Force and acceleration
IGCSE 1
Forces
• What is a force?
• A force is a push or a pull.
• An objects behaviour is
dependant on all the
forces acting on it.
• Force is measured in
Newtons (N)
Effects of forces
• The size and direction of the forces acting on an
object will determine how that object moves or
behaves.
Forces can:
1. Change the speed of an object
2. Change the direction of movement of an object
3. Change the shape of an object
Types of forces
Weight – the gravitational force between the earth and an object.
What is the difference between mass and weight?
Weight = mass x gravitational acceleration
𝑾 = 𝒎𝒈
The weight of an object changes according to
its position in the universe because the value of
g changes.
Other forces
• Tension:This is the force
that acts through a rope.
• Friction: Friction is a force
that acts to oppose
motion.
• Normal:The normal force is
the force exerted by a
surface on an object with
which it is in contact.
Adding Forces
Forces acting in a straight line:
10N
5N
10N
4N
10N
What will be the total Force?
10N
5N
4N
Adding Forces
Forces acting in a straight line:
8N
3N
10N
4N
What will be the total Force?
10N
8N
3N
4N
A car of mass 900kg is travelling along a road at 20𝑚. 𝑠 −1 .
Forces that act on the car:
Accelerating force of the engine (𝐹𝑎𝑝𝑝𝑙𝑖𝑒𝑑 )
Weight of the car (𝐹𝑔 )
Friction of road on tyres (𝐹𝑓𝑟 )
Normal force of the road (𝐹𝑁 )
Adding Forces: Parallelogram Law
Go to page 81 in your textbook and follow the
instructions on the Parallelogram Law.
Worked Example
• Find the resultant of two forces of 4.0𝑁 and 5.0𝑁
acting at an angle of 45° to each other.
• Using a scale of 1cm = 1N, draw parallelogram ABDC
with AB = 5cm, AC = 4N and the angle 𝐶 𝐴𝐵 = 45°.
• Use the parallelogram law to find the resultant of these
two forces. (it must have magnitude and direction).
• Answer = 8.3N acting at an angle of 20° to the 5.0N
force.
Vectors and Scalars
• Scalars are quantities with magnitude ONLY e.g. speed,
distance
• Vectors are quantities with BOTH magnitude AND
direction e.g. velocity, displacement, acceleration
• A vector is represented by an arrow, where the line
indicates the magnitude and the arrow points in the
direction of motion.
•
Questions
• Do the questions on pg 70
Newton’s 1st Law
• What causes a car to come to rest when the
engine is switched off?
• What would happen if these forces weren’t
around?
Newton’s 1st Law
• Force is not needed to keep a body with
uniform velocity in motion as long as no
opposing forces act on it.
• This is summed up in Newton’s First Law
A body stays at rest, or continues to move at
constant velocity, unless acted upon by an
external force.
Mass and Inertia
• Inertia is the property of a body that resists a
change in it’s motion. i.e. if it is at rest, it
wants to stay at rest.
The Egg Experiment
Mass and Inertia
• The larger the mass of a body, the larger its
inertia (resistance to movement)
Newton’s Second Law
If there is an unbalanced force acting on an
object, the object will accelerate in the
direction of the force. The acceleration is
directly proportional to the force and inversely
proportional to the mass of the object.
𝑭𝒏𝒆𝒕 = 𝒎𝒂
Newton’s Second Law
• A CONSTANT force causes a CONSTANT
acceleration
• CONSTANT VELOCITY means there is NO
resultant force acting on the object.
• CONSTANT ACCELERATION = CONSTANT
FORCE acting on the object
Worked Example
1. A block of mass 2kg is pushed along a table
with a constant velocity by a force of 5N.
When the push is increased to 9N, what is:
a) The resultant force
b) The acceleration
Worked Example
1. A car of mass 1200kg is travelling at
72𝑘𝑚/ℎ is brought to rest in 4s. Find:
a) The average deceleration
b) The average braking force
c) The distance moved during the deceleration.
Newton’s Third Law
If body A exerts a force on body B, then body B
will simultaneously exert a force on body A.
The forces are equal in magnitude but opposite
in direction.
These forces are called an ACTION-REACTION
pair.
Note: the forces are applied to different objects
so no resultant force can be found.
Newton’s Third Law
F2: Table
pushes book
up
F1: Earth
pulls book
down
F3: Book
pushes table
down
F4: Book pulls
earth up
• The book does not move because F1 = F4 (balanced forces)
• What are the action-reaction pairs? (F1+ F2 and F3+F4)
Newton’s Third Law
Newton’s Third Law
Example 3: Horse pulling a cart
Cart pulls horse backwards
Horse pulls cart forward
Friction
The cart will only move when: pull on cart > friction on cart
The cart will not move if pull on cart = friction on cart
Newton’s Third Law
Example 4: Motion of a rocket
Exhaust gases push
rocket up = THRUST
Rocket pulls earth
up
Earth pulls rocket
down
Engine pushes exhaust
gases down
Questions
• Do the questions on page 108
Hookes Law
When an elastic object - such as a spring - is stretched, the
increased length is called its extension. The extension of an
elastic object is directly proportional to the force applied to it:
𝑭 = 𝒌 ×𝒙
• F is the force in newtons, N
• k is the 'spring constant' in newtons per metre, N/m
• 𝑥 is the extension in metres, m
• This equation works as long as the elastic limit (the limit of
proportionality) is not exceeded. If a spring is stretched too
much, for example, it will not return to its original length
when the load is removed.
The spring constant
The spring constant k is different for different objects and
materials.
It is found by carrying out an experiment. For example,
the unloaded length of a spring is measured.
Assuming the limit of proportionality (elastic limit) is not
exceeded, a graph of force against extension produces a
straight line that passes through the origin.
The gradient of the line is the spring constant, k. The
greater the value of k, the stiffer the spring.
How are materials affected by
stretching?
• A spring (or length of wire) will stretch if
weight is added .
• The wire will stretch in proportion to the load
up to a certain point (the limit of
proportionality)
• What happens after this point?
Moments
• Moments make things turn or
rotate.
• A moment is the turning effect
of a force around a fixed point
called a pivot.
Moments
The size of a moment depends on two factors:
1. the size of the force applied
2. the perpendicular distance from the pivot to the line of
action of the force
Moments
SMALL MOMENT
The distance from the fulcrum to the
line of action of force is very small
LARGE MOMENT
The distance from the fulcrum to the
line of action of force is large
Moments
• M = the moment of the force in newtonmetres, Nm
• F = the force in newtons, N
• d = the perpendicular distance from the line of
action of the force to the pivot in metres, m
Worked example
A spanner is used to undo a nut. A force of 25 N
is applied to the end of the spanner, which is 10
cm away from the centre of the nut. Calculate
the moment when the spanner is horizontal.
Balancing moments
• Where an object is not turning around a pivot,
the total clockwise moment must be exactly
balanced by the total anti-clockwise moment.
sum of the clockwise moments = sum of the anti-clockwise moments
Are they balanced??
Levers
• A lever is a simple machine that makes work easier to do.
Examples of simple levers include cutting with scissors, or
lifting the lid on a tin of paint with a screwdriver.
• Levers reduce the force needed to perform these tasks.
• When someone uses a lever, they exert a force (the effort)
around a pivot to move an object (the load).
Levers
Practical: Verifying the Principle of
Moments
• Follow the instructions on pg 60 of your
textbook to verify the principle of moments
When a body is in equilibrium the sum of the
clockwise moments about any point equals the
sum of the anticlockwise moments about the
same point.
𝑭 𝟏 × 𝒅𝟏 = 𝑭 𝟐 × 𝒅𝟐
Questions
• Do the questions on pg 62
Centre of Mass
• Mass is the amount of matter an object has.
• Centre of Mass: This is the point at which any
object with mass will balance.
Finding the centre of mass of an
irregular object: plumb line
1.
Drill a small hole in the object and hang it
up so that it is free to swing without
obstruction.
2.
Hang a plumb line (a piece of string with a
weight hanging from it) from the same
suspension point. This lets you mark the
vertical line directly below the suspension
point.
3.
Drill another hole at a different location
within the object.
4.
Again hang a plumb line to determine the
vertical and mark it on.
5.
The point at which the two marked lines
cross is the centre of mass.
Toppling
• A body topples when the vertical line through
its centre of mass falls outside its base.
Which is more stable? Why?
What makes
objects
stable?
Toppling
The stability of a body is increased by:
1. Lowering its centre of mass.
2. Increasing the area of its base.
Motion in a curved path due to a
perpendicular force.
• Newton’s 1st law – an object with no resultant
forces acting on it will continue to move in a
straight line at constant velocity.
Motion in a curved path due to a
perpendicular force.
• If an object is moving in a circular path the
direction is always changing – but a force must
be present to create this change!
• If the direction is constantly changing then the
force must also be constantly changing.
Motion in a curved path due to a
perpendicular force.
• Centripetal force - the force that always acts
towards the centre of the circle.
• This force acts perpendicularly to the motion
of the object
Motion in a curved path due to a
perpendicular force.
Examples of circular motion:
1. The moon orbiting the earth
2. A car turning a corner
3. A train going around a bend
Motion in a curved path due to a
perpendicular force.
What would happen if the string that was
spinning an object around broke?
Questions
• Do questions 1, 3, 4 and 5 on page 67