Download 3.2.1 dynamics

Forces
There are essentially only three types of forces in the universe:
• gravitational
• electric
• nuclear
All forces are vectors.
They have an associated direction attributable to them as well as magnitude
(size)
e.g. weight is a force which acts towards the centre of the Earth
(scalars only have magnitude e.g. mass).
Adding and subtracting vectors is easy! consider the
following forces:
10 N
10 N
7N
OR
=
-7 N
17 N
3N
=
Note that these forces act through one point.
That is convenient for the moment and practical as it is often
true - the point is often the centre of gravity (mass), as
described earlier.
 The
resultant force calculated acting on a
given mass will cause it to accelerate.
 When mass is in kilograms and acceleration is
in m/s/s, the unit of force is in Newtons (N).
Definition - One Newton is equal to the force
required to accelerate one kilogram of mass at
one meter/second/second.
F = ma
 How
much force is needed to accelerate a
1400 kilogram car 2 ms-2
 Write the formula
F = m x a
 Fill in given numbers and units
 F = 1400 kg x 2 ms-2
 Solve for the unknown
 2800
kgms-2 or 2800
N
 1.
What acceleration will result when a 12
N net force applied to a 3 kg object? A 6
kg object?
 2.
A net force of 16 N causes a mass to
accelerate at a rate of 5 ms-2. Determine
the mass.
 3.
How much force is needed to
accelerate a 66 kg skier 1 m-2?
 4.
What is the force on a 1000 kg elevator
that is falling freely at 9.8 m-2?
• So what is gravity and what does it cause??
• These are two questions, the answers to which we
normally take for granted!
• Gravity is the force that pulls us towards the centre of
the Earth
• It causes our Weight
• So why is it different on different planets?
• They have different masses
• So do all objects have a gravitational pull?
• Yep! The difference is that the more “massive” an object
is the greater the pull of gravity.
• Therefore terrestrial objects do not exert a big enough
force to notice compared to that of the Earth!
Might help explain why you are not
attractive!!
So what is the link between the mass of an object and its
weight?
First the definitions.
The mass of an object is a measure of the amount of matter
contained in it.
Measured in Kg.
The weight is the force of gravity pulling a mass towards the
centre of the object causing the gravitational field.
Measured in N
So what is the link between Weight and Mass?
Try to measure the masses and weights as accurately as possible
and plot a graph of them.
If it is a straight line what is the gradient?
It should be the value for the gravitational field strength of 9.81 NKg-1
or acceleration due to gravity  g = 9.81 ms-2
We therefore get the relationship
Weight = mass * gravitational field strength
W = mg
Weight is a force measured in Newtons
Mass is measured in Kilograms
“g” is either in ms-2 OR Nkg-1
 Tension -
the force that is transmitted through a
string, rope, cable or wire when it is pulled tight
by forces acting from opposite ends. The tension
force is directed along the length of the wire and
pulls equally on the objects on the opposite ends
of the wire
 Normal contact force – is the component,
perpendicular to the surface of contact, by an
object. for example, the surface of a floor or wall,
preventing the object to fall.
 Upthrust
– the force that a fluid will exert
upward on a body if it is partly or wholly
submerged within it.
 Friction - refers to any force that resists
relative tangential motion (or intended
motion). Its direction is opposite the relative
velocity (or intended velocity).
 Free-body
diagrams are diagrams used to
show the relative magnitude and direction of
all forces acting upon an object in a given
situation. A free-body diagram is a special
example of a vector diagrams.
 The
size of the arrow in a free-body diagram
reflects the magnitude of the force.
 The direction of the arrow shows the
direction that the force is acting.
 Each force arrow in the diagram is labelled
to indicate the exact type of force.

http://www.physicsclassroom.com/Physics-Interactives/Newtons-Laws/Free-BodyDiagrams/Free-Body-Diagram-Interactive
Newton’s First Law of Motion
 Any
body will remain in it’s state of rest or
uniform motion in a straight line unless caused
by some external NET FORCE to act otherwise.
It essentially means that a body will do one of two
things:
· accelerate if you apply a force to it
· not accelerate if you don’t
Explain the motion of the following, refer to all the forces acting on the
object:
•a car going “flat out” at 120 kmh-1
No acceleration as balanced forces of drag
and weight reach equilibrium
•a parachutist hitting the ground at 200 kmh-1 without a parachute if he jumps from
2000m or 5000m
Has reached this equilibrium point - terminal velocity before he has fallen 2000m
•the rate of acceleration of car decreasing as it gets faster.
Engine produces a constant force - accelerates and so drag
increases. This decreases the net accelerating force
• In order to decide whether forces or velocity vectors
do cause a resultant in any given direction we need to
“add” them, taking into account their direction.
•How can we calculate the resultant?
• In all cases the Resultant is the “vector sum” of the
components…………WHAT!!!!!
For example, if you were swimming in a moving river,
what direction would you end up moving in and how
fast?
Again you can get a feel for this from your everyday
experience – USE THIS “FEEL” IN THE EXAM TO GAUGE
IF YOU ARE RIGHT!
There are two methods to solve this
1) Using Trigonometry and Pythagoras
2) Drawing a scale diagram and measuring the
size and direction of the resultant (but we don’t really
want to do this!)
1)
Trigonometry and Pythagoras
If a person can swim at 1.5 ms-1 in still water but the current of the stream
flows at 2 ms-1 at 90o to the swimmer. What is their speed and direction?
A person swims at
1.5 ms-1 in still
water
The RESULTANT is the
vector that joins the start
of one vector with the end
of the last one after
joining them as described!
The vectors should always be
drawn “nose to tail” as shown
on the left.
The
current
flows at
2 ms-1
1.5ms-1

Tan = 2 / 1.5
 = 53.10
2 ms-1
Using Pythagoras’ theorem
1.52 + 22 = 6.25
so R = 6.25 = 2.5ms-1
So the RESULTANT is the
person travelling at 2.5ms-1 in
a direction 53o from the
direction that the person was
swimming in.
Example
A body of mass 0.6kg falls vertically. A wind blows
horizontally with a force of 8N. What is the magnitude
and direction of the resultant force on the mass? (g=10
Nkg-1)
6N
Tan() = 6/8
R2 = 62 + 82
  = 37o
R2 = 36 + 64
R2 = 100
8N
R = 10N
Which angle on the diagram is measured though?!
These forces can be investigated using a force board where the forces are in
equilibrium and the angles indicated by the string and magnitude by the
weights suspended at the 3 points.
Resolving Vectors
If we want to know what the effect of a force is in a certain direction or if we are
to add vectors, we need to know what they are doing in specific directions. The
easiest to use are vertical and horizontal directions ie.
Tension in
the rope
Vertical
component
Horizontal
component
Resolve them vertically and
horizontally
Wind direction
Force produced by keel
Direction of boat
As you can see from the example above we can make a
triangle of forces from just about any situation.
If a force is not acting vertically or horizontally we can
consider it being made up of a vertical and horizontal force,
just as you can walk somewhere by going forwards,
backwards, left and right without moving diagonally!
Sideways pull
of rope on
barge
Forward
pull of
horse
Actual Pull
of horse
Show your working and annotate
the actions you are taking in these
questions!!
So how can we calculate the
components of a force at 90o
to each other?
If the Horse pulls with a force
of 750 N at an angle of 45o
What would be the forwards
force?
Diagonal
force
upwards eg
dragging a
sledge

If the force
needed to pull
this sled is 100 N
and you pull at
an angle of 25o
what are the
vertical and
horizontal
components of
this force?
If a husky pulls a sled at an angle of 10o to it’s line of travel,
what is the vertical component of the force and the horizontal
component if the dog pulls with a force of 700N.
If the sled and load weighs 100Kg what acceleration will the
dog cause the sled to have?
Discuss the following situations with the other members of your group.
Try to come up with specific and complete answers. ("Gravity", for
instance, is not a complete answer.) Each individual in the group should
record their own answer.
Situation: A book is lying at rest on a table. Why? In other words, what
causes the book (or any object) to remain at rest?
Situation: The Voyager spacecraft is moving out of the Solar System in a
straight line with constant speed. Why is it doing that? What causes an
object to move with constant velocity?
Situation: A pencil rolls off the desk and falls to the floor. Why does it
move the way it does? We know a lot about this motion (free fall) - but
what causes it to happen? Why do objects accelerate?
Situation: A book sliding across a table gradually comes to a stop. Why?
What causes a moving object to gradually come to a stop?
 Practical
4.4 – Drag and TV