FORCES 1. What are scalar and vector quantities?
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What is a force? Contact forces and non-contact forces
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?
Sub-index for this
page
(a)
What is a force?
(b)
What are scalar and
vector quantities?
(c)
Comparing contact
forces and non-contact forces examples
(c)(i)
Contact force
examples
(c)(ii)
Non-contact
force examples
(d)
More examples of
interactions between objects involving gravity
(e)
More complex force
situations involving moving objects
See also
Calculating resultant forces using vector
diagrams
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(a)
What is a force?
The first thing to say is you can't see a
force!
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.
You can have forces of
repulsion and attraction or from friction of materials rubbing against each
other etc.
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, the engine of a road vehicle or
the motion of planets.
You also will learn formulae to do calculations on
gravity and acceleration.
Arrows are used on
diagrams to show the direction and magnitude of a force -
but first check out you know the difference between scalar and vector
quantities explained in the next section.
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(b)
What are scalar and vector quantities?
A scalar quantity only has magnitude
(a numerical quantity, size), but
no specific direction.
Examples:
Speed, distance, mass, time,
temperature (K or oC), potential difference (V), current (A).
Non of these automatically
implies the use of direction.
However if you apply a direction
to speed or distance, it becomes a vector quantity.
A vector quantity has both magnitude
(size) and
specific direction.
Examples:
Velocity (m/s),
is the 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),
is the rate
of increase in velocity/speed in a specific direction
Momentum
(kg m/s)
the product of the mass x velocity of an object moving in a
particular direction.
Displacement
(m) is
the distance an object has moved in a particular direction.
Force
(N) is also considered to act in a specific direction.
ALL
forces are vector quantities
They all have a magnitude, and, at
any point, act in a specific direction.
e.g. electrostatic
(attraction/repulsion), gravitational, magnetic, (attraction/repulsion) pushing, pulling, tension,
compression.
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
down!).
Diagrams illustrating force
vectors
Two forces acting on an object.
The length of the arrows are
proportional to the magnitude of the forces involved - in this case two
acting forces and a resultant force.
One force is acting to the right and
the other to the left (blue arrows).
The net force, resultant force, is
acting to the right - do you see its a simple logical calculation?
Which is net force to the right =
780 - 330 = 450 N
Lots more on resultant forces on
this page and also on
Calculating resultant forces using vector
diagrams
1.
2.
3.
A parachutist and parachute
These diagrams show the relative
magnitude of the two forces acting on a descending parachutist.
Note the relative size and direction of
the arrows. The weight force F2 is constant.
1. When the parachutist opens the
parachute, there is an immediate large drag force due to big increase in
air resistance (air friction).
2. As the parachutist slows down (decelerates) the air
resistance (F1) reduces and continues to do so until F1 = F2.
3. When drag force F1 equals the
weight force F2 (arrows of equal length), the parachutist is descending
at a steady speed - a terminal velocity.
Remember the drag force on an object
due to friction (air resistance), increases with speed i.e. as more air
brushes over the surface of the object in the same time.
This parachute situation is fully
explained on
Acceleration,
friction, drag effects and terminal velocity
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(c)
Comparing contact forces and non-contact forces examples
Forces between objects can be divided into
two main categories.
The interactive forces involved when two objects are in physical
contact - contact forces.
The interactive forces when the two objects are apart,
non-contact forces, 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.
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(c)(i) Contact force
examples
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.
(1) Friction
is a contact force 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.
the tyre of a car in contact with the road,
pressing the
brake pad onto the disc of a car's braking system,
rubbing your hands together.
(2) Air resistance
is also a contact force as an object
moves through the atmosphere, friction between the object and air, even
though the downward motion is caused by the non-contact force of
gravity.
An object resting on a surface
involves weight and compression (see 'interactions' section further down
the page).
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
things.
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
springs.
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.
(3) Forces of tension and
compression
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.
Most of
the forces involved in a suspension bridge design are those of
tension and
compression, illustrated with pictures and diagrams below for any budding
young engineer!
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
yellow arrows.
Each of the two vertical towers of the
Humber Bridge, consist of a pair of hollow vertical concrete columns.
These
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.
These cables
in turn support the slightly angled (from the vertical) steel rods that support
the roadway.
Therefore there is a tremendous vertical force of
compression
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
themselves.
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
rods.
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
website!
(4) The bow and
arrow! (the physics of 'Robin Hood' and the 'Battle of Agincourt' in
1415!
English longbow (picture 1 above), and other
bows are
classified by the tension in lbs on pulling the bow string to its maximum
tension.
In old 'weight' units this equates to typically 50 lb
(23 kg)
to 150 lb (68 kg). (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
(picture 2).
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).
weight (N) = mass (kg)
x gravitational field constant (g)
Therefore the tension in the string is
typically 224 to 667 N, and the bow and arrow is now an elastic potential
energy store!
To reduce the force of friction (drag
force) between the
arrow and air, the arrow shaft is thin, as are the flight feathers, and a sharp metal point at the front end
(picture 3).
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
bow structure.
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 increases its gravitational potential energy store.
As it falls, the GPE is converted back
to kinetic energy, and the arrow can be as penetrating as when first
fired.
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
about physics
but he was pretty good with words!
(5) Normal contact forces
Any object standing on a
surface in a gravitational field involves normal contact forces.
The object has weight due to
gravity, so the object presses down on the surface e.g. a
stationary book lying on a table or you standing on the floor or
sitting on a chair.
The atoms of the table are
compressed and push back on the surface against the weight of the
book.
The two normal contact forces are
equal, but acting in opposite directions - no change in motion!
If the they were not equal, the
book would either move upwards or sink into the table!
Its the same argument for you
standing on the floor.
Your body weight force acts down
on the floor and the compressed atoms of the floor push back up with
a force equal to your weight - otherwise you would move up or down!
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(c)(ii) Non-contact
force examples
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.
Any object in a gravitational
field experiences the force of gravity.
note:
(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 with
each other will
still experience the 'non-contact' force of gravitational
attraction - any object standing motionless on a surface.
Magnetism -
the magnetic attraction between a magnetised material and another magnet
material.
Any object that is magnetic or
can be magnetised, will experience a force from the magnetic field
of a magnet.
This can be the magnetic force
of attraction of iron towards a magnet (permanent and induced N-S pole
attraction), two magnets attracted by their opposite poles (N-S
<= N-S), or two like poles of magnets
repelling each other (N<=>N or S<=>S poles) - 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
in contact.
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
field effects
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
repulsion.
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(d)
More examples of interactions between objects
involving gravity
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
opposite reaction,
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
quantities.
The solar system
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!
If the
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
operating!
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.
Diagram
for the two examples above.
Two pairs of forces interacting on the
same objects!
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!
A bit more
messy to analyse than you think!
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
two up!
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
throughout everything!).
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).
See also
3. Calculating resultant forces using vector
diagrams and work done calculations gcse physics revision notes
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(e)
More complex force situations involving moving objects
(a)
A 'free body force diagram' of a cyclist showing all the forces acting on the
body (not to a force scale)
A
'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 friction forces 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, net resultant force
of zero.
If F3 > F1 the cyclist
accelerates - speeds up, net resultant force = F3 - F1
and, if F1 > F3 the cyclist decelerates
- slows down, net resultant force = F1 - F3
See
Newton's 1st law of motion.
F2 is the weight of the bike +
cyclist combination due to the Earth's gravity field effect, weight of object acting on the road with the normal contact
force
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, net
resultant force of zero.
(b)
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)
When F1 = F4 the swimmer floats at an average
stable height above the water.
When F2 = F3 the swimmer moves at more or
less a constant speed.
In both cases there is a slight variation due to the
swimming stroke cycle.
(c)
A 'free
body force diagram' of a parachutist showing all the forces acting on the body
(not to a force scale)
F1
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
vertically.
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!
(d)
Skiing
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
surface).
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.
See also
3. Calculating resultant forces using vector
diagrams and work done calculations gcse physics revision
At the moment for
amusement only!

  all
non-equilibrium situations!
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