Download 3.5.1 newtons laws

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
Using your knowledge of balanced forces draw on the
size of forces and direction to simplified diagrams of
these people travelling at constant velocity. Remember
the size of the arrow indicates the size of the force.
Objects in Equilibrium
Decide for yourself what would happen to these
objects!
In all cases there is no
resultant force so the balls
stay in place!
• 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.
• We have done this since Year 7 with Forces acting
along the same line of action, even in 2 or 3D.
• However the previous slide showed 3 forces at totally
different angles. How, apart from the general feeling,
can we prove they cancel each other out?
• 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.
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
Using Pythagoras’ theorem
1.52 + 22 = 6.25
so R = 6.25 = 2.5ms-1
2 ms-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.
How do you add vectors if they are not in the
same line of action or at 90o ?
This is best achieved at A level by drawing
2) A scale diagram and measure the angle between the
vectors accurately. Make sure you specify the direction of the angle
eg from the horizontal, vertical or one of the vectors
This method is known as the parallelogram law as the two forces make
up 2 sides of the parallelogram allowing us to measure the size of the
resultant!
RESULTANT R =
A+B
A
B
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?!
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
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?
The rate of change of momentum is directly
proportional to the resultant force acting on an
object and takes place in the direction of the
resultant force.
..and we therefore get the maths bit!!!
Force = Change in Momentum/Time Taken
Force = (Final Momentum – Initial Momentum)
Time Taken
Force = (mv – mu)/t = m(v-u)/t
F = ma
F = kma is used to define the Newton and so k=1.
Therefore a Force of 1N applied to a 1Kg mass, causes
it to accelerate at 1ms-2.
So …
F = ma
Note that this is not Newton’s second law.
F  dp/dt is!
Impulse
Generally we say that impulse is the product of the applied force and the
time over which it is acting or the change in momentum
Impulse = Ft = p
Considering a car crash we all know how violent they are but how can we
make them safer for the passengers?
If the impact is made to last longer by slowly crushing the car the impulse
will be less. In other words the impact will be less violent and therefore
less damaging to the frail humans inside the car.
Unfortunately the car will be smashed! Look at the simulations on
multimedia motion looking at the graphs of car crashes, tennis balls being
hit and air track collisions.
If we consider catching a cricket
ball we all know there good ways
and bad. You can really smack your
hand or not. What is the difference
– the impulse!!
Which catch would hurt your
hands the most is the balls were all
traveling at the same speed??
If a ball hits a wall we can say the average force that the
ball exerts on the wall is F1.
According to Newton’s Third Law there should be an
equal and opposite force exerted on the ball F2
Wall
F2
F1
So
Wall
F1 = - F2
If the force acts for a short period
of time t then
F2
F1 t = - F2 t
F1
Newton’s second law tells us that F= p/t
And so p = F1t
This implies that the units of IMPULSE are the same as
MOMENTUM. Using your training in Base units and Quantities
you should be able to prove that
Ns = Kgms-1
Force
The impulse can also be calculated from the
area under a force time graph.
Time
Questions
1. A ball has a mass of 150g and is travelling at 20ms-1.
It is caught and brought to rest in 75ms.
What is the average force on the ball which brings it to rest?
1.
F t =  p
F x 75X10-3 = 20x0.150
F = 20x0.150 / 75X10-3
F = 20x0.002x103
F = 40N
2.Over what distance did the force act?
Work Done = Force * distance
In this case the work done is in slowing the ball down
to zero velocity so Work done = ½ mv2
½ mv2 = F*d
0.5*0.150*202 = 40*d
d = 0.075*400/40
d = 0.75m
Remember the discussion about catching cricket balls and
how to avoid hurting your hand!
The following graph represent the force acting on a
floor as a ball bounces on it.
The ball changes direction because the force on
the floor changes direction - Newton’s third law
will show that this force acts on the ball too in
the opposite direction.
Force
Time
Explain what you can deduce about the motion of the ball
and why.
The change of momentum as it speeds up
(second part of graph) is less that than the
change in the first part. This means the ball
leaves
the floor travelling more slowly than
it hit the floor.
Force
Time
The area under the
second part is less than
the area in the first part.
(area = impulse = p)
 For
every action there is an equal and opposite
reaction
A moving object can have a number of forces acting
on it and yet doesn’t change it’s motion – Newton’s
first law – as long as the forces are balanced.
Reaction
Drag
Thrust
Weight
In this case you can imagine that the cyclist carries on
moving at the same speed as the forces are all equal and
opposite.
However what happens if you try to push an object?
If the car handbrake is on the
woman will be pushing as hard as
she can and yet the car won’t
move it must therefore be pushing
her back with an equal force!
Most people have tried
to jump out of a dinghy
or something on water.
What happens and why?
When the person tries to
jump they have to exert a
force on the boat which
pushes the boat backwards,
the boat exerts a force on
them pushing them forwards.
If this was not the case then
the person couldn’t jump
forwards!! The boat
accelerates backwards and
the person accelerates
forwards.
This animation should highlight the fact that … … …
Forces always come in pairs
and leads us to Newton’s first law
 https://www.youtube.com/watch?v=Xx9kiF0
0rts
 https://www.youtube.com/watch?v=cP0Bb3
WXJ_k
Whenever a an object exerts a force on another object an
equal but oppositely directed force of the same type acts
on the first object.
In other words… … …
For every force there is an equal
and opposite force.
Whenever a force acts on a body an equal but oppositely
directed force of the same type acts on a different body.
Statement
Meaning
Example
“Equal”
They have the same
magnitude or size
10 N and 10 N
“opposite
direction”
They act in opposite
directions
Left and Right or Up and Down
etc.
They act through the same
point so no turning effect
(Moment) is experienced
Same line of action
NOT
“Same type” The force on one body will
be of the same type as the
force on the other
“acts on
different
bodies”
The forces that act on each
of the object come from a
different object.
As this would cause the block
to spin!
If one is magnetic the other
one will be too!
Eg. Magnetic forces on two
magnets, forces come from
each magnet.
Pairs of forces obeying Newton’s first law don’t necessarily
obey his third!
Why not??
If a body is in
equilibrium
A person
standing
on the
floor.
Normal reaction
• all forces acting on it
will sum to zero and
• act through the
same point.
Weight
This, however, is NOT a Newton Pair
The man pulls the Earth up with
a gravitational force of 800 N
In Newton pairs there
are several key ideas:
• Same line of action
• Acting for the same
period of time
• Same type of force
Weight
Pull of man on Earth
The Earth pulls the man
down with a gravitational
force of 800 N
You should notice the
two statements are
identical except for the
swapping of the objects
causing and feeling the
forces!
In summary
• They occur in pairs
• Are the same in type
• Equal in magnitude
• Act in the opposite
directions
• But in the same line of
action
• They act on different bodies
 Factsheet
12
 Laws of Motion Support
 Calculation sheet 7.2
 Practical 7.2 – Investigating Collisions
 Practical 7.3 – Newton II