that a gate will open more easil/ if pulled or pushed at the edge.
Law of Moments
$ravit/ exerts forces F, and F0 on the masses m, and m0 at distances d, and d0.
F, is tr/ing to turn the ob1ect anticloc2wise. !F, x d, = the moment" F0 is tr/ing to turn the ob1ect cloc2wise. !F0 x d0 = the moment" 3hen the ob1ect is in balance we sa/ it is in e4uilibrium. (f the ob1ect is balanced !in e4uilibrium" then& The anticloc2wise moment should e4ual the cloc2wise moment.
F, x d, = F0 x d0 The Law of Moments %5% the Law of the Lever states& 3hen an ob1ect or bod/ is in e4uilibrium the sum of the cloc2wise moments about an/ point e4uals the sum of the anticloc2wise moments about the same point.
3or2ed #xample The see6saw balances when 7usan !+08" sits at % Tom weighing *98 sits at ' and :arr/ weighing 3 sits at ;. Find 3.
%nticloc2wise Moment& !+08 x +m" < !*98 x ,m" = ,*88m
;loc2wise Moment& 3 x +m
;loc2wise Moments = %nticloc2wise Moments 3 x +m = ,*88m 3 = ,*88m+m 3 = *88.
;omplete 3or2sheet
Moments and Levers 3or2sheet ,.
The diagram below shows 0 half6metre rules that are mar2ed off at *cm intervals and (>#T(;%L metal discs are placed on the rules as shown. (n each case state whether the rules will turn anticloc2wise cloc2wise or remain in the horizontal position. 7:)3 ?)U@ 3)@5($
0.
The metre rule in the diagram below is supported at its centre.
(f the rule is balanced the respective values of x and / are& % ;
+cm !x" *cm !/" Acm !x" ,8cm !/"
' >
*cm !x" +cm !/" ,0cm !x" 08cm !/"
7ow /our wor2ing and give /our answers in cm. +.
(n the above diagrams the distance %; = ;'. ;alculate in both cases the force B which is 2eeping the s/stem stationar/.
Levers %n/ device that can turn about a pivot is 2nown as a lever. % force called the effort is used to overcome the resisting force !the load". The pivotal point is called the fulcrum.
#xamples of Levers
(f we use a bar to move a heav/ roc2 our hands appl/ the effort and the load is the force exerted b/ the roc2. #.$. (f the distances from the fulcrum ) are shown and the load is given !,888" the effort re4uired can be calculated using the Law of Moments.
;loc2wise moment = %nticloc2wise moment #ffort x 088cm = ,888 x ,8cm Therefore& effort = ,8 888cm = *8 088cm (n effect using the bar to move the roc2 magnifies the effort 08 times but the effort must move further than the load.
;onditions for #4uilibrium (f a number of parallel forces act on a bod/ob1ect so that it is in e4uilibrium we can sa/&
a"
The sum of the forces in one direction e4uals the sum of the forces in the opposite direction.
b"
The Law of Moments must appl/.
#.$.
0 painterdecorators weighing *88 and -88 respectivel/ stand on a plan2 of wood at positions % and '. The plan2 is resting on 0 trestles !supports" and weighs 988. The trestles exert upward forces P and C on the plan2 !2nown as reactions".
;alculate the upward forces P and C.
From a" The sum of the forces in one direction e4uals the sum of the forces in the opposite direction. Therefore& P < C = *88 < 988 < -88 = ,A88 Ta2ing the moment at ; gets rid of an/ moments due to C .
;loc2wise Moment = P x 9m %nticloc2wise Moment = !*88 x *m" < !988 x 0m" < !-88 x ,m" = 9888m ;loc2wise Moment = %nticloc2wise Moment Therefore&
P x 9m = 9888m P = 9888m 9m P = ,888 C = ,A88 D ,888 C = A88
