Download Physics: Understanding Motion

Physics: Understanding
Motion
Year 10 Core Science 2012
What do we need to learn?
How do we convert units?
What do these terms mean?
Distance, displacement, vector, scalar,
speed, velocity, acceleration, force and
momentum
How can we describe and analyse
motion?
What do we need to learn?
How are changes in movement caused
by the actions of forces?
What are Newton’s 3 laws of motion?
How do we explain and apply them to the
real world?
What is momentum and how does it
apply to real life situations?
There’s lots to learn…
What’s going to help us?
Asking lots of
Questions
Conducting
experiments
Drawing graphs
Applying the theory to
real life situations
1.0 An Ideal World
To make life easier for
Physics students,
situations or events
which require
mathematical analysis
are often described as
occuring in an ideal,
frictionless world.
In the ideal world an object under
the influence of Earth’s gravity will
accelerate at 9.8 ms-2 throughout its
journey never reaching a terminal
velocity.
In the ideal world the
laws of motion apply
exactly, eg. objects
which are moving will
continue to move with
the same speed unless
or until something
occurs to change this.
In the ideal world energy
transformations are always
100% efficient, so that the
potential energy of a
pendulum at the top of its
swing is all converted to
Kinetic Energy (motion
energy) at the bottom.
In the ideal world perpetual motion
machines are common place.
Physics language
Some units we will be using.
Quantity (Unit)
Fundamental Units
Force (Newton)
Mass (kg), length (m), time (s)
Acceleration (ms-2)
Length (m), time (s)
Momentum (kgms-1)
Mass (kg), length (m), time (s)
Velocity (ms-1)
Mass (kg), length (m), time (s)
Work (Joule)
Note: W = F.d
Length (m), time (s)
Standard International units are: meter, kilogram, second, ampere
Why do we need standard units?
When things go wrong…
Why do we need standard units?
It is important that scientists can share their data and findings.
To do this, they use a common set of units. The SI unit for both
distance and displacement is the metre (m) and the SI unit for
speed is metres per second (m/s).
You may have seen ‘metres per second’ also written as ‘ms−1’.
This expression is derived from the rule for calculating speed:
Speed
=
distance =
time taken
metres
seconds
When shifting the ‘seconds’ from the denominator to the
numerator of the fraction, the index (or power) becomes
negative. Hence, the seconds are written with an index of −1 in
ms−1 (we’ll learn more about this later…)
What’s the difference?
Scalars have magnitude
(size) only
Vectors have magnitude
and direction.
Eg distance traveled is
300meters
Eg distance traveled is
300m north
Other scalar quantities:
Shown by a
Speed, mass, time, temp,
energy
Line showing
magnitude
arrow showing
direction
Motion in motion
What is the relationship between
100
and
27.78
To change units from m/s
to km/h
X 3.6
100km/h
27.78
÷ 3.6
m/s
Convert the following
1. 40km/h to m/s
2. 60km/h to m/s
3. 80km/h to m/s
4. 100km/h to m/s
5. 110km/h to m/s
6. 1m/s to km/h
7. 10m/s to km/h
8. 12m/s to km/h
9. 60m/s to km/h
10.15m/s to km/h
Convert the following
1. 40km/h = 11.11m/s
2. 60km/h = 16.67m/s
3. 80km/h = 22.22m/s
4. 100km/h = 27.78m/s
5. 110km/h = 30.56m/s
6. 1m/s = 3.6km/h
7. 10m/s = 36km/h
8. 12m/s = 43.2km/h
9. 60m/s = 216km/h
10.15m/s = 54km/h
Fundamental skills
Show that 1 ms-1 = 3.6 kmh-1
Two relevant conversion factors are: 1 km = 1000 m, 1 h = 3600 s
These can be written as: 1km
or
1000m
1000m
and
1km
1h
or
3600 s
3600s
1h
Which ones to use ?
Easy, you want to end up with km on the top line and h on the bottom
1m x 1km x
s
1000m
3.6
3600s
1h
so 1 ms-1 = 3.6 kmh-1
Who are these men?
Who are these men?
Who are these men?
So who is faster?
Did Usain Bolt run the 100m faster than
Michael Johnson ran the 400m?
Calculate the speed of the two men.
Speed (m/s)= distance (m) ÷ time taken (sec)
World records
100m- Usain Bolt
400m Michael Johnson
9.58 seconds
43.18 seconds
How many meters per
second? 10.44 m/s
How many meters per
second? 9.26 m/s
How many km per
hour? 37.59 km/h
So the faster runner was…
How many km per
hour? 33.34km/h
Usain Bolt
Motion
Aim:
To convert:
meters per second (m/s or ms-1)
to
kilometers per hour (km/h or kmh-1)
using a formula
World records
Distance
Time
100m
9.58
400m
43.18
1km
2:12
2km
4:45
20km
55:48
Distance
in meters
Time in
seconds
m/s
km/hr
World records
Distance
Time
100m
9.58
Distance
in meters
100
Time in
seconds
9.58s
m/s
km/hr
10.44
37.58
400m
43.18
400
43.18s
9.26
33.34
1km
2:12
1000
132.96s
7.52
27.07
2km
4:45
2000
284.79s
7.02
25.28
20km
55:48
20000
3348s
5.97
21.51
Converting units
Position & Displacement
In order to specify the position of an object we first need to
define an ORIGIN or starting point from which measurements
can be taken.
For example, on the number line, the point 0 is taken as the
origin and all measurements are related to that point.
-40 -35 -30 -25 -20 -15 -10 -5
0
5
10
15 20 25 30 35 40
Numbers to the right of zero are labelled positive
Numbers to the left of zero are labelled negative
A number 40 is 40 units to the right of 0
A number -25 is 25 units to the left of 0
Position Questions
1. What needs to be defined before the position of any object can be
specified ?
A zero point needs to be defined before the position of an object can be
defined
2. (a) What distance has been covered when an object moves from
position +150 m to position + 275 m ?
Change in position = final position – initial position
= +275 – (+150) = + 125 m. Just writing 125 m is OK
(b) What distance has been covered when an object moves from
position + 10 m to position -133.5 m ?
Change in position = final position – initial position
= -133.5 – (+10) = - 143.5 m. Negative sign IS required
Distance & Displacement
Distance is a
measure of length
travelled by an
object. It has a
Unit (metres).
Displacement is the
shortest possible
length between the
start and finish of the
travelling object.
Distance is best
defined as “How far
you have travelled in
your journey”
Displacement is best
defined as “How far
from your starting
point you are at the
end of your journey”
Distance & Displacement
Distance is a scalar
measurement.
Remember:
Scalar
measurements are
expressed only as a
size, with no
direction.
Displacement is a
vector
measurement.
Remember:
Vector
measurements are
expressed as a size
and a direction
Distance & Displacement
The difference between distance &
displacement is easily illustrated with a simple
example. You are sent on a message from
home to tell the butcher his meat is off.
Positive Direction
2 km
At this point in the journey, Distance travelled = 2km and Displacement = + 2km
At the end of the journey, Distance travelled = 2 + 2 = 4km
while Displacement = +2 + (-2) = 0 km
Let’s see if this
makes sense…
Lets read through
pages 262-263 and
attempt some
questions
Let’s recall distance and
displacement…
Distance
Is how far on object has traveled, from
point A to point B.
Distance has only magnitude (scalar)
Eg the distance traveled by the runner
was 9km
Displacement
Is the change in position or the shortest
distance between two points.
Displacement has a magnitude and
direction (vector)
Eg the runner ran 6km to the right and
3km down, (displacement 6.7km south
east)
How far did the person
travel?
start
6km
3km
Distance: 6 + 3 = 9km
Displacement: 6.7km south east
finish
Let’s visualise the
difference…
Speed and Velocity
So what’s the difference?
Speed & Velocity
These two terms are used interchangeably
in the community but strictly speaking they
are different:
Speed is the time
rate of change of
distance, i.e.,
Speed = Distance
Time
Velocity is the time rate of
change of displacement,
i.e.,
Velocity = Displacement
Time
Speed & Velocity
Speed is a SCALAR
QUANTITY, having a
unit (ms-1), but no
direction.
Thus a speed would
be:
100 kmh-1 or,
27 ms-1
Velocity is a VECTOR
QUANTITY, having a
unit (ms-1) AND a
direction.
Thus a velocity would
be:
100 kmh-1 South or
- 27 ms-1
Instantaneous & Average Velocity
The term velocity can be misleading,
depending upon whether you are
concerned with an Instantaneous or an
Average value.
The best way to illustrate the
difference between the two is
with an example.
You take a car journey out of a city to
your gran’s place in a country town 90
km away. The journey takes you a
total of 2 hours.
The average velocity for this journey,
vAV = Total Displacement = 90 = 45 kmh-1
Total Time
2
Questions
Instantaneous & Average Velocity
Recall:
The average velocity for this journey,
vAV = Total Displacement = 90 = 45 kmh-1
Total Time
2
However, your instantaneous velocity measured at a
particular time during the journey would have varied between
0 kmh-1 when stopped at traffic lights, to, say 120 kmh-1 when
speeding along the freeway.
Average and Instantaneous velocities are rarely the same.
Unless otherwise stated, all the problems you do in this
section of the course require you to use Instantaneous
Velocities.
Questions
Speed and Velocity
Average speed- total distance by the total time
Average Speed =
total distance traveled (m)
Total time taken (s)
Velocity- is the displacement by the time taken
Velocity
=
displacement (m)
time taken (s)
Speed vs. Velocity
Speed is simply how fast you are travelling…
This car is travelling at a speed of
20m/s-1
Velocity is “speed in a given direction”…
This car is travelling at a velocity of
20m/s-1 east
Quick questions
A female runner completes a 400 m race (once around the track)
in 21 seconds what is:
(a)Her distance travelled (in km),
(b) her displacement (in km),
(c) her speed (in ms-1) and
(d) her velocity (in ms-1) ?
(a) Distance = 0.4 km
(b) Displacement = 0 km
(c) Speed = distance/time = 400/21 = 19ms-1
(d) Velocity = displacement/time = 0/21 = 0 ms-1
6km
The runner takes half
and hour to finish
start
3km
Distance= 9km
Displacement= 6km

Speed= 18km/hr
Velocity= 12km/hr

finish
Motion prac
Let’s collect some data. . . .
Motion by Graphs
Distance
(a)
Describe how the
object moving?
Time
Displacement
(b)
Time
Graphical Relationships
Graphs are used to help
give us an image of
movement of an object
Graphs “tell you a story”.
There are two basic types of
graphs used in Physics:
You need to develop the
skills and abilities to “read (a)Sketch Graphs – give a “broad
brush” picture or show the
the story”.
“trend”.
(b) Numerical Graphs – give the
exact relationship between the
two variables graphed and may
be used to calculate other
values.
Sketch Graphs
Sketch graphs have labelled axes but no numerical values,
they show a “trend” between the quantities.
Velocity
Distance
Displacement
Time
The Story:
The
Story:
The
object
begins its journey
The
The
Story:
Story:
As
time
passes
itsthe
at
the
origin
at
t = 0.the
As
time
As
As
time
time
passes
passes,
passes
its displacement
displacement
gets
larger
velocity
distance
remains
of
the
object
increases at a constant rate
atfrom
an isincreasing
rate.
constant.
its
starting
(slope
constant).
So point
time
This
is
the
graph
of
rate
ofischange
of displacement
This
does
anot
graph
change.
of anan
which
equals
velocity
is
object
moving
with
object
This
travelling
is
the
graph
at
of a
constant.
constant
acceleration
constant
stationary
velocity
object
This
is a graph
of an object
travelling at constant velocity
Sketch Graphs
Distance
(a)
Time
Displacement
(b)
Time
Distance versus time graph.
As time passes
displacement remains the
same. This is the graph of a
stationary object
Displacement versus time
graph. As time passes its
displacement is increasing in
a uniform manner. This is a
graph of an object travelling
at constant velocity.
Sketch Graphs
(c)
Velocity versus time graph. As
time passes the velocity of the
object remains the same. This is
a graph of an object travelling
at constant velocity.
Velocity
Time
(d)
Displacement
Time
Displacement versus time graph.
As time passes its displacement
gets larger at an increasing rate.
This is a graph of an accelerating
object.
What a graph can tell you.
The graphs you are required to interpret mathematically are those where
distance or displacement, speed or velocity or acceleration are plotted
against time.
The information available from these graphs are summarised in the
table given below.
Graph Type
Read directly
from the graph
Obtained from
slope of graph
Obtained from
area under the
graph
Distance or
Displacement Vs
Time
Distance or
displacement
Speed or velocity
No useful
information
Acceleration
Distance or
displacement
Speed or Velocity
Speed or velocity
Vs Time
Displacement-time graphs
2) Horizontal line =
4) Diagonal line downwards =
Remaining stationary
Returning to the starting position
40
Distance
30
(metres)
20
10
Time/s
0
20
1)
Diagonal line =
Moving forwards
40
60
80
100
3) Steeper diagonal line =
Moving forwards faster
40
Distance
(metres)
30
20
10
0
20
40
60
80
100 Time/s
1) What is the speed during the first 20 seconds? Distance/time = 0.5 ms-1
2) How far is the object from the start after 60 seconds?
Read from
40 m
graph
3) What is the speed during the last 40 seconds?
4) When was the object travelling the fastest?
Distance/time = 1 ms-1
Between 40 & 60 seconds at 1.5 ms-1
Acceleration
Acceleration is defined as the time rate of
change of velocity, i.e.,
Acceleration = Change in velocity
Time
a = ΔV
t
= Vf - Vi
t
Acceleration has units of (ms-2)
Acceleration simply means how
much an object is speeding up
by every second
Acceleration means an
increase in velocity over time,
while Deceleration means a
decrease in velocity over time.
v
a
When v and a are in the same direction,
the car accelerates and its velocity will
increase over time.
a
v
When v and a are in the opposite
direction, the car decelerates and its
velocity will decrease over time.
Acceleration
For example
If an object has an acceleration
of 2ms-2, this means that an
object will increase its speed by
2ms-1 every second
v
a
If a= 2ms-2 and its initial speed is
10ms-1 then
t=0
t=1
t=2
v = 10ms-1
v = 12ms-1
v = 14ms-1
v
a
If a = -2ms-2 and its initial speed is 20ms-1,
then
t=0
t=1
t=2
v = 20ms-1
v = 18ms-1
v = 16ms-1
Acceleration
A roller coaster, at the end of its journey, changes it’s velocity from 36
ms-1 to 0 ms-1 in 2.5 sec. Calculate the roller coaster’s acceleration.
a=
=


V
t
0  36
2.5
= - 14.4 ms-2
Practice Acceleration questions
Acceleration =
change in velocity (in m/s)
(in m/s2)
time taken (in s)
1) A cyclist accelerates from 0 to 10m/s in 5 seconds.
What is her acceleration? 2 ms-2
2) A ball is dropped and accelerates downwards at a rate
of 10m/s2 for 12 seconds. How much will the ball’s
velocity increase by? 120 ms-1
3) A car accelerates from 10 to 20m/s with an acceleration
5s
of 2m/s2. How long did this take?
4) A rocket accelerates from 1,000m/s to 5,000m/s in 2
seconds. What is its acceleration? 2000 ms-2
Velocity-time graphs
1) Upwards line =
4) Downward line =
6
0
Velocity
40
m/s
20
0
2) Horizontal line =
10
20
30
40
3) Upwards line =
50
T/s
80
Velocity
m/s
60
40
20
0
10
20
30
40
1) How fast was the object going after 10 seconds?
2) What is the acceleration from 20 to 30 seconds?
3) What was the deceleration from 30 to 50s?
4) How far did the object travel altogether?
50 Time/s
Graphical Interpretation
1) Given below is the Distance vs Time graph for a cyclist riding along a straight
path.
(a) In which section (A,B,C or D) is the
Distance
cyclist stationary ?
A
B
C
D
(b) In which section is the cyclist
travelling at her slowest (but not zero)
20
speed ?
(c) What is her speed in part (b) above
?
10
(d) What distance did she cover in the
first 40 seconds of her journey ?
(e) In which section(s) of the graph is
Time (s)
her speed the greatest ?
0
(f) What is her displacement from her
20 30 40 50 60
10
starting point at t = 50 sec ?
(a) Stationary in section C
(b) Section B
(c) Travels 10 m in 20 s  speed = 10/20 = 0.5 ms-1
(d) 20 m (read directly from graph)
(e) Section D (travels 20 m in 10 s) speed = 2 ms-1
(f) Displacement at t = 50 s is 0 m (i.e., back at starting point)
Graphical Interpretation
Velocity
2) Shown below is the Velocity vs Time
graph for a motorist travelling along a
straight section of road.
(ms-1)
10
8
6
4
Time(s)
2
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
-2
-4
-6
-8
-10
(a) Displacement = area under velocity time graph.
Between t = 0 and t = 4 s. Area = ½ (10 x 4) = 20 m
(b) Acceleration = slope of velocity time graph
= (10 – 0)/(4 – 0) = 2.5 ms-2
(c) Distance = area under graph (disregarding signs)
Total area = ½(10 x 4) + (6 x 10) + ½(10 x 2) + ½(9 x
2) + (6 x 9) = 20 + 60 + 10 + 9 + 54 = 153 m
(d) Displacement = area under graph (taking signs into
account) = ½(10 x 4) + (6 x 10) + ½(10 x 2) - ½(9 x 2)
- (6 x 9) = 20 + 60 + 10 - 9 – 54 = 27 m
(a) What is the motorist's
displacement after 4.0 sec ?
(b) What is the motorists
acceleration during this 4.0 sec
period ?
(c) What distance has the
motorist covered in the 20.0 sec
of his journey ?
(d) What is the motorist's
displacement at t = 20.0 sec
(e) What happens to the
motorists velocity at t = 20.0
sec? Is this realistic ?
(f) Sketch an acceleration vs
time graph for this journey.
Graphical Interpretation
3) An object is fired vertically upward on a DISTANT PLANET. Shown below is the
Velocity vs Time graph for the object. The time commences the instant the object
leaves the launcher
(a) What is the acceleration of
Velocity (ms-1)
the object ?
30
(b) What is the maximum height
attained by the object ?
(c) How long does the object take
to stop ?
Time (s) (d) How far above the ground is
0
2
4
6
8
10
12
the object at time t = 10.0 sec ?
-30
(a) Acceleration = slope of velocity time graph.
Slope = (30 – 0)/(0 – 6) = -5.0 ms-2
(b) Displacement = area under velocity time graph = ½ (6 x 30) = 90 m
(c) Stops at t = 6.0 sec
(d) The rocket has risen to a height of 90 m in 6 sec. It then falls a distance of ½ (4
x 20) = 40 m, so it will be 90 – 40 = 50 m above the ground at t = 10 s
Measuring Acceleration with a ticker timer
Forced Change
What is a Force ?
"A force is an interaction between two material
objects involving a push or a pull."
How is this different from the usual textbook
definition of a Force simply being a “push or a pull” ?
First, a force is an "interaction".
You can compare a force to another common
interaction - a conversation.
How is Force like a Conversation?
A conversation is an interaction between 2 people
involving the exchange of words (and ideas).
Some things to notice about a conversation (or any
interaction) are:
To have a conversation, you need two people. One
person can't have a conversation
A conversation is something that happens between
two people.
It is not an independently existing "thing" (object),
in the sense that a chair is an independently existing
"thing".
How is Force like a Conversation?
Forces are like conversations in that:
To have a force, you have to have 2 objects - one
object pushes, the other gets pushed.
In the definition, "(material) objects" means that
both objects have to be made out of matter - atoms
and molecules. They both have to be "things", in the
sense that a chair is a "thing".
A force is something that happens between 2
objects. It is not an independently existing "thing"
(object) in the sense that a chair is an independently
existing "thing".
Force Questions
1. A force is an interaction between 2 objects. Therefore
a force can be likened to
A: Loving chocolate
B: Fear of flying
C: Hatred of cigarettes
D: Having an argument with your partner
2. Between which pair can a force NOT exist ?
A: A book and a table
B: A person and a ghost
C: A bicycle and a footpath
D: A bug and a windscreen
What Kinds of Forces Exist ?
For simplicity sake, all forces (interactions) between
objects can be placed into two broad categories:
1. Contact forces are types of forces in
which the two interacting objects are
physically contacting each other.
Examples of contact forces include
frictional forces, tensional forces,
normal forces, air resistance forces, and
applied forces.
2. Field Forces are forces in which the two interacting
objects are not in contact with each other, yet are able
to exert a push or pull despite a physical separation.
Examples of field forces include Gravitational Forces,
Electrostatic Forces and Magnetic Forces
What Kinds of Forces Exist ?
Force is a quantity which is measured
using the derived metric unit known
as the Newton.
One Newton (N) is the amount of
force required to give a 1 kg mass an
acceleration of 1 ms-2.
So 1N = 1 kgms-2
Force is a vector quantity, you must describe both
the magnitude (size) and the direction.
Contact or Field Forces
1. Classify the following as examples of either Contact or Field forces in action (or
maybe both acting at the same time).
EXAMPLE
(a) A punch in the nose
(b) A parachutist free falling
(c) Bouncing a ball on the ground
CONTACT
FORCE
FIELD FORCE
√
√
√
√
(d) A magnet attracting a nail
√
(e) Two positive charges repelling each other
√
(f) Friction when dragging a refrigerator across the
floor
(g) A shotput after leaving the thrower’s hand
√
√
√
What Do Forces Do ?
BEGINNING MOTION:
A constant force (in the same direction as
the motion) produces an ever increasing
velocity.
Forces affect motion. They can:
• Begin motion
• Change motion
• Stop motion
• Have no effect
FR
NO EFFECT:
A total applied
force smaller
than friction will
not move the
mass
CHANGING MOTION:
A constant force (at right angles to the motion)
produces an ever changing direction of velocity.
STOPPING MOTION:
A constant force (in the opposite
direction to the motion) produces an
ever decreasing velocity.
Net Force
1. A body is at rest. Does this necessarily mean that it has no force acting on it ?
Justify your answer.
NO – A body will remain at rest if the NET FORCE acting is zero – it could have any
number of forces acting on it. So long as these forces add to zero it will remain at
rest.
2. Calculate the net force acting on the object in each of the situations shown.
(a)
(b)
900 N
1200 N N
300 N Left
75 N
95 N
20 N Left
(c)
250 N
0N
250 N
(d)
300 N Down
150 N
450 N
Mass V’s Weight
What’s the difference?
Mass
Mass is the matter that makes up an object
Weight
Weight is the outcome of a gravitational field acting on a mass
Weight is a FORCE and is measured in Newtons.
Its direction is along the line joining the centres of the two bodies which,
between them, generate the Gravitational Field.
1 kg
9.8 N
Near the surface of the Earth, each kilogram of mass is
attracted toward the centre of the earth by a force of 9.8 N.
(Of course each kilogram of Earth is also attracted to the
mass by the same force, Newton 3)
So, the Gravitational Field Strength near the Earth’s surface =
9.8 Nkg-1
Weight and mass are NOT the same, but they are
related through the formula:
W = mg
Where:
W = Weight (N)
m = mass (kg)
g = Grav. Field
Strength (Nkg-1)
1 kg
Weight vs Mass
Earth’s Gravitational Field Strength is 10N/kg. In other words, a 1kg mass is pulled
downwards by a force of 10N.
W
Weight = Mass x Gravitational Field Strength
(in N)
(in kg)
(in N/kg)
M
1)
g
What is the weight on Earth of a book with mass 2kg?
2) What is the weight on Earth of an apple with mass 100g?
3) Dave weighs 700N. What is his mass?
4) On the moon the gravitational field strength is 1.6N/kg. What will Dave weigh if
he stands on the moon?
Mass & Weight
Fill in the blank spaces in the table based on a persons mass of 56kg on earth.
Planet
Mass on planet
(kg)
Grav Field Strength
(Nkg-1)
Weight on planet
(N)
Earth
56
9.81
549.4
Mercury
56
0.36
20.2
Venus
56
0.88
20.2
Jupiter
56
26.04
1458.2
Saturn
56
11.19
626.6
Uranus
56
10.49
587.4
Your Mass & Weight
Fill in the blank spaces in the table based on your mass on earth.
Planet
Mass on planet
(kg)
Grav Field Strength
(Nkg-1)
Earth
9.81
Mercury
0.36
Venus
0.88
Jupiter
26.04
Saturn
11.19
Uranus
10.49
Weight on planet
(N)
Newton’s Laws of
Motion
Newton’s Laws
Newton developed 3 laws which cover all aspects of
motion (provided objects travel at speeds are well
below the speed of light).
Law 1 (The Law of Inertia)
A body will remain at rest, or in a state of uniform
motion, unless acted upon by a net external force.
Law 2
The acceleration of a body is directly proportional to net
force applied and inversely proportional to its mass.
Mathematically, a = F/m more commonly written as F = ma
Law 3 (Action Reaction Law)
For every action there is an equal and opposite reaction.
Newton, at age
26
Motion at or near the speed of light
is explained by Albert Einstein’s Theory of
Special Relativity.
Newton’s
Objects want
to keep on
doing what
they are doing
st
1
Newton’s 1st Law states:
A body will remain at rest, or in
a state of uniform motion,
unless acted upon by a net
external force.
Another way of saying this is:
Law
If NO net external force exists
No Net Force
means No
Acceleration
There is no experiment that
can be performed in an
isolated windowless room
which can show whether the
room is stationary or moving at
constant velocity.
Newton 1 deals with non
accelerated motion.
It does not distinguish
between the states of
“rest” and “uniform
Most importantly:
It requires an
motion” (constant
unbalanced force
Force is NOT needed to
velocity).
to change the
keep
an
object
in
motion
velocity of an
As far as the law is
object
concerned these are the
same thing (state).
Is this how you understand the world works ?
Newton’s
Newton’s 2nd Law states:
The acceleration of an object as
produced by a net force is directly
proportional to the magnitude of
the net force FNET, in the same
direction as the net force, and
inversely proportional to the mass
of the object.
Mathematically, a = FNET/m more
commonly written as FNET = ma
nd
2
Law
Using the
formula
FNET
= ma is only
valid for
situations
where the mass
remains
constant
Newton actually expressed his 2nd law in
terms of momentum.
The Net Force on
Newton 2 deals with accelerated
an object equals
motion.
the rate of change
of its momentum
FNET is the VECTOR SUM
of all the forces acting on
an object.
Momentum (p) = mass x velocity
The acceleration and FNET
are ALWAYS in the same
So, FNET = change in momentum = Δp = mΔv = ma
direction.
change in time
Δt Δt
Force and acceleration
If the forces acting on an object are unbalanced
then the object will accelerate, like these
wrestlers:
Force (in N) = Mass (in kg) x Acceleration (in m/s2)
F
M
A
Force, mass and acceleration
1)
A force of 1000N is applied to push a mass of
500kg. How quickly does it accelerate?
F
2) A force of 3000N acts on a car to make it
accelerate by 1.5m/s2. How heavy is the car?
3) A car accelerates at a rate of 5m/s2. If it weighs
500kg how much driving force is the engine
applying?
4) A force of 10N is applied by a boy while lifting a
20kg mass. How much does it accelerate by?
M
A
Newton’s
nd
2
Law
Unbalanced force or Net force causes
Terminal Velocity
Consider a skydiver:
1)
At the start of his jump the air
resistance is _______ so he _______
downwards.
2) As his speed increases his air resistance
will _______
3) Eventually the air resistance will be big
enough to _______ the skydiver’s
weight. At this point the forces are
balanced so his speed becomes
________ - this is called TERMINAL
VELOCITY
Terminal Velocity
Consider a skydiver:
4) When he opens his parachute the air
resistance suddenly ________, causing
him to start _____ ____.
5) Because he is slowing down his air
resistance will _______ again until it
balances his _________. The skydiver
has now reached a new, lower
________ _______.
Velocity-time graph for terminal velocity…
Parachute opens – diver
slows down
Velocity
Speed
increases…
Terminal
velocity
reached…
Time
New, lower terminal velocity
reached
Diver hits the ground
Newton’s
Newton's 1st and 2nd Laws tell you what
forces do.
Newton's 3rd Law tells you what forces
are.
For every action
there is an equal
and opposite
reaction
rd
3
Law
2. People associate action/reaction
with "first an action, then a reaction”
For example, first Suzie
annoys Johnnie (action) then
Johnny says "Mommy! Suzie’s
annoying me!" (reaction).
This is NOT an example what
is going on here!
The action and reaction forces
exist at the same time.
This statement is correct, but
terse and confusing. You
need to understand that it
means:
"action...reaction" means that
"equal" means :
forces always occur in pairs.
Both forces are equal in magnitude.
Single, isolated forces never
Both forces exist at exactly the same time.
happen.
They both start at exactly the same instant, and
"action " and "reaction " are
they both stop at exactly the same instant.
unfortunate names for a
They are equal in time.
couple of reasons :
1. Either force in an interaction can be "opposite" means that the two forces
the "action" force or the "reaction"
always act in opposite directions - exactly
force.
180o apart.
Questions
Friction is a Force
Force on box
by person
Force on floor by box
Force on person
by box
Force on box
by floor
It’s the sum of all the forces that determines the acceleration.
Every force has an equal & opposite partner.
89
Spring 2008
Friction Mechanism
Corrugations in the surfaces grind when things slide.
Lubricants fill in the gaps and let things slide more easily.
Spring 2008
Why Doesn’t Gravity Make the Box Fall?
Force of Floor acting on Box
Force from floor on box
cancels gravity.
If the floor vanished, the
box would begin to fall.
Force of Earth acting on Box (weight)
What’s missing in this picture?
Force on box
by person
Force on floor by box
Force on person
by box
Force on box
by floor
A pair of forces acting between person and floor.
Don’t all forces then cancel?
How does anything ever move (accelerate) if every
force has an opposing pair?
The important thing is the net force on the object of
interest
Force on box
by person
Net Force
on box
Force on box
by floor
93
Spring 2008
Newton’s Laws
29. At what speeds are Newton’s Laws applicable ?
At speeds way below the speed of light
30. Newton’s First Law:
A: Does not distinguish between accelerated motion and constant velocity motion
B: Does not distinguish between stationary objects and those moving with constant
acceleration
C: Does not distinguish between stationary objects and those moving with constant
velocity
D: None of the above
31. Newton’s Second Law:
A: Implies that for a given force, large masses will accelerate faster than small masses
B: Implies that for a given force, larger masses will accelerate slower than smaller masses
C: Implies that for a given force, the acceleration produced is independent of mass
D: Implies that for a given force, no acceleration is produced irrespective of the mass.
Newton’s 2nd Law
34. A car of mass 1250 kg is travelling at a constant speed of 78 kmh-1 (21.7 ms-1). It suffers a
constant retarding force (from air resistance, friction etc) of 12,000 N
(a) What is the net force on the car when travelling at its constant speed of 78 kmh-1 ?
At constant velocity, acc = 0 thus ΣF = 0
(b) What driving force is supplied by the car’s engine when travelling at 78 kmh-1 ?
At constant velocity ΣF = 0, so driving force = retarding force = 12,000 N
(c) If the car took 14.6 sec to reach 78 kmh-1 from rest , what was its acceleration (assumed
constant) ?
Use eqns of motion
u = 0 ms-1 , v = 21.7 ms-1, a = ?, x = ?, t = 14.6 s
use v = u + at -> 21.7 = 0 + 14.6(a) -> a = 1.49 ms-2
Momentum
Newton described Momentum as the “quality of motion”, a measure of the
ease or difficulty of changing the motion of an object.
Momentum is a vector quantity having both magnitude and direction.
Mathematically,
p = mv
Where,
p = momentum (kgms-1)
m = mass (kg)
v = velocity (ms-1)
In order to change the momentum of an object a mechanism for that change
is required.
Airbags/Crumple Zones
39. Explain why, in a modern car equipped with seat belts and an air bag , he
would likely survive the collision whereas in the past, with no such safety devices,
he would most likely have been killed.
The change in momentum in any collision is a fixed value thus impulse is also fixed,
but the individual values of F and t can vary as long as their product is the that fixed
value.
In modern vehicles seat belts and crumple zones are designed to increase to time it
takes to stop thus necessarily reducing the force needed to be absorbed by the
driver because Impulse = Ft.
This reduced force will lead to reduced injuries.
In the old days the driver would have been “stopped” be some hard object like a
metal dashboard and his time to stop would have been much shorter and thus the
force experienced would have been larger leading to more severe injury and likely
death.