Forces in Equilibrium

Components of forces, moments

Vectors and Scalars

·      A scalar quantity has a magnitude but no direction e.g. mass

·      A vector quantity has a magnitude and direction e.g. velocity

Resultant Vectors

·      This is the single vector that could take the place of two (or more) other vectors. Commonly taken with velocities and forces at AS level

·      Can be found using a scale drawing or mathematically

Scale Drawing

            - choose a scale that will fit on your paper

- draw the two (or more vectors) end to end at the correct angles (use a protractor)

- measure the resultant length and convert to a value using your chosen scale

- measure the resultant angle with a protractor


-       200N50Nfor two forces in the same plane



choose a positive direction, in this case, right

The resultant is then the sum in that direction: 200 – 50 = 150N right

-       for two forces at right angles

Draw a simplified diagram

By Pythagoras to find R and the angle, _
R=√(_20_^2+_15_^2 )=25N
tan__=20/15  _ _=tan^(-1)__(20/15)=_  _53.1_^0

 Components of Vectors

·      This is the opposite process to finding the resultant

·      The components are a horizontal and vertical vectors that could be combined to give a resultant of the vector you have

The horizontal and vertical components of the force F are FX and FY.



(draw a triangle with the vectors and use SoCaToa if you need to)





Free Body Diagrams of Forces

·      This is a simplified diagram of an object showing only the forces acting on the object as arrows in the direction the forces act

·      It does not have to be to scale (unless it is to be used to find a resultant force by scale drawing) – however lines are drawn different lengths to denote the magnitude of forces. E.g. longer arrows for larger forces

·      Force arrows are drawn from the point at which they act in the direction of the force

e.g. for an object in equilibria on a slope:

Types of Forces

·      Contact forces are those which arise due to the interaction of particles e.g. the support force felt by a person leaning on a desk is provided by the interaction of particles in the persons arms with the particles in the desk (complicated actually – a result of electromagnetic repulsion from the negative electrons in the arms and the table)

Friction is another common contact force

·      Forces due to a field are those which arise because of a property of the object e.g. Some metals are magnetic and so feel a magnetic force – people contain very little of these materials and so do not feel it. Gravitational, Magnetic and Electric fields will be studied at A2 level

Weight	=	Mass x	Gravitational Field Strength 
W		=	m	x	g (=9.81 on earth)
(N)		=	(kg)		(Nkg-1)

Weight is a common example of this kind of force at AS level. Weight is the action of the gravitational field strength of the earth acting on a mass:


Forces in Equilibira

·      Rules arise from Newtons 1st Law of Motion

“Objects remain at rest or in constant uniform motion unless acted upon by an external resultant force”

·      The forces on static objects must therefore be balanced : this means a zero resultant force

·      A scale diagram of the forces forms a closed shape

·      Forces left = Forces right
Forces up = Forces down
It can be usefully broken down into 2 rules for an object in equilibria:







Moment =	Force x	Perpendicular distance from pivot
(Nm)		(N)		(m)

The moment of a force is its turning effect : this depends not only on the size of the force but also on how far away it is from the pivot point

·      A moment can be in either a clockwise or anti-clockwise direction

·      Sum of clockwise moments = Sum of anti-clockwise momentsThe principle of moments applies to Newtons 1st law again to situations where an object is in equilibria and has balanced moments acting on it:


·      The centre of mass of an object is the point where a single force acting at that point produces no moment.


Moment of couple =	Force x	Perpendicular distance between forces
(Nm)				(N)		(m)

A couple is when there are a pair of equal forces acting in opposite directions around a pivot point.


Stability and Toppling

·      An object is stable if the line of action of its weight, drawn vertically downward from its centre of mass, passes through its base


A stable equilibrium is when an object is stable, then displaced from its equilibrium position will return to its original equilibrium position

·      An unstable equilibrium is when it will not return to the equilibrium position