Transcript force - Reilly Physics

Unit 2 Forces …
… the saga continues!
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1
Isaac Newton

Sir Isaac Newton was born
on 4 Jan 1643 and died on 31
March 1727. He was a
scientist and mathematician.
He did work on movement
and light.
He devised three laws of motion. We will
investigate his first law in this activity.
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Inertia


The tendency of a body to maintain its state
of rest or of uniform motion in a straight line
is called inertia
As a result Newton’s first law is often called
the law of inertia
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Balanced Forces and
Newton’s First Law
Balanced forces means that the forces
acting on an object are equal and opposite.
20 N
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20 N
4
Example of balanced forces
hand pushing iron = 10N
friction = 10N
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If an object has balanced forces acting on
it, it does not change its speed or direction.
For example a stopped car will stay still
but a moving car keeps moving at the same
speed in the same direction.
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Newton’s first law of motion says that,
“an object stays stationary or keeps
moving at constant speed in a straight
line if no unbalanced force acts on
it”.
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Some examples of Newtons First Law are:
a car skidding on ice
keeps going straight
off the road at a
corner
without a safety belt a passenger
in a car keeps going at constant
speed into the windscreen when
the car stops suddenly
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you ‘fall’ to the outside of a
bus when it turns a corner
a spacecraft in deep space
only needs its engines to
change speed or direction
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Physics in Car Safety
Car safety has been improved by putting physics
to use.
Examples are:
safety belts exert a
retarding force on people
causing them to slow down
and stop with the car
- otherwise they would keep
going at constant speed into
the windscreen.
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crumple zones lengthen
the time of impact in an
accident and so reduce
the forces on the
occupants.
collapsible steering
columns and air bags
prevent the wheel being
forced back and into the
driver’s chest.
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Types of Force
Force, Mass and Acceleration
If the force acting on an object increases, the
acceleration increases;
and if the mass of the object is increased, the
acceleration decreases.
Sir Isaac Newton was the first scientist to
discover the precise relationship between these
three quantities.
We now call the relationship “Newton’s second
Law of motion”.
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Demonstration – we will prove it

Copy this table
Pulling Mass
(Fun)
Pulling
Force
Trolley
Mass
0.05 kg
0.5 N
0.5 kg
0.1 kg
1N
0.5 kg
0.1 kg
1N
1.0 kg
0.1 kg
1N
1.5 kg
Acceleration of
trolley
When the unbalanced force (or net force), Fun,
acting on an object doubles, the acceleration, a,
doubles.
When Fun triples, the acceleration triples.
We say that the acceleration and the net force
are directly proportional to each other.
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When the mass, m, doubles, the acceleration, a,
halves.
When the mass triples, the acceleration
reduces to a third.
We say that the acceleration and the mass are
inversely proportional to each other.
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The formula for the above relationships is,
Unbalanced (net) force = mass x acceleration
Fun = m x a
mass is measured in kg
Fun is measured in Newtons and
a is measured in m/s2
When more than one force acts on the object,
the unbalanced force, Fun, must first be
calculated.
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Force, mass and acceleration
1) A force of 1000 N is applied to
push a mass of 500 kg. How quickly
does it accelerate?
2) A force of 3000 N acts on a car to
make it accelerate by 1.5 m/s2.
What is the mass of the car?
3) A car accelerates at 5 m/s2. If it
has a mass of 500 kg how much
force is acting on it?
4) A force of 10 N is applied by a boy
while pushing a 20 kg suitcase. How
much does it accelerate by?
F
m
a
Example
A car of mass 600 kg experiences a driving force
of 900 N and frictional forces of 150 N.
What is its acceleration?
Frictional force
= 150N
Driving force
= 900N
Fun = 900 - 150 = 750 N
a=
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Fun
750
=
m
600
= 1.25 m/s2
Gravity on other planets
We know that the mass of an object is a measure
of the total amount of substance in it.
It has something to do with the total number
(and type) of atoms making up the object.
This means that the mass of an object is the
same whatever planet it is on (or even if it is in
deep space).
Mass is measured in kilograms (kg).
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The force of
attraction on an object
due to gravity is
different on different
planets.
This means that an object has a different weight
on different planets.
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The gravitational field strength, ‘g’, of a planet
states the force of attraction it exerts on
every kilogram of mass
e.g. the gravitational field strength of the
earth is 10 N/kg .
This means that
every kilogram
experiences an
attractive force
of 10 N towards
the centre of the
earth.
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10 N
1 kg
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The gravitational field strength, ‘g’, is different
on different planets.
The weight of an object is calculated from,
Weight = mass x g
W
W = m x g
m
g
mass is measured in kg
weight is measured in Newtons and
g is measured in N/kg or m/s2
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Terminal Velocity
Consider a skydiver:
1) At the start of his jump the air resistance
is big/small 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 _____ ____.
5) Because he is slowing down his air
resistance will _______ again until it
balances his _________. The skydiver
has now reached a new, lower ________
_______.
Newton's Third Law
Interaction Forces



A force is an interaction of two objects..
If you are in contact with an object you
exert a force on it, it also exerts a force on
you….
Skater B
Skater A
Forces
F
B on A
F
A on B
Newtons Third Law


The force on A on B is equal in magnitude
and opposite in direction of the force of B
on A
Or
F
A on B
= - F B on A
Examples….


A 5.0 kg brick rests on the ground, identify
the interaction forces and draw a free body
diagram.
A 5.0 kg brick falls through the air, identify
the interaction forces and draw free body
diagram (ignore air resistance)
More examples


A suitcase sits on a airport luggage
cart, draw free body diagram for each
object and identify interaction pairs…
Poloma hands a 13 kg box to 61 kg
Stephanie, who stands on a platform.
What is the normal force exerted by
the platform on Stephanie? Draw free
body diagram.
Energy Changes for Moving Vehicles
Most of our vehicles are
powered by internal
combustion engines.
These petrol (or diesel)
engines burn fuel, changing
its chemical energy into
kinetic energy and wasting
some in the form of heat
energy and sound energy.
Whenever a vehicle is moving, frictional
forces cause some of its kinetic energy to
change to heat energy.
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For an accelerating vehicle,
chemical energy -> kinetic energy
For a braking vehicle,
kinetic energy -> heat energy
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For a vehicle going at constant
speed there are two energy
changes happening at the same
rate;
chemical energy -> kinetic
energy (in the engine)
and kinetic energy -> heat energy (due to
frictional forces)
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For a vehicle going uphill,
kinetic energy -> potential energy
(the vehicle will slow down if the
engine does not supply extra
kinetic energy)
For a vehicle going downhill,
potential energy -> kinetic energy
(the vehicle will speed up if there
are not extra frictional forces e.g.
by braking)
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Work
Work is said to be done whenever a force
causes an object to move.
The amount of work is greater if either the
force is greater or the distance moved is
greater.
Work done is a measure of the energy
transferred when a force acts on an object.
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The formula for calculating the amount of work
done is,
Work done = force x distance
Ew
Ew = F x d
F
d
F is measured in Newtons and
d is measured in metres
The units of work (Ew) are joules (J).
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Example 1
A father pushes a pram with a force of
150 N.
If he pushes the pram a distance of
200m, how much work has he done ?
Ew = F x d
= 150 x 200
Ew
F
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d
= 30000 J
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Example 2
An artic explorer pulls his
sledge to the top of a ridge.
He does 1 500 joules of work
and pulls the sledge a distance
of 50 metres.
With what force does he pull
the sledge?
Ew
F
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d
Ew
F = d
1500
F = 50
F = 30 N
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Power
This means how much work is done each second.
Or the number of joules of energy which
changes form each second.
For example a more powerful car could:
accelerate faster,
reach a higher speed,
pull a heavier caravan, etc.,
than a less powerful car.
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The formula for calculating power is,
energy
Power =
time
E
P =
t
E is measured in joules and
t is measured in seconds
E
P
t
The units of power (P) are joules per second (J/s)
We can also use Watts (W) as the units of power.
1 W = 1 J/s
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Example 1
If a toy motor boat
gains 360 J of energy in
30 seconds calculate the
power of its electric
motor.
Ew
P = t
Ew
P
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t
360
P = 30
P = 12 W
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Example 2
In the summer months, the
Banff Gondola is used to carry
tourists up to the top of the
mountain. The motor driving one
of the gondolas has a power
output of 30 kW. How long
would it take this chair lift to
do 12.7 MJ of work?
Ew
P
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t
Ew
t = P
12700000
t =
30000
t = 423 s
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Gravitational Potential Energy (Ep)
This is the type of energy an object has because
it is at a height.
An object has more potential energy if it is at a
greater height
or it has a greater mass
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The formula for calculating the amount of
potential energy is,
Potential energy = mass x gravity x height
Ep = m x g x h
M is measured in kg
g is measured in N/kg or m/s2 and
d is measured in metres
Ep
m g h
The units of potential energy (Ep) are joules (J).
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Example 1
Calculate the potential energy
lost by a cat of mass 3.5kg when
it jumps from a wall 2 m high.
Ep
m g h
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Ep = m x g x h
= 3.5 x 10 x 2
= 70 J
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Example 2
Calculate the mass of the chest
if it has gained 72000J of
potential energy when it was
lifted up a height of 30m
Ep
m g h
m
Ep
=
gxh
=
=
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72000
10 x 30
72000
300
= 240 kg
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Kinetic Energy (Ek)
This is the type of energy an object has
because it is moving.
An object has more kinetic energy if it is
moving faster
or it has a greater mass.
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The formula for calculating the amount of kinetic
energy is,
Kinetic energy = 1/2 x mass x velocity2
Ek = 1/2 x m x v2
m is measured in kg
v is measured in m/s
Ek
2
m
v
0.5
The units of kinetic energy (Ek) are joules (J).
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Example 1
A tortoise is moving along the
ground with a speed of 5 cm/s.
If its mass is 3 kg, how much
kinetic energy does it have?
Ek
0.5 m v2
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Ek = 0.5x m x v
= 0.5 x 3 x 0.052
= 0.5 x 3 x 0.0025
= 0.00375 J
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Example 2
A space capsule travelling at
5000 m/s has 6 x 1010J of kinetic
energy.
What is the mass of the capsule?
m
Ek
0.5 m v2
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=
Ek
0.5 x v2
6 x 10 10
=
0.5 x 50002
6 x 10 10
=
0.5 x 2.5 x107
= 4800 kg
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Example 3
What is the speed of a ball which
has 114 J of kinetic energy and a
mass of 2·28 kg?
Ek
2
v =
0.5 x m
114
=
0.5 x 2.28
Ek
=
0.5 m v2
v
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114
1.14
= 100
= 100
= 10 m/s
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Ep -> Ek (and vice versa)
When an object goes downhill it loses potential
energy and gains kinetic energy.
example :
An object of mass 5.0 kg slides down a
frictionless slope as shown,
5.0 kg
4.0 m
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9.0 m
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5.0 kg
4.0 m
9.0 m
To calculate its speed at the bottom of the slope,
Final Ek = initial Ep
=> 1/2 m v2 = m g h
=>
1/
2
v2 = g h
=>
1/
2
v2 = 10 x 4
=>
=>
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v2 = 80
v = 8.94 m/s
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When an object moves upwards it loses kinetic
energy and gains potential energy.
example :
An object of mass 3.0 kg is thrown vertically
upwards with a speed of 20 m/s.
What height does it reach before falling back
down ?
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Initial Ek = final Ep
=>
=>
1/
2
m v2 = m g h
1/
2
v2 = g h
=> 1/2 (20)2 = 10 x h
=>
=>
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200 = 10 h
h = 20 m
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