Download Motion and Forces - 10Science2-2010

Motion and Forces
Outcomes
• 5.6.2a) describe qualitatively the relationship
between force, mass and acceleration
• 5.6.2b) explain qualitatively the relationship
between distance, speed and time
• 5.6.2c) relate qualitatively acceleration to a
change in speed and/or direction as a result of a
net force
• 5.6.2d) analyse qualitatively common situations
involving motion in terms of Newton’s Laws.
• 5.6.6a) distinguish between the terms ‘mass’ and
weight
Skills
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5.13.1e) identify the appropriate units to be used in collecting
data
5.13.1g) formulate a means of recording the data to be
gathered or the information to be collected
5.13.2 a) identify variables that need to be held constant if
reliable first-hand data is to be collected
5.13.2 b) specify the dependent and independent variables
when planning controlled experiments
5.13.2 c) describe a logical procedure for undertaking a simple
or controlled experiment
5.14 a) follow the planned procedure when performing an
investigation
5.14 d) record data using the appropriate units
5.15 a) make and record observations and measurements
accurately over a number of trials
5.15 b) use independently technologies such as ticker timers
5.18 d) use symbols to express relationships, including
mathematical ones, and appropriate units for physical quantities
5.18 f) graphs and tables to show relationships and present
information clearly and/or succinctly
5.18 g) select and draw the appropriate type of graph to convey
information and relationships clearly and accurately
Spelling List
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Motion
Velocity
Distance
Speed
Direction
Gravitational
Inertia
resistance
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Mass
Weight
Displacement
Qualitative
Gravity
Calculating
Relationship
• Motion
• Distance is measured in metres (m) for
calculations.
• time is measured seconds (s).
• Note; Displacement is distance with a
difference. Displacement is how far you end
up from where you started, and in which
direction (up, left, north, towards the
window). It is distance with direction. You
travel a considerable distance each day, but
your overall displacement is likely to be
zero. You will end up in the same bed that
you crawled out of this morning.
• Speed is a derived quantity, a measure of how far
you can go in a certain time period. (Speed is the
rate at which distance is covered.)
• Note
• Velocity is speed in a given
direction. Wind movement is an
example of velocity.
• Unit: metres per second
• Unit abbreviation: m/s or m s–1
• History note; The speed limit for cars in
France was 13 km/h in 1893. Originally
all cars in Great Britain had to have a
man walking in front of them with a red
flag to alert horseriders! In 1896 the
speed limit was raised to 20 km/h, and in
1904 to 33 km/h. The first Australian
speeding ticket was given to a
Tasmanian,
• George Innes, who was recklessly driving a car
through Sydney at 13 km/h.
Graphing Speed a
distance/time graph
The gradient of distance
verses time is speed
The other graphs show
constant speed, slow and
faster and stationary (at
rest).
In this graph motion is described as
A to B constant speed
B to C at rest, stationary.
C to D constant speed but slower
D to E constant speed to travel back home (fastest
speed)
D
D
IS
T
A
N
C
E
B
This represents
the distance
travelled
C
E
A
TIME
• Speed–time graph
• A graph of speed against time
gives another picture of what is
happening in the motion of an
object. As before, time is placed
on the horizontal axis. If the object
is getting faster, the graph rises. If
slowing, the graph falls. Constant
speed gives a flat graph. The area
under a speed–time graph
gives the distance that the
object has travelled up to that
point.
The total distance
travelled is the area
under the graph. The
area here is
6 + 8 = 14.
The object has
moved 14 metres.
Problems
1. Light travels at a speed of 300 000 km/s.
Calculate how long it takes to travel:
• a from the Sun to Earth, a distance of 149 600
000 km
• b the 384 403 km distance between the Moon
and Earth
• c from Earth to Pluto, 5 750 400 000 km away
2. If the distance to the sun is 149600000kms
and assume a circular orbit path, then calculate
the speed that Earth travels around the Sun.
3. If earths radius is 6750kms, calculate it speed
of rotation.
4. For the motions shown in
the diagram calculate:
i the distance travelled
ii the displacement
iii the average speed for the
whole trip
iv the average velocity for
the trip
5. Sharnie graphed a trip she took.
She drew the displacement–time
Calculate the following:
a the total distance Sharnika
travelled
b her displacement
c the time she was away
d her speed for the first leg
of the trip
e her return speed
f the times she was at rest
g her average speed for the
whole trip
• The ticker-time;- measuring speed
• A ticker-timer is an instrument that breaks
movement into a series of small intervals. It
gives us a way of accurately measuring
distances travelled and times taken, and
provides the data from which speeds can be
calculated. A small electric hammer strikes a
piece of carbon paper at the same frequency
as the AC power supply, 50 times a second or
50 Hz. Motion is then recorded as dots on a
strip of paper that passes under the hammer.
Fifty dots are produced every second, so a
space between dots takes only one-fiftieth of a
second or 0.02 seconds to produce.
• Homework; research how
• i a radar gun or speed camera is
used to measure speed
• ii a fish finder measures depth and
locates schools of fish
• iii What is the meaning of ‘sonic
boom’ and the speed at which it
occurs.
• Ticker Tape Experiment
• Aim To analyse motion using a ticker-timer
• Equipment
• AC ticker-timer, carbon paper circles and
tape, power pack, scissors, ruler, graph
paper, paper glue
• Method
• 1 Tear off about 1 m of tape and thread it through the
timer.
• 2 Start the timer, then pull the tape through, changing
speed as you go.
• 3 Repeat with new tape, so everyone in the group has
their own tape.
• 4 Draw a line through the first clear dot, then every
fifth dot after that. There should be five spaces per
section. This represents a time of 0.1 seconds.
• 5 Number each section, then cut along the lines.
• 6 Paste the pieces in order onto paper to produce a
speed–time graph
• 7 Measure the length of each section in millimetres
• 8 Add axes to the cut-and-paste graph and use the
values in the table to mark appropriate scales along
each axis.
Questions
1 Explain why it was important to number the
sections
before cutting.
2 Describe any trends or patterns in the graphs
you have
constructed.
3 State how many dots an AC ticker-timer makes in
one
second.
4 Once started, describe how long the ticker-timer
takes
to produce:
a a new dot (this is equivalent to a single space
between the ‘old’ dot and the new one)
b five new dots (equivalent to five spaces
Acceleration
Acceleration is measured in speed units per time unit.
The most common
unit for acceleration is metres per second per
second, m/s2 or m s–2.
• Calculating acceleration
• If the speed of a car changes from 0 to 60 km/h in 6 seconds, then
its acceleration is
(60 – 0)
• a = ----------- = 10
6
• The unit here would be speed units (km/h) per time unit (s) or
k/h/s: the car gained an extra 10 km/h every second.
• For an athlete, speed is better measured in m/s. For example, a
runner is jogging along at 2 m/s but then slows her speed over the
next 5 seconds until she is running at 1 m/s. Her acceleration
would be:
(1 – 2)
• a = --------- = - 0.2
5
• The units here would be her speed units (m/s) per time unit (s),
i.e. m s–2 or m/s2.
• You can say that her speed decreased by 0.2 m/s every second, or
her speed changed by –0.2 m/s every second. The negative sign
Problems
a. In November 2003, New South Wales dropped the urban street
speed limit from 60 km/h to 50 km/h. Contrast the stopping
distances at each speed limit.
b. It is recommended that the distance between your car and the car
in front be equivalent to the reaction distance at that speed.
Evaluate how many car lengths a driver travelling at 60 km/h and
100 km/h should leave in front of them.
• Calculate the area and the
gradient of each section of the v–t
graph in Figure 5.2.8 to find the
distance travelled and the
acceleration.
• Calculating speed
• Let’s say a rocket launches
with an acceleration of
• 50 m/s2. It started at rest,
but 50 m/s is added to its
speed every second that
passes.
• Its speed will then follow
the pattern shown in the
diagram
• If the rocket was already
moving at, say, 500 m/s,
• then the speeds would be
those shown in the figure
• another 500 m/s added to
them.
• You can write this as:
• final speed = starting speed
What is a force?
• a push, pull or twist that causes an
object to either:
• • increase its speed (accelerate)
• • decrease its speed (decelerate)
• • change its direction, or
• • change its shape.
• If any of these things happen, then a
force caused it.
Types of forces
Contact and non-contact forces
• • Friction: acts between any two
surfaces that try and slide over one
another. Acts in the opposite direction
to the movement or attempted
movement.
• • Air resistance and drag: friction of air
(or liquid or other gases) as it travels
across a moving object. Like friction, it
acts in a direction opposite to the
movement.
• • Buoyancy: ‘floating’ force. Acts
upwards, opposing the weight force.
• • Surface tension: tiny forces between
particles on the surface of a liquid that
form a ‘skin’ on the liquid.
• • Lift: caused by air moving over a wing
or airfoil. Acts at 90° to the surface of
the airfoil.
• • Thrust: caused by gases or liquid
being pushed out the rear of an engine,
jet or rocket.
Non-contact
forces
• • Weight: caused by gravity. Acts
‘downwards’, towards the centre of
the planet.
• • Electrostatic: repulsion of like
charges (+/+ or –/–) or attraction
of unlike charges (+/–).
• • Magnetic: repulsion of like poles
(N/N or S/S) or attraction of unlike
poles (N/S).
Newton’s First
Law the law of
inertia
• Newton’s First Law examines the
forces on an object that is:
• at rest ( stopped) or in motion.
(moving)
• Anything at rest will stay that way
unless acted upon by a net
unbalanced force.
• That is, a force is required to get
something moving.
• If an object is moving it will
continue to do so in a straight line
• Crash test dummies have been
used for over 30 years to develop
safer cars. Before that, live but
anaesthetised pigs were used in
crash tests. A large pork BBQ often
followed. Human corpses
(cadavers) were also used in tests.
Accelerometers and force meters
were implanted in the cadavers to
measure what was occurring. The
results from these experiments led
to the development of the modern
crash test dummy, the Hybrid 3.
Crash test humans
Crash test dummies were first developed by the US Air Force to
determine the injuries that pilots would sustain if they ejected
from aircraft in flight. Live humans were tested before the
invention of the dummies, and Colonel John Stapp underwent
26 tests. In one, he sat in a rocket-powered open sled that
accelerated to a speed of 1000 km/h in five seconds, but then
was stopped in less than a second. Inertia kept his internal body
parts and blood moving and he stated later that he felt as if his
eyes would fly out of his skull.
Blood vessels in his eyes burst and they bled profusely for 10
minutes after the test. His lungs also collapsed, but he recovered
quickly, proving that it was possible to survive such extreme
forces.
Newton’s Second
Law
“I’ve just crashed into a
• Newton’s Second Law states:
brick wall!”
• Something will happen if a force is
applied: the object will accelerate and
the acceleration will depend on the
mass of the object.
• force = mass × acceleration
or F = ma
• This formula can also be arranged to give:
• m = F/a and a = F/m
NEWTON’S THIRD LAW :
“ACTION AND REACTION ARE ALWAYS EQUAL
AND OPPOSITE”
“IF A BODY A EXERTS A FORCE ON BODY B,
THEN B EXERTS AN EQUAL AND OPPOSITELY
DIRECTED FORCE ON A”
devishly
clever
I’LL
PULL
HIM
WELL ACTION AND REACTION ARE
ALWAYS EQUAL AND OPPOSITE!!
Problems
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1. Calculate the force being applied if:
a a 5 kg box accelerates at 4.1 m/s2
b a 1.3 tonne car accelerates at 2 m/s2
c a 400 g ball accelerates at 4 m/s2
2. Calculate the acceleration caused by:
a a 40 N force applied to a 0.5 kg mass
b a 0.5 N force applied to a 50 kg mass
3. A 35 N force causes a mass to
accelerate at 7 m/s2.
• Calculate the mass.
More problems
• 4. A 3.5 kg body accelerates from rest to 20 m/s
in 5 s.
• Calculate:
• a its acceleration
• b the force required
• 5. The brakes of a car can exert a stopping force
of 3000 N. The car is 1.5 t. Calculate the
following:
• a the mass of the car in kg (note: 1 t = 1000 kg)
• b the deceleration of the car
• c how long it would take to stop if it was
travelling
• initially at 10 m/s
ROCKETS
• Rocket engines are sometimes called reaction
engines, as they use the action/reaction pair of
forces to provide the thrust needed for launch.
Rockets expel massive quantities of gases in one
direction, which push the rocket in the opposite
direction, usually upwards. The exhaust gases are
tiny particles but their effect is dramatic due to their
high acceleration.
• The exhaust is produced when fuel, called
propellant, undergoes chemical combustion
• The resulting
exhaust
stream
produces
thrust—the
force which
propels the
rocket.
• When thrust
equals weight
the rocket
begins to
hover, and
when thrust is
• Flying frozen chickens!
It is estimated that 30 000 birdstrikes occur worldwide
each year, leading to damaged aircraft windscreens
and even engine failure. The USA designed a unique
device for testing the strength of windscreens on
aeroplanes. It is a gun that launches a dead chicken
at a plane’s windscreen at about the speed the
plane flies. The theory is that if the windscreen
doesn’t crack from the impact of the carcass, it will
survive a real collision with a bird during flight. The
British decided to test a windscreen on a new ultrafast train. They borrowed the FAA’s chicken launcher,
loaded a chicken and fired. The ballistic chicken
shattered the windscreen, smashed the driver’s seat
and embedded itself in the aluminium back wall. The
British were stunned and contacted the FAA to see if
everything had been done correctly. The FAA
Gravity
Is measured as the rate of acceleration
at which objects fall. On the Earth’s
surface the acceleration of all objects is
9.8 m/s/s. This means that the speed of
a falling object increases about 10 m/s
every second of its fall. This value is for
objects falling in a vacuum. In air,
acceleration will be slightly less. An
object pushes air out of its way as it
falls. The air pushes back with an equal,
upward force called air resistance.
velocity
Air resistance increases as speed
increases—the faster you are falling,
the more the resistance. Eventually it
balances weight, and so the total force
acting is zero. There can be no more
acceleration and the object falls at a
constant speed, called its terminal
velocity. All objects have a terminal
velocity, but its value will depend on
the shape and size of the object. A
sheet of paper has high air resistance
and a low terminal velocity, while the
same paper crumpled has lower air
resistance and will reach higher speeds.
sky
• Without a parachute humans
have a terminal velocity of
about 50 m/s.
• However, skydivers can
control their descent by
changing the shape of their
body as they fall. An open
parachute reduces the
terminal velocity to 5 m/s,
which is just about the
terminal velocity of a
raindrop (7 m/s). Pulling on
the chute’s strings changes
Weight
The force on a mass that is caused
by gravity is called weight. It is
the force that pulls objects down to
the surface of a planet. Weight
depends on the mass of the object
and the acceleration due to the
gravity of the planet itself. You can
write this as:
weight = mass × acceleration due to
gravity or
Weightlessness
• You have weight whenever gravity is
around. True weightlessness (where g = 0)
only happens far from the influence of stars
and planets. You sometimes ‘feel’
weightless, however, in rides such as the
Tower of Terror and the Giant Drop at
Dreamworld, when the seat (with you in it)
falls. During the fall, the seat cannot push
back to give your normal ‘feelings’ of
weight. When in orbit, the space shuttle and
space stations fall towards Earth. They don’t
hit, however, since they are travelling at
such high speed ‘horizontally’ that they
always miss the planet.
• Astronauts aboard them have the ‘feeling’ of
• Work
• Movement involves energy. Energy is
the ability to do work. Work happens
whenever things are shifted or
rearranged by a force. The bigger the
force, the more work done. Likewise if
something is shifted a long way, then
more work is done than if it only moves
slightly. If it doesn’t move, then no work
has been done on it.
• work = force applied × distance shifted
or W = Fs
• Force is always measured in newtons
(N) and distance in metres (m). Work is
a form of energy and, like all energy, is
measured in joules, abbreviated as J.
If a heavy box takes a force of 500 N to
shift it 3 m,
• then the work done on it is:
• W = 500 × 3 = 1500 J
Kinetic energy
• Movement is needed for cars to crash:
no accident will happen if everything is
stationary. When something moves it
has kinetic energy. The heavier the
car, the more kinetic energy it has and
the more work and damage it can do.
Likewise, the faster you travel, the
more work will be done. In fact, if you
double your speed, the work done in a
collision and the damage caused will be
four times what it was at the slower
speed.
• Kinetic energy = 1/2 × mass × speed × speed
• Kinetic energy is measured in joules (J),
mass in kilograms (kg) and speed in
metres per second (m/s). Compare the
kinetic energies of a typical 1.5 tonne
car (1500 kg). At 50 km/h (13.9 m/s),
the car has a
• kinetic energy of
•
• KE = 1/2 × 1500 × 13.92
• = 144 908 J
• At 100 km/h (27.8 m/s), the kinetic
energy is quadrupled:
• KE = 1/2 × 1500 × 27.82 = 579 630 J
• On braking, all this kinetic
energy is converted into heat
energy that is dissipated by
the brake pads or discs. In a
collision, it converts into heat
and sound, but mainly into
work as the car crumples or
crumples other cars or
objects—a lot of rearranging is
done in an accident.
Gravitational potential
energy
Potential energy is stored energy—it
gives the object the potential to do
work.
• If you lift an object to a height you give
it gravitational potential energy.
The heavier the object and the higher
you lift it, the more energy it will have,
and the more damage it will cause
when let go.
• Gravitational potential energy = mass ×
acceleration × height due to gravity
•
• GPE = mgh
• GPE is measured in joules (J), m
in kilograms (kg) and h in metres
(m). Like all accelerations, g is
measured in metres per second
squared (m/s2). On Earth g is 9.8
m/s2.
• As something falls it picks up
speed—gravitational potential
energy is converted into kinetic
energy. When it hits the bottom,
most will be converted into work
done on the ground and the object
itself. Both the ground and the
object will dent and change shape
or break.
Elastic potential energy
• Elastic bands and springs store energy
when they are stretched or extended.
They store it as elastic potential
energy. They have the potential to
release energy and do work when they
are let go. They may spring back to
their original shape. Eg slingshot is
stretched and let go.
• You put energy into stretching the
elastic band. The more a slingshot is
stretched, the more energy it stores,
the more kinetic energy the projectile
will have, the faster it will go and the
more damage (work done) it will do.
• Springs store energy when
squashed or compressed. Tennis
balls act as a store of elastic
potential energy when compressed
on a bounce or when hit. The more
the ball stores, the more it
releases and the higher it will
bounce.
• Some materials are stiff—they
need high forces to change their
shape. Others are highly elastic.
One measure of stiffness is the
spring constant of the material.
The higher the constant, the stiffer
(and less elastic) it will be.
Efficiency
• Friction between moving surfaces
wastes useful energy, converting
some of it into heat and sound.
Efficiency is a measure of how
much useful energy is retained in a
conversion:
• A rolling ball will eventually stop due to
friction. All the kinetic energy it once
had has been converted into heat and
sound: the efficiency is 0%. A 100%
efficient machine would be perfectly
quiet and would run forever, because all
the energy conversions would be
perfect. A ball loses a little of its useful
energy each time it bounces. Squash
balls have very little bounce and are
incredibly inefficient, losing most of the
energy to heat. The ball gets hot
quickly, which then gives it more
elasticity and better bounce.
• 1. Calculate the work done:
Problems
a by a 7 N force that shifts a box 2 m
b in shifting a trolley 50 cm by a 20 N force
• 2. Calculate the kinetic energy in the following:
a A 400 kg motorbike travels at 25 m/s.
b A 50 kg skateboarder is freewheeling at 9 m/s.
c A 20 g stone is thrown at 2 m/s. (Note: 1000 g = 1
kg)
d A 30 mg spider runs about at 5 cm/s. (Note: 1000
mg = 1 g)
• 3. Calculate the gravitational potential energy that
the following objects have:
a Travis stands on a diving board, 11 m above the
surface. His mass is 60 kg.
b A 2.5 kg textbook is on a desk that is 70 cm high.
(Note: 100 cm = 1 m)
c Matthew (65 kg) is on the Centrepoint observation
deck, 250 m above the street.
d Yee is piloting Flight 007 at a height of 9500 m. Her
• 4. Calculate the gravitational potential
energy before and after a bounce, if a
30 g ball is dropped from 2 m and
bounces to a height of 1.5 m.
• b Calculate its efficiency.
• 5. Calculate the elastic potential
energy stored in each spring (make
sure all lengths are in metres):
• a A slinky spring with a spring constant
5 N/m is extended 3 m.
• b A spring (k = 25 N/m) is squashed
0.5 m.
• c A slinky has a natural length of 15
cm, but is stretched to a new length of
90 cm. Its spring constant is 30 N/m.