Mechanics Class Notes

MECHANICS

Year 114 External Credits

Achievement Standard

SLO

Use SI units for distance, speed, time and acceleration.

Quantity Unit Symbol

Time

Distance

Speed

Acceleration

Mass

Force

Energy and WorkPower

Standard Units

td

v d

vt

dtv

d v t dv t

d v t

Finding d with a triangle

Rearranging Formula

dt

v d

tvd

v t

dt

v

Finding t with a triangle

Rearranging formulas

Although the formulas are supplied for the exam, they usually need to be rearranged before being used.

Given: Given:

Given: Given:

dt

v

v a t

Fm

a

workt

P

dv

t

va

t

F ma workP

t

1A 1 Units and formulas

t v

tm

If you wanted to know how much you’d grown in the last year, you’d take your height now and subtract your height last year:

Change in height = height now – height last year

= 163 cm – 157 cm

= _________

All ‘change in’ calculations in physics are done this way:

change in distance = final distance – initial distance

d = df − di

Finding ‘change in’

Converting UnitsUnit Conversion Unit

Kg gKw WKJ JKm mKPa PaMinutes secondsHours secondsMetres mmMetres cmKg N

Speed

_____________________NOT

Km/sec or m/hr

Success Criteria Complete page Units of Speed 159 of

Scipad

Complete the following table:Unit Conversion Unit1300 Kg ? g

Kw 60 W

750KJ ? J

Km 600m

KPa 10 Pa

30 Minutes ? seconds

Hours 3600 seconds

12 Metres ? mm

Metres 200 cm

65 Kg ? N

SLO

Define Speed

http://lgfl.skoool.co.uk/content/keystage3/physics/pc/learnPathLessons/QW5/frameset.htm




Speed and Velocity

An object has speed when it travels a _____________ in a ___________________.

____________ is speed in a given _____________

Velocity and speed are measured in metres per second (ms-1) or kilometres per hour (kmh-1)

Speed and velocity (S or V) = ________________

Therefore our formula

Where: v is the symbol for __________d is the symbol for __________t is the symbol for __________

td

v

is written in an equation as:

time in changedistance in change

Speed

The Δ symbol means _____________

Speed, distance and time

Distance is how far something moves. Unit: metre, m

Speed is the rate of change of distance.Unit: metres per second, m s-1

td

v

In equation form this is written as:

Where: v is the symbol for speed, d is the symbol for distance and t is the symbol for time.

time in changedistance in change

Speed

d = dfinal − dinitial

(Δ means ”change in”.)

Scientific calculationsThere are a lot of calculations in physics, but once you master this simple method you will find that they are all much the same.

1. Sort out the _______ from the question.

2. ____________the relevant formula, rearranging if necessary (eg to find current instead of voltage).

3. Put the data from the ________ in the formula.

4. __________the answer and write it down with the correct _________

You will not get ________ marks in an exam unless you show working (at least steps 2–4).

Example: calculating speed

td

v

How fast is John moving if he covers in ?

d = ,

s 12m 60v

1-s m 5v

t = , v =s 12 s 12 see answer

s 12 s 12

m 60 m 60

How fast

?

m 60

v

m 60

1. Sort out the ________.

2. Write the _________.

3. Plug in the ________.

4. Write the answer with its _________.

Example: Calculating speed

td

v

How fast is John moving if he covers in ?

d = ,

s 12m 60v

1-s m 5v

t = , v = ?s 12 s 12

s 12

m 60 m 60

m 60Sort out the data from the question.

Write the relevant formula.

Put the data into the formula.

Calculate the answer and write the correct unit.

Example: Calculating distance

d = v = 1-

s m 6 t =

How far does Samantha travel if she runs at for ?

?

How far1-

s m 6minutes 10 minutes 10

td

v Rearrangin

g

dtvv t

tvd

d

d

1-s m 6

Minutes is not an SI unit: convert it into seconds.

Your SpeedAim:To find out the walking, jogging and sprinting speeds in m/s for yourself and members of your group.

Method:1. Mark out 20m2. Have a starter with stop watch3. Have a person at finish line to raise hand

when person crosses it.4. Record time in seconds to the nearest

whole second

WalkingName Distance

(m)Time (sec) Speed

(m/s)

JoggingName Distance

(m)Time (sec) Speed

(m/s)

SprintingName Distance

(m)Time (sec) Speed

(m/s)

Success Criteria1. The parachutist falls through a distance of

400 m during the first 60 seconds. Calculate the average speed of the parachutist during this time. (remember to show ALL working)

2. Complete scipad pages 160-162 Calculating Speed, Using Triangles and More Speed Calculations

NCEA Questions

SLO

Use distance time graph to describe the motion of an object

Calculate the speed of an object using the gradient of a distance-time graph.

Motion graphs are graphs that describe a motion in graphical form.

You will need to interpret distance–time and speed– time graphs for this standard.

distance

(m)

time (s)

Motion graphs

Distance-time graphs

14/04/2023

40

30

20

10

020 40 60 80 100

4) Diagonal line

downwards =

____________

3) Steeper diagonal line =

_________________

1) Diagonal line =

____________

2) Horizontal line =

____________

Distance

(metres)

Time/s

14/04/2023

40

30

20

10

020 40 60 80 100

1) How far had the object gone after 20 seconds?

2) How far had the object gone after 60 seconds?

3) When is the object standing still?

4) When was the object travelling the fastest?

Distance

(metres)

Time/s

If the line curves, the object is getting faster or slower.

Speeding up

Slowing down

0 2 4 6 8 10 12 14

20

40

60

80

100

distance

(m)

time (s)

0

Curves on distance-time graphs

Shaun _____________

0 2 4 6 8 10 12 14

20

40

60

80

100

distance

(m)

time (s)

0

Success Criteria

Complete Scipad pages Distance – Time graphs pages 163-167.

SLO

Define acceleration

Use formulae to calculate acceleration, change in speed or change in time

Acceleration is the rate of change of speed:

Acceleration_____________is when an object either speeds up or slows down.

time in changespeed in change

onaccelerati

Acceleration is measured in metres per second squared, _______________

Acceleration is ________ when speeding up.

Acceleration is ___________ when slowing down.

Slowing down is also called ___________.

In an equation this is written as:

Where: a is the symbol for ___________.

v is the symbol for ___________.

t is the symbol for ____________.

Remember Δ means ”change in”.

tv

a

Example: Calculating acceleration

How quickly is Brian accelerating if he increases his speed from to in ?

1-s m 10

1-s m 20 s 5

1-s m 10

1-s m 20 s 5

i) Change in speed

if ddd

d

ii) Calculate acceleration

td

a

a

v

v

Example: Calculating speed from acceleration

t = ,a = ,

tv

a

If Sam accelerates from rest at for , what is his final speed?

tav

v

v =

Rearranging

vta

va t

?

2-s m 2.5 s 5

final speed

2-s m 2.5 s 5

‘From rest’ means his speed started out at zero.

Success Criteria Complete page 168-169 Scipad,

Acceleration

SLO

Use speed-time graphs to describe the motion of an object

Calculate acceleration using the gradient of a speed-time graph

Calculate the distance travelled from the area under a speed-time graph

Each strip shows the distance travelled by the trolley over the 0.1 s interval.

We have made a speed-time graph of the trolley’s journey as it slowed down.

1B 4 Testing ticker-timers 1B 5 Going dotty

Velocity(Speed)-time graphs

14/04/2023

80

60

40

20

010 20 30 40 50

Velocity

m/s

Time (sec)

1) Upwards line =

_____________

2) Horizontal line =

_______________

3) Upwards line =

_____________

4) Downward line =

____________

14/04/2023

80

60

40

20

0

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 50 seconds?

10 20 30 40 50

Velocity

m/s

Time

sec

Slope of speed–time graph gives acceleration The steeper the gradient (slope) of the line, the

___________ the acceleration. If the line is horizontal, the speed is ___________;

zero acceleration. If the gradient is negative, the acceleration is

_________________.

Speed

(m s-1)

time (s)

Speed

(m s-1)

time (s)

The area under a speed-time graph shows the __________________________

Area = distance travelled

Find the acceleration of the object between five and twenty seconds.

va

t

v1 = v2 = t1 = t2 = a =

2 1

2 1

v va

t t

Speed(m s-1)

time (s)

00 5 10 15

20

40

20

10

30

50

25

Δv

t

Example: Acceleration from a speed-time graph

Distance-time graph for non-uniform motion

14/04/2023

40

30

20

10

020 40 60 80 100

Distance

(metres)

Time/s

Object is __________ up to here

Object is now __________

Success Criteria Complete Scipad pages 170-175 on

Acceleration graphs and distance travelled

Revise

Complete Scipad pages 176-181, 158

Complete worksheets

Complete purple book pages

SLO

Define Force

Name the four forces that act on many everyday objects

Forces Force (F) has both ___________ and

_________

Force is measured in __________

Forces are drawn as _________, the arrow head shows the _________ and the __________ shows the __________of the force.

14/04/2023

Forces

http://lgfl.skoool.co.uk/content/keystage3/Physics/pc/learningsteps/FCDLC/launch.html

14/04/2023



Types of Forces

14/04/2023

A force is a “push” or a “pull”. Some common examples:

________ (mg) – pulls things towards the centre of the Earth

________________– a contact force that acts against anything moving through air or liquid

__________ – keeps things afloat

_____ – a contact force that acts against anything moving

Success Criteria

Complete Scipad page 183-

Section B is a student cycling at a constant speed:

SLO

Describe the effect of balanced and unbalanced forces on motion

Balanced and Unbalanced Forces

The movement or lack of it, of an object depends on the forces acting on it.

Balanced forces = ________________________ Unbalanced forces = ______________________

Whatever direction the force is greatest in will be the direction, in which the object moves.

14/04/2023

Success Criteria

SLO

Calculate for using F=ma

Investigating the relationship between force and accelerationWe shall use a falling mass to apply a steady force on a trolley, and use a ticker-timer to measure its acceleration.

Use the following slides to help you to set up the equipment below.

The dots on the tape get further apart, indicating that the trolley was accelerating.

Results

Mark off every 5th dot...

... cut up the tape...

... and join the strips together to make a speed-time graph.

Label your finished graph with the mass used.

Repeat the experiment using a mass of 300 g.

5 x 50 g weightsplus

1 x 50 g carrier

The greater mass has produced a greater acceleration – the dots are further apart and gradient of the graph is steeper.

The gradient of the second graph is exactly double that of the first.

When the force pulling the trolley doubles, its acceleration doubles.

Force, acceleration and massAn unbalanced force acting on an object will cause it to _______________.

We know now that the acceleration produced is proportional to the force.

We could carry on making ticker-tape graphs to show the relationship between acceleration and mass for a constant force.

Another way to think of the relationship between force, mass and acceleration is to imagine pushing cars.

The greater the force on the car, the f_________ it will accelerate.

Pushing cars

If the forces are equal but the mass is doubled, then the acceleration __________.

Two people pushing two cars has the _______ acceleration as two separate people each pushing one car.

We have seen that acceleration goes up as force goes up, and acceleration goes up as mass goes down.

Thus:

or

f orceacceleration =

mass

Where F, force is measured in newtons (N)m, mass, is measured in kilograms (kg)

And a, acceleration, is measured in metres per second squared (m s–2)

Success Criteria

http://multimedia.mcb.harvard.edu/anim_rhino.html

Complete Scipad pages 186-187




SLO

Explain the Difference between mass and weight

Mass

Mass is the bulk of an object, the amount of __________ there is

remains ___________ (is unaffected by gravity)

measured in ___________________

_______________are used to compare the mass of two objects

Gravity

Gravity is a force which ______________(matter) together

The bigger the masses the greater the __________

The acceleration due to earth’s gravitational pull is _______________

Weight

Weight is the force of __________ on a mass

also known as __________ force

measured in ________________

varies depending on the _________acting on a mass (greater the gravitational force, greater the weight), which changes on different planets

Measured with a ___________ in _________

Mass, Weight and Gravity

WEIGHT = MASS X GRAVITATIONAL FORCE

Weight = mg g = 10 ms-2 on Earth mass = Kg . . . so when we say my weight is 65Kg we actually mean . . . If my mass is 65 Kg and I weigh (65 Kg X 10 ms-2) 650 Newton’s

An astronaut has a mass of 80 kg. On Earth her weight is given by: gm Weight

On the Moon g = 1.7 N kg–1 and her weight is 136 N.

Her mass on the Moon is the same as it is on Earth: ________.

gm Weight

Success Criteria

Complete scipad page 188-189

A car now hangs motionless on the end of a crane’s cable. The force applied by the crane is 13 000 N. Use the value of the crane’s force to determine the mass of the car. Give an appropriate unit for you answer. In your answer, you should include an explanation of the difference between mass and weight.HINT: Gravity on earth is 10 ms-2 )

SLO

Define Friction and understand its effect on motion

On Earth, _____________acts as a __________opposing the motion (it pushes in the opposite direction to your movement).

Air resistance or friction only happens when an object is moving.

Friction forceGoing up

Stopped at the top

As the speed of a falling object increases, its air resistance ________________.

Eventually the friction force (air resistance) is equal to the __________________.

When the forces are balanced, the object stops accelerating. Physicists say that the object has reached ___________.

A parachute has a large surface area, giving it a high ______________. With the parachute open, the sky-diver slows down until the forces again balance at a much slower ______________

Gravity is the force that makes objects _______.

Gravity is __________pulling objects down, whether they are moving downwards, stationary, or going up.

All falling objects in the same gravitational field will accelerate at the same rate (_________________).

Gravity and falling

Here an astronaut on the Moon dropped a hammer and a feather.

Without air resistance, the hammer and the feather fall with the same acceleration and land ____________________. See the drop onlin

e.

feather

http://history.nasa.gov/alsj/a15/a15v_1672206.mpg

http://history.nasa.gov/alsj/a15/a15v_1672206.mpg

Success Criteria

Complete Scipad page 190-191

SLO

Calculate pressure using P=F/A

Rearrange P=F/A to solve an unknown variable

Where Pressure, Force, Area,

Do you weigh less when you stand on one leg? Of course not. Since your weight is now spread over a smaller area, the pressure on the ground under your foot is greater.

f orce

pressurearea

Why are wooden floors often damaged when people wear stiletto heels?

PressureD

If you walk through snow in ordinary shoes, you’ll _________and your shoes will get wet.

Snow shoes have a ______________that distributes the weight of the wearer over a larger area, reducing the __________ on each patch of snow.

The caterpillar tracks on military tanks also reduce the _______ on the ground by __________ the surface area of contact.

Success Criteria

Complete scipad pages 192-199, 182

The image shows an example of a crater produced by the golf ball. The students found that the golf ball always produced a deeper crater than the table-tennis ball.

Explain why the golf ball produces a deeper crater than the table-tennis ball, even though the balls are the same size and shape, and dropped from the same height

SLO

Describe different forms of energy

Identify energy Transformations

Energy

Energy is the ability to __________

Energy is measured in ____________

Types of Energy

/Stored

/Active

14/04/2023

The 9 types of energyType 3 example sources

Heat

Kinetic (movement)

Nuclear

Sound

Light

Chemical

Electrical

Gravitational potential

Elastic potential

Type 3 example sources

Success Criteria

Complete Scipad page 201

Law of Conservation of Energy

Energy can neither be _________ nor it is _________, however energy can be

____________-from one form of energy to any other form

of energy

Energy ChangesTo describe an energy change for a light bulb we need to do 3 steps:

Electricity Light + heat

1) Write down the starting energy:

3) Write down what energy types are given out:

2) Draw an arrow

What are the energy changes for the following…?

1) An electric fire

2) A rock being dropped from a cliff

3) An arrow being fired

Energy Chains

What are the energy changes for the following…?

1) An electric fire

2) A rock dropping from cliff

3) An arrow being fired?

Success Criteria

Complete Scipad pages 202

SLO

Define the term gravitational potential energy

Use the formula Ep=mgh to calculate gravitational potential

energy

Gravitational Potential Energy Gravitational potential energy is the energy due

to an object’s ______________ above ground.

To get an object off the ground, _________ must have been done to move it

Gravitational Potential Energy Ep

Fw = m x g (mass x gravity (10))

h = height (metres)

What factors determine the climber’s gravitational potential energy (Ep) in joules?

His __________in metres – the higher he climbs, the ________ energy he had to put in, and the greater his Ep.

His ____________in kilograms – the heavier he is, the _________ energy is needed to overcome gravity for the climb.

The _________ due to gravity (g) in m s–2 – it’d be much _________ to do this climb on the Moon.

Thus: ΔEp = m g Δh

E.g. 1

Calculate the gravitational potential energy of a 400Kg pile driver if it can fall 3 metres. G = 10NKg-1

Ep = m x g x h

=

A weightlifter lifts a 120 Kg barbell 2.4 metres above the ground. What is the weight of the barbell (g = 10NKg-1) Weight Fgravity = mg

=

How much work is done lifting the barbell? Work = Fd

=

What is the gravitational potential energy of the barbell at the top of the lift? Ep = m x g x h

=

Success Criteria

Complete Scipad page 203

SLO

Define the term kinetic energy

Use the formula Ek= 1/2mv2 to calculate kinetic energy

Kinetic energy (Ek) is the energy of ________objects.

The greater an object’s __________, the greater its kinetic energy.

If two objects are travelling at the same speed, the one with the greater ___________ has more kinetic energy.

Where Ek is the kinetic energy in __, m is mass in kg, v is __________in m s-1.

Notice that when mass is ________, Ek doubles, but when ________ is doubled, Ek goes up by a factor of __________ (22). (faster you go the bigger the mess)

Kinetic energy

Kinetic Energy The energy possessed by a moving object is called

____________

Kinetic Energy Ek Kinetic Energy = ½ mv2

M = mass Kg, v = velocity or speed in m/s

No movement = ________________

Kinetic energy depends on the ___________of the velocity, so if velocity is double, kinetic energy increases four times

So a car going twice as fast has ______________the amount of kinetic energy to lose before it will stop (four times the breaking distance)

E.g. Calculate the kinetic energy of a 5 Kg cat running at 2m/s Kinetic Energy = ½ mv2

= Task:Complete questions 1-3 purple book page 144

Success Criteria


Rosemary skis down a slope in a straight line, as shown in the diagram below. At the bottom of the slope, her speed is 8 ms-1. The combined mass of Rosemary and her skis is 80 kg.

Calculate the kinetic energy of Rosemary and her skis as she reaches the bottom of the slope when she is moving at 8 ms-1. Give an appropriate unit for your answer.

The kinetic energy gained by Rosemary when she reached the bottom of the slope does not equal the energy she had when she was stationary at the top of the slope. Explain using the principles of physics why her energy at the top of the slope and her energy at the bottom of the slope are not equal. In your answer, you should: name the type of energy Rosemary has at the top of

the slope calculate the difference between her kinetic energy at

the bottom of the slope and her energy at the top of the slope

justify the difference between her kinetic energy at the bottom of the slope and her energy at the top of the slope.

SLO

Define the term work

Use the formula W=Fxd to calculate work, force or distance

Work Work is done when a _______________an object over a

distance If work is done to an object, then ___________is

transferred The gain in energy is _____________ to the work done

Work is in joules (J), Energy is in joules (J)

Work done = _______________

Work done =

No movement = no work!

E.g. Calculate the work done when a 12 N force moves an object through 0.2 m W = Fd

Complete questions 1-4 on page 135 purple book

Success Criteria


A crane lifting a car from the bottom of a cliff. The cable of the crane pulls the car with a force of 14 000 N for 25 seconds but is not ableto move it

Explain why no work has been done on the car even though the cable pulls with a force of 14 000 N for 25 s.

Sam accelerates for the first 2 seconds of a race. During this time, he covers a distance of 9 m. His mass is 60 kg. Calculate Sam’s accelerationduring the first 2 seconds, AND then calculate the work done to cover the distance of 9 m

SLO

Define the term power

Use the formula P= W/t to calculate power, work or time

Power Power is a measure of ________________at which

work is done or energy is supplied or used. Power P watts

E.g. A weight lifter lifts a weight in 3.5 seconds. The work done is 2880J (this can be calculated from Wk = Fd). Calculate the power that his muscles generated. P = W/t

= Complete questions -4 on page 150 purple book

Success Criteria

Complete Scipad pages 209-215

A force of 16 000 N is used to pull a car upwards using a crane. The car is lifted 24 m over a period of 80 s.

Calculate the power output of the crane to pull the car up 24 m. Give an appropriate unit for your answer. (HINT: you need to calculate work done first)

Mechanics Class Notes

Education

Transcript of Mechanics Class Notes