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• 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• Motion• Velocity• Distance• Speed• Direction• Gravitational• Inertia• resistance

• 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

DISTANCE

TIME

This represents the distance travelled

A

B C

D

E

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)

• 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 away2. 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

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

5. Sharnie graphed a trip she took. She drew the displacement–time

• 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.

• 9 On graph paper, plot a distance–time graph for your hand’s motion using the values from your table.

Questions

1 Explain why it was important to number the sections

before cutting.2 Describe any trends or patterns in the graphs you

haveconstructed.3 State how many dots an AC ticker-timer makes in

onesecond.4 Once started, describe how long the ticker-timer

takesto produce:a a new dot (this is equivalent to a single spacebetween the ‘old’ dot and the new one)b five new dots (equivalent to five spaces

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.

Acceleration

• 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 tells you that it is a deceleration.

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

+ acceleration × time taken• or v = u + at

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 forcesContact 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 at a constant speed unless acted upon by a net unbalanced force

• 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

• Newton’s Second Law states:• 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 × accelerationor F = ma• This formula can also be arranged to give:• m = F/a and a = F/m

“I’ve just crashed into a brick wall!”

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”

I’LL PULL HIM

devishlyclever

WELL ACTION AND REACTION ARE ALWAYS EQUAL AND OPPOSITE!!

Problems• 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 larger than weight, it lifts off

• 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 ultra-fast 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 reviewed the test and had only one recommendation: ‘Don’t use a frozen chicken’.

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.

Terminal 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.

Falling from the 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 its shape, which changes its speed and direction.

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

w = mg

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 weightlessness because both they and the floor fall at the same rate.

• 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 • or KE = 1/2 mv2

• 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.

Problems• 1. Calculate the work done:a by a 7 N force that shifts a box 2 mb 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

mass is 55 kg.

• 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.

• d The slinky in part c is stretched from 15 cm to 4 m in length.