FORCES 1. What is a force? Contact forces and non-contact forces
Doc Brown's Physics Revision
Suitable for GCSE/IGCSE Physics/Science courses or
This page will answer questions such as
What are scalar and vector quantities?
What is a force? What does it do?
What is a contact force?
What is a non-contact force?
Calculating resultant forces using vector
What is a force?
The first thing to say is you can't see a
BUT, you can observe its effect and often
quantify it with equations.
The unit of force is the newton (N)
and there are all sorts of forces e.g.
A force is a 'mechanical' push or pull effect, acting
on an object when it interacts with something or you can have forces of
repulsion and attraction or from friction of materials rubbing against each
The result of the interaction depends on the
nature and magnitude of the forces involved.
The value of force can be very small or very
large, from zero to an 'immeasurable' value at the centre of a black hole!
You are familiar with the results of
electrical, magnetic or gravitational forces and mechanical forces such those
acting in the spring of a clock or the engine of a road vehicle.
You also will learn formulae to do calculations on
gravity and acceleration.
What are scalar and vector quantities?
A scalar quantity only has magnitude
(a numerical quantity, size), but no specific direction.
speed (m/s), distance, mass, time,
temperature (K or oC), potential difference (V), current (A)
A vector quantity has both magnitude
velocity (m/s), rate of change of
position in a specific direction (compare with speed above)
(you can think of velocity as
'speed in a particular direction', but take care in how you use the
words speed and velocity!)
acceleration (m/s2), rate
of increase in velocity in a specific direction
momentum (mass x velocity)
forces are vector quantities
e.g. electrostatic, gravitational, magnetic, pushing, pulling, tension,
On diagrams vector quantities are
usually depicted with an arrow, the length of the arrow can show the
magnitude and the angle of the arrow shows the direction along
which the quantity acts.
In the diagram above, you have two
cyclist travelling at the same speed of 2 m/s, but in opposite
directions. Therefore, although they have the same speed
(same length of arrow), they have different velocities because
they are travelling in different directions. Note that the velocity of
the left cyclist is formally given a negative sign to indicate the
opposite direction of motion (it doesn't mean going slower or slowing
Contact forces and non-contact forces
- a comparison with examples
Forces between objects can be divided into
two main categories.
The interactive forces involved when two objects are in physical
The interactive forces when the two objects are apart,
non-contact, described as 'action at a distance force'.
Sometimes non-contact forces are
acting between objects that are actually in contact e.g. you sitting
in front of your computer is an example!
This involves gravity
(non-contact) and weight and compression (contact forces).
See the flask standing on
a bench example later.
If two objects have to be touching for
the force to act, the force would be described as a contact force. The two
objects will be pushing or pulling on each other e.g.
Friction between two surfaces
rubbing against each other, the force moving an object forwards is
partially countered acted by a force of friction acting in the opposite
direction e.g. tyre of a car in contact with the road, pressing the
brake pad onto the disc of a car's braking system,
Air resistance as an object
moves through the atmosphere, friction between the object and air,
An object resting on a surface
involves weight and compression (see 'interactions' section further down
When a spring is stretched you have 'in tension'
force as the spring tries to recover to its original shape acting
against the weight or force applied to stretch it e.g. when you use a
spring force meter in the laboratory or a spring balance for weighing
You get the opposite force 'in compression' if you push a
spring to compress it to a shorter length it tries to regain its
original shape e.g. the weight of a car acting on its suspension
Forces - elasticity
and energy stored in a spring
the tension in the wires attached to
the hook of a crane, if stationary, the tension in the cable is balanced
by the weight of the object the crane is lifting.
When dealing with major civil engineering
projects like building a bridge, complex calculations must be done to ensure the
bridge is stable and able to support the roadway with vehicles on it.
the forces involved in a suspension bridge design are those of tension and
compression, illustrated with pictures and diagrams below for any budding
The Humber Bridge over the Humber estuary, north-east England,
walked over and photographed in November 2018.
When it was completed in 1981 it was the World's longest single
span suspension bridge and in 2018 it still holds 8th place!
Despite the obvious complexity of the bridge
structure most of the contact forces involved are 'in tension' or
'in compression' forces which I've indicated by
Each of the two vertical towers of the
Humber Bridge, consist of a pair of hollow vertical concrete columns.
support the weight of the two main 'sagging cables' - which actually comprise
thousands of parallel steel wires (~15,000) bound together in a black casing.
in turn support the slightly angled (from the vertical) steel rods that support
Therefore there is a tremendous vertical force of
acting in the two load bearing vertical concrete towers, as they must hold up the
whole weight of the bridge!
Within the 'sagging' main cable, and the
almost vertical steel rods holding up the roadway, are the forces of tension.
These are pulled downwards by the weight of the roadway and of the cables
However, unlike the two towers which bear the whole weight of the bridge, the
total force of tension is split between the main cable and nearly vertical steel
For this reason, the rods supporting the roadway can be relatively thin
(62 mm diameter),
but there are a lot of them!
For more pictures see
Humber Bridge in the 'doscpics' section of my otherwise science
The bow and
arrow! (the physics of 'Robin Hood' and the 'Battle of Agincourt' in
English longbow (picture 1 above), and other
classified by the tension in lbs on pulling the bow string to its maximum
In old 'weight' units this equates to typically 50 lb
to 150 lb. 1 lb = 0.454 kg.
Imagine these 'weights' hanging from
the bow string.
You can measure this with a spring balance
by attaching it to the bow string and pulling it back and noting the reading
So the tension in the bow string is
equivalent to hanging on it 'weights' of typically 23 kg to 68 kg.
In terms of weight equalling the tension
force in the bow string you multiply the mass by 9.8 N/kg (due to gravity).
Therefore the tension in the string is
typically 224 to 667 N, and the bow and arrow is now an elastic potential
To reduce the force of friction between the
arrow and air, the arrow shaft is thin and a sharp metal point at the front end
When the bow is bent by drawing back the string,
the string is
in tension, AND there are forces of both tension and compression in the
On the inner curved surface of the bow you
get compression as the layers are pressed together.
On the outer curved surface of the arched bow
you get the tension as the outer layers are stretched.
When you let go of the arrow all this stored
potential energy is released and converted into kinetic energy of the fast moving arrow.
The drawn bow and arrow are an elastic
potential energy store.
The arrow becomes a kinetic energy store,
much of it is retained on flying back down to Earth.
As the arrow flies upwards it loses
kinetic energy and gains its gravitational potential energy store.
As it fall the GPE is converted back
to kinetic energy and the arrow can be as penetrating as when first
History note (not required
for GCSE physics, not sure about GCSE history!):
The rapid firing of many longbows
was a major factor in the English winning the Battle of Agincourt
(1415) in the 100 years war between France and England. The French
archers uses a crossbow that fires a bolt - deadly and very
effective, BUT the bolt must be drawn back by a mechanical winding
system to build up the store potential energy in the bolt mechanism. With no
mechanism to deal with, just muscle power, a skilled English archer
could pull back his bow and fire arrows at ten times the speed of
the French crossbow men. No contest! Shakespeare built the whole
thing up in his play "Henry the Fifth", he didn't know much physics
but he was pretty good with words!
If the objects are subjected to a force,
but do not need to be in contact with each other, the force would be
described as a non-contact force e.g. three classic non-contact force
fields acting between objects that are not touching ...
gravity - the gravitational
attraction force between any two objects
(i) A falling object in air,
experiences the non-contact force of gravity and the contact force
of friction between the object and air - air resistance.
(ii) Objects in contact will
still experience the 'non-contact' force of gravitational
attraction - any object standing motionless on a surface.
magnetism - the magnetic force
of attraction of iron towards a magnet (N-S poles) or two like poles of magnets
repelling each other (N-N or S-S poles) - the two possible magnetic field effects.
You see the magnetic field
non-contact force in action as a magnet attracts and picks up an
iron nail. Initially there is no contact, but once attached there is
contact, but the attractive force is still present even if they are
You can have an object is
suspended by magnetic repulsion, where there is no contact at all.
electrostatic force - the
attraction (+ -) or repulsion (- - or + +)
interaction of two objects carrying an electrical charge - electrical
A simple example is a rubbed charged
plastic rod picking up tiny bits of paper.
See Static electricity and electric fields, uses
and dangers of static electricity
note: gravity only
involves attraction (as far as we know?), but magnetic and
electrical forces involve both the forces of attraction and
More examples of interactions between objects
A 'force' interaction is a pair of equal and
opposite forces acting on two different objects e.g.
If you push down on the floor, the floor
pushes back up on you.
The forces of you and the floor are equal
and both objects experience a force.
This is an example of
Newton's 3rd Law which
can be stated in various ways:
to every action there is an equal and
whenever a force acts on one body, an
equal and opposite force acts on some other body,
when two objects interact, the forces
they exert on each other are equal in magnitude, but act in opposite in direction.
The two forces are called an
interaction pair of forces and they must be of the same type and the
same size but acting in opposite directions on the different objects.
On diagrams both forces will be shown
by arrows indicating both the direction and magnitude of the vector
When the moon is pulled towards the Earth by
the Earth's gravitational field force, there is an equal and opposite force
operating as the moon's gravitational field pulls the Earth towards!
forces were not equal, either the moon would drift away into space or collide
with the Earth! Fortunately, its a good example of a gravitational non-contact force
The same argument applies to explain the
Earth orbiting the Sun, both bodies experience the same numerically equal
force, but acting in opposite directions. The diagram below illustrates
these two gravitational force situations.
for the two examples above.
Two pairs of forces interacting on the
All objects standing motionless on the ground
are examples of opposite contact forces operating.
The weight of the object
acting as a downward force due to gravity is balanced by an upward push from the
ground as the atoms are minutely compressed.
If the forces were not balanced, either the
ground would sink or the object would be raised up!
BUT, take care with such descriptions,
analysis of the above situation reveals some complications!
messy to analyse!
Consider the flask of liquid standing
motionless on a laboratory bench.
There are two sets of forces operating shown
by the arrows of opposing direction, but the same length - same magnitude of
force for each pair.
Both sets of forces are examples of Newton's 3rd Law, but don't mix the
The normal contact force due to the
weight of the object acting (pushing) down on the surface of the bench (F1) is
balanced by the bench under minute compression pushing back up to an equal and
opposite extent onto the flask (F2).
At the same time both the flask and the Earth
(including the bench) are mutually attracting each other (F3 and F4) to an equal
and opposite extent due to the non-contact force of gravity (it makes no
difference whether the objects are in contact or not, here gravity acts
In the cases described so far there is no
resultant force, everything is balanced.
If the forces were not balanced and
there was some net resultant force, the object would move or be reshaped
- something would change!
For stationary objects, if the resultant
force acting on the object is zero the object is said to be in equilibrium (effectively means a state of balance).
More complex force situations
A 'free body force diagram' of a cyclist showing all the forces acting on the
body (not to a force scale)
'free body force diagram' should show every force acting on an isolated object
(body) or system but shows none of the forces it exerts on the surroundings.
The size of the arrows should indicate the relative magnitude (size) of the force.
There are four forces acting on the body
(= bike + cyclist):
F1 is the air resistance due to
friction between the surface of the bike + cyclist combination and the air,
also friction between the wheels and road, and, friction in moving parts of the
bike. All three combined oppose the forward motion of the bike and rider.
F3 is the thrust or push of the
bike from the power generated by the cyclist.
If F1 = F3 the cyclist continues at
the same speed and direction - constant velocity.
If F3 > F1 the cyclist
accelerates - speeds up, and, if F1 > F3 the cyclist decelerates
- slows down.
Newton's 1st law of motion.
F2 is the weight of the bike +
cyclist combination due to gravity, weight of object acting on the road with the normal contact
F4 is the normal contact force of the
atoms of the road surface pushing back up on the bike.
If the bike and rider are moving
along smoothly without jumping up or down, F2 = F4
A 'free body force diagram' of a swimmer showing all the forces acting on the
body (not to a force scale)
F1 is the water resistance due
to friction between the swimmer and the water
F2 is the weight of the
swimmer acting on the water
F3 is the thrust or push of
the swimmer from the power generated by the swimming action
F4 is the upthrust of the
water on the swimmer (buoyancy effect)
body force diagram' of a parachutist showing all the forces acting on the body
(not to a force scale)
is the air resistance (drag effect) due to friction between the
parachutist and the air.
F2 is the weight of the
parachutist due to gravity, 'pulling' the parachutist downwards.
If F1 = F2 the parachutist will
fall at a constant speed, a constant velocity if no side wind.
F3 is a push on the
parachutist by a side wind. If it is zero the parachutist will fall
Note that the parachutist can pull on
the cords of the chute to alter the direction of the drag effect to
manoeuvre into a safe and intended landing location!
involves the forces of F1 weight (gravity force acting on skier), F2
friction (between snow and ski) and F3 air resistance (friction
between skier's clothing and the surrounding atmosphere brushing over the
In diagrams to resolve numerical problems,
the length of the arrow should equal the magnitude of the force OR a numerical
force value indicated on the arrow.
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