Download Mechanics Notes 2011

Year 11 Mechanics
AS90940 Version 1
Achievement Standard
Subject Reference
Science 1.1
Title
Demonstrate understanding of aspects of mechanics
Level
1
Subfield
Science
Domain
Science - Core
Credits
4
Assessment
External
Status
Registered
Status date
30 November 2010
Planned review date
31 December 2014
Date version published
30 November 2010
This achievement standard involves demonstrating understanding of aspects of
mechanics and may include using methods when solving related problems.
Achievement Criteria
Achievement
Achievement with Merit
Achievement with
Excellence
 Demonstrate
understanding of
aspects of mechanics.
 Demonstrate in-depth
 Demonstrate
understanding of aspects
comprehensive
of mechanics.
understanding of aspects of
mechanics.
Explanatory Notes
1
This achievement standard is derived from The New Zealand Curriculum, Learning
Media, Ministry of Education, 2007, Level 6. It is aligned with the Physical
Inquiry and Physics Concepts achievement objectives in the Physical World strand
and the Communicating in Science achievement objective in the Nature of Science
strand, and is related to the material in the Teaching and Learning Guide for
Science, Ministry of Education, 2010 at http://seniorsecondary.tki.org.nz.
2
Demonstrate understanding of aspects of mechanics typically involves providing
evidence that shows awareness of how simple facets of phenomena, concepts or
principles relate to given situations. This may include using methods for solving
problems involving aspects of mechanics.
Demonstrate in-depth understanding of aspects of mechanics typically involves
providing evidence that shows how or why phenomena, concepts or principles
relate to given situations.
3
1
4
Demonstrate comprehensive understanding of aspects of mechanics typically
involves providing evidence that shows how or why phenomena, concepts and
principles are connected in the context of given situations. Statements must
demonstrate understanding of connections between concepts.
5
Evidence may be written, mathematical, graphical or diagrammatic.
6
Aspects of mechanics will be limited to a selection from the following:
 Distance, speed, interpretation of distance and speed time graphs, average
acceleration and deceleration in the context of everyday experiences such as
v
d
journeys, sport, getting going. The relationships v =
.
a
t
t
 Mass, weight and the acceleration due to gravity, balanced and unbalanced
forces, in the context of everyday experiences such as being stationary, moving
at constant speed, accelerating. The relationship Fnet = ma.
 Force and pressure in the context of everyday experiences. The relationship
F
P=
.
A
 Work and power, gravitational potential energy, kinetic energy, and the
conservation of mechanical energy in free fall situations in the context of
everyday experiences such as sports performance, dropping things, tossing
balls. The relationships EP = mgh EK =
7
W
1
mv2 W = Fd P =
.
2
t
Assessment Specifications for this achievement standard can be accessed through
the Science Resources page found at www.nzqa.govt.nz/ncea/resources.
Points 2-4 describe what students will need to do for achieved, merit
and excellence.
Point 6 contains the content we will need to cover in this topic for you
to achieve points 2-4
2
Exploring Motion with Bloom’s Revised Taxonomy
Remembering
Draw and label a car in motion and label all the forces
acting on it.
Understanding
Explain what you can tell about the motion of the car
by looking at the size of the arrows in your diagram.
Applying
(a)What information do you need to calculate the
speed of a moving car, what formula will you use and
what are the units.
(b)When you have answered part (a) your teacher will
give you some actual data to find the speed.
Analysing
Have you calculated the average speed or the actual
speed and what is the difference between these two
values.
Evaluating
When would the average speed be a useful piece of
data and when would the actual speed be a useful
piece of data.
Creating
Imagine a journey to school on a school bus where
the speed of the bus is measured every minute, draw
what a speed time graph for the journey might look
like then explain what the sections might represent
3
Using Equations as Tools in Physics
Equations are used to calculate unknown information from the
information we are given. It is very important that you recognize what
the letters in these equations stand for and what the units of the
variables are.
These are the eight equations you may need to use in this topic
v=
d
t
EP = mgh
a
v
t
EK =
1
mv2
2
Fnet = ma
P=
F
A
W = Fd
P=
W
t
Firstly you need to know a couple of important facts
  or delta means ‘a change in…’ so t means the change in
time or how much time it took
 P has two different meanings, power and pressure. LABEL THE
ABOVE EQUATIONS TO DISTINGUISH THEM.
How much of the following table can you complete?
Equation
Quantities
SI Units
-1
d
v = velocity
ms , metres per
v=
t
second
m , metres
d = change in
distance
s, seconds
t = change time
a
v
t
Fnet = ma
4
P=
F
A
EP = mgh
EK =
1
mv2
2
W = Fd
P=
W
t
The next step is to be able to put numbers into these equations and
calculate unknowns.
Why are only SI units used in calculations?
5
Problem Solving Template
In physics problems we often have to do calculations, if the following
method is used you will find problems easier and minimise the
chance of mistakes.
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Example 1
Mr Kee is late for class and runs 85 metres from the science office to
K7. It takes him 25 seconds. What is his average speed?
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
6
Example 2
A force of 120N is applied over an area of 0.5m2 what is the
pressure?
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
Example 3
A car has a mass of 3500kg, it is traveling at 50ms-1, what is the
kinetic energy (EK) of the car?
Step 1
Step 2
Step 3
Step 4
Step 5
Step 6
QuickTime™ and a
decompressor
are needed to see this picture.
7
Task
It isn’t always as straightforward as you sometimes have to rearrange
a formula and the units sometimes have to be changed. For example
you may be given a speed in km/hr instead of m/s and a distance and
asked to work out a time. Write a problem which contains both of
these problems then answer it showing your working out.
Summary
Fill in the following conversions of units:
The SI unit for velocity/speed is m/s or ms-1.
Distance conversions:
?
?
Km
m
cm
?
m
mm
m
Time conversions:
?
hour
?
s
min
s
LEARN THESE AS YOU ARE EXPECTED TO KNOW THEM!
8
Real life calculations
The following tasks are designed to allow you to use physics to
analyse real life situations and use known measurements to calculate
unknown information. In each case plan what you are going to do and
then carry out the task and record your measurements and
calculations clearly. If you are unable to complete a task ask for the
help sheet for that task. If you make any assumptions to help you
complete the task record them.
Task 1
Calculate your top speed for running forwards and backwards.
What will you measure?
Results
Calculations
Final answer
Task 2
Catch a mini beast and calculate its average speed, make at least 3
sets of measurements.
What will you measure?
Results
Calculations
Final answer
9
Task 3
Calculate the pressure you exert on the ground
when stood on one foot.
QuickTime™ and a
decompressor
are needed to see this picture.
Task 4
Calculate the kinetic energy (Ek) you have when you are walking and
running.
10
QuickTime™ and a
decompressor
are needed to see this picture.
Task 5
Devise a method to measure the distance and
speed at 5 different positions of a person traveling
at a steady speed on a skateboard.
Design a table and record your results.
Plot graphs of distance against time and speed
against time on your own graph paper. Make sure
they are PLUSST.
Method
Results
Conclusion
Write a few sentences to summarise what your graphs show.
11
Task 6
Devise a method to measure the distance and the speed at 5
different positions of a person traveling from rest down a steady slope
on a skateboard.
Design a table and record your results.
Plot graphs of distance against time and speed against time on your
own graph paper. Make sure they are PLUSST.
Calculate an acceleration from the graph.
Method
Results
Calculation
Conclusion
Write a few sentences to summarise what your graphs show.
12
Task 7
Find the work done to get you from the bottom of the science stairs to
the top and then work out your power.
Task 8
Use the slingshot to fire a water balloon vertically, work out the
speed/velocity when it leaves the slingshot and from this the force
provided by the slingshot.
13
Distance vs Time graphs and Speed vs Time Graphs
Distance time graphs tell the story of a moving object in terms of the distance
travelled and the time taken, different shapes on the graph represent different
types of motion. Speed time graphs also tell the story but are not the same shape
as the distance time.
Your teacher will demonstrate how distance and velocity sensors can be used to
plot distance vs time and speed vs time graphs.
Distance vs Time
sketch graph
Description of
motion
Speed vs Time
sketch graph
14
Distance vs Time
sketch graph
Description of
motion
Speed vs Time
sketch graph
15
Summary
Part A
On the axis below draw a sketch of a distance vs time graph, which has the
following features:
a section that represents
 low speed
 high speed
 acceleration
 deceleration
 a stationary object
Label each axis and section clearly.
Part B
On the axis below draw a sketch of a speed vs time graph, which has the
following features:
a section that represents
 low speed
 high speed
 acceleration
 deceleration
 a stationary object
Label each axis and section clearly.
16
What other information can we get from motion graphs?
Once we have a graph that tells us the story of the motion of an object there are
other things we can work out.
1. Gradient/Slope
When you work out the gradient/slope of a graph you use the following formula:
Gradient/Slope =
Change in y
Change in x
OR
y
x
Look back at the summary graphs you drew on page 16. Fill in the labels on
the x and y axes into the formula below. What does it calculate?
Part A
Gradient/Slope = change in _________ = ………………..
change in
Part B
Gradient/Slope = change in _________ = ………………..
change in
2. Distance Travelled
Also on a speed vs time graph the area under the graph represents the
distance travelled.
Revision
Find the area under the following speed vs time graphs. Hence, calculate d the
distance travelled.
1.
25 m/s
10 s
2.
20m/s
32 s
28 s
17
Use these facts and what you have already learned to help you answer the
following NCEA questions.
QUESTION ONE: CYCLING
NCEA 2006
Toni cycles each day on her mountain bike.
The distance-time graph below shows part of her journey on one day.
(a)
How far, in metres, does Toni travel in the first 360 seconds?
(b)
Calculate Toni’s average speed over the 540-second bike journey.
Average Speed =
ms–1
(c) Describe the motion of Toni and the bike during Section A.
(d) Using the graph above, show that the speed of Toni and the bike during
Section B is 8.3 ms–1
18
QUESTION TWO: SPORTS TRAINING NCEA 2007
The speed-time graph below represents sprint training for an athlete.
(a)
State the speed of the athlete at 10 seconds.
(b)
Speed = _______ ms–1
Describe the motion of the athlete between 12 and 13 seconds.
(c)
Calculate the acceleration of the athlete during the first 8 seconds.
acceleration =
(d)
ms–2
Using the graph, calculate the total distance travelled by the athlete in
the first 12 seconds.
19
QUESTION 3 SKYDIVING NCEA 2005
The speed-time graph below shows the motion of Ariana and the jumpmaster
from when they leave the plane until after the parachute is released.
(a)
Describe the motion of Ariana and the jumpmaster during the first 10
seconds.
(b)
Calculate how far Ariana and the jumpmaster fell during the first 60
seconds.
Distance travelled =
(c)
_________ metres
Calculate the acceleration in the first 10 seconds.
20
Compare and Contrast
Distance time graphs
Speed time graphs
How are they alike
How are they different
With regard to
Patterns of significant similarities and differences
Conclusion
21
Dynamics
Dynamics is the study of the forces acting on objects and what effect
they have.
Your teacher will give a lecture to the class using a powerpoint
presentation, as you watch the presentation make notes from the
relevant slides.
Slide 1
What are forces measured in?
Slide 2
Describe three types of motion caused by
forces.
What two pieces of information do the arrows
in a force diagram give you?
Slide 3
Describe the motion of objects with balanced
forces.
Slide 4
Describe the motion of objects with unbalanced
forces.
Slide 5
Why is the second truck more suitable for the
job?
Slide 6
Can you name four forces acting on a moving
car?
Slide 7
Slide 8
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Slide 9
Slide 10
Explain why a falling object reaches a terminal
velocity.
Slide 11
How many names of friction forces do you
know?
Slide 12
Slide 13
Slide 14
23
Investigating Force and Motion
Your teacher will demonstrate a simple experiment using rubber
bands and blocks of wood.
You need to change two variables but only one at a time,
 vary the force initially using more rubber bands
 secondly vary the mass of the block
For each experiment this is called the ……………………. variable.
What variables will you always keep the same?
What variable will you measure (this is called the dependent
variable)?
Investigation 1 The independent variable is…………………..
Results
Force
(N)
You are going to discuss your results by describing two sets of data
from each investigation. Draw pictures and annotate the diagrams to
highlight similarities and differences and try to explain the differences.
You should draw and label each block at least three times on its
journey.
Words you may, or may not find useful are listed below:
Mass, Friction, Energy, Speed, Distance, Time, Acceleration, Force,
Balanced, Unbalanced.
24
Force 1
Force 2
Conclusion
25
Investigation 2 The independent variable is…………………..
Results
Mass
(kg)
Mass 1
Mass 2
Conclusion
26
Is that right?
Read the following information and pick out the correct and incorrect
statements and write them below.
Mass and weight are really the same thing. It doesn’t matter which
word you use. An average science teacher weighs about 80kg. They
have a mass of 80kg which would not change wherever they were in
the universe. Their weight is their weight force it is measured in
Neutrons, you can calculate your weight by dividing your mass by 10
(which is the gravity force on Earth). So a science teacher has a
weight of about 800N.
Correct
Incorrect
QuickTime™ and a
decompressor
are needed to see this picture.
From discussion of these ideas write your own definitions for the
following:
Mass is
Weight is
To calculate weight
27
Calculating Forces
We have shown:
 acceleration of an object is proportional to the net force applied
symbol:
a
 acceleration is inversely proportional to the mass of the object
symbol:
a
Putting these two expressions together we get the following formula:
Fnet = m a
Rearrange the formula to make m the subject:
Rearrange the formula to make a the subject:
Weight is a force so we can use this formula to calculate the weight of
objects on Earth.
Fgravity =
28
Mass of box = 2kg
Qui ckTime™ and a
Use these formulae to solve the problems on the next few pages.
Problems
decompressor
are needed to see thi s pi cture.
1. Calculate the weight of a 35 kg crate.
2. What is the acceleration produced by a 45 N force applied to a
1.25 kg ball?
3. What is the acceleration of a car stopping with 254 N of force if
it has a mass of 2500 kg?
4. What is the mass of a 35 kg dog falling from a bridge?
5. Calculate the acceleration on a 3000 kg car going from 4 m/s to
24 m/s in 5 seconds. Then calculate the net thrust force
required to produce this acceleration.
6. What is the acceleration of a 2.5 kg box if it is pushed with
7.7 N of force?
29
7. What is the net force (Fnet) when 45 N of force is moving a 5 kg
cart at constant velocity?
8. What is the mass of a box that weighs 25 N?
9. What does net force (Fnet) mean?
10.A box is pushed with 200N of force at constant velocity across
a concrete floor. How much is the frictional force that is working
against it?
11.A rocket can accelerate (increase velocity) very quickly from a
launching pad. The acceleration usually is not constant
however. In fact it usually accelerates more and more as the
flight increases. If the net force from the engine remains
constant, why does this happen?
Hint: Think about the mass of the rocket.
12. A baseball falls from a fifty story building. After 6 seconds the
ball reaches terminal velocity. What does this mean?
a. Draw a force diagram of the ball at terminal velocity.
b. What is the net force on the ball at terminal velocity?
30
NCEA Questions
Question 1 2007
(a) Describe the relationship between the push force and the
friction
force during the 8 seconds that the athlete is accelerating.
(b) When sprinting, the athlete wears sport shoes with spikes like
the ones shown below.
Explain how the effect of the spikes on the sport shoes changes
the effect of forces acting on the athlete and how this leads to an
improvement in performance.
31
Question 2
(a) On the diagram below, draw and label arrows to show the
directions of the following four forces:
gravity, support, push and friction
Question3
While travelling home, the bike accelerates at 1.5 m s–2 over a
distance of 25m as shown in the diagram (not to scale).
Toni and the bike have a mass of 70 kg.
(a) Using the equation F = ma, calculate the net force acting on the
bike when it is accelerating.
Four forces act on Toni and the bike while she rides: weight, support,
friction and push.
(b) On the diagram below, draw in arrows to show the directions of
ALL FOUR forces acting on Toni and the bike. Label the forces.
32
The four forces in the above diagram add together to give a net
force of zero.
(c) Explain why a net force of zero would result in Toni and the bike
moving at a constant speed.
33
Bank Robbery Shock !
Locals were stunned in Warkworth this weekend as details of a
daring, dastardly bank robbery emerged.
Local teachers Mr. Walker (1.72m, 85kg, 35 years) and Mr.Kee
(1.8m, 95kg, 21 years) are the prime suspects and are still at large in
the community.
Walker entered the bank and brandishing a metre rule demanded
money at 3.05pm exactly last Friday and was heard muttering about
a new sail for his dearest. The cashiers handed over $10,000 in used
notes and Walker fled the scene.
He left the bank at exactly 3.06pm stopping at the door just as the
getaway car(blue, 1020 kg, 1972 Falcon) driven by Kee rolled past at
a steady speed of 3m/s. Showing amazing physical stamina Walker
accelerated steadily until he caught up to the car after 4 seconds and
threw himself in through the open passenger window.
Kee put the pedal to the metal and, in a cloud of green smoke the car
accelerated to 21m/s in 3s as it passed Books and More. With Irish
cool and muttering ‘Go boyo, go’ he continued on at that speed for
another 23 seconds towards the college.
Police attempted to intercept the vehicle as it arrived on state
highway one but Kee switched on the nitrous oxide boosting the
thrust force to 5000N for 5 seconds. Even with the opposing friction
force of 1400N the car blasted away from the cops
Unfortunately just as the car reached top speed it ran into a school
bus(5000kg) turning into Woodcocks road and locked together in a
mass of twisted metal they came to rest in 2 seconds. In a miracle of
physics over common sense both suspects escaped unhurt with the
cash and haven’t been seen since.
34
What could you do with all this information?
Use the Fw = mg formula
to find the weight force
of.......
Draw a d/t graph for…
Find the average
speed of…..
Draw a v/t graph for…
Work out the speed
of..
Find an acceleration
using a change in
speed over a certain
time
Draw a diagram
showing the forces
acting on…….
Find an acceleration
using F=ma of…..
Find an acceleration
on a v/t graph of…..
Find a distance
travelled on a v/t graph
of……..
Find the net force
when……
And…….
35
Pressure and Force
Experiment 1
Place a 1kg mass in a tray of flour, look at the depth of the imprint in
the flour. Repeat the experiment but place the mass on a large
cardboard square, how deep is the imprint?
What is the mass of the 1kg mass?
What is the weight of the 1kg mass?
Why is there a difference in the experiment?
What formula have we used that could be used to analyse the
results?
Can you think of some everyday applications of this principal?
What is the difference between the pressure and the force?
Experiment 2
Collapsing can demo, watch the demo and explain what you see.
Use scientific keywords to explain your observations.
36
Power, Work and Energy
The following excerpt from a Physics website describes power work
and energy. Read it carefully.
“What is Work, Energy and Power?
Definitions
Work can be defined as transfer of energy. In physics we say that work is done on
an object when you transfer energy to that object. If one object transfers (gives)
energy to a second object, then the first object does work on the second object.
Work is the application of a force over a distance. Lifting a weight from the ground
and putting it on a shelf is a good example of work. The force is equal to the weight
of the object, and the distance is equal to the height of the shelf (W= Fxd).
Work-Energy Principle --The change in the kinetic energy of an object is equal
to the net work done on the object.
Energy can be defined as the capacity for doing work. The simplest case of mechanical
work is when an object is standing still and we force it to move. The energy of a moving
object is called kinetic energy. For an object of mass m, moving with velocity of magnitude
v, this energy can be calculated from the formula E= 1/2 mv2
Types of Energy
There are two types of energy in many forms:
Kinetic Energy = Energy of Motion
Potential Energy = Stored Energy
Forms of Energy
Solar Radiation -- Infrared Heat, Radio Waves, Gamma Rays, Microwaves, Ultraviolet Light
Atomic/Nuclear Energy -energy released in nuclear reactions. When a neutron splits an atom's
nucleus into smaller pieces it is called fission. When two nuclei are joined together under millions
of degrees of heat it is called fusion
37
Electrical Energy --The generation or use of electric power over a period of time expressed in
kilowatt-hours (kWh), megawatt-hours (NM) or gigawatt-hours (GWh).
Chemical Energy --Chemical energy is a form of potential energy related to the breaking and forming
of chemical bonds. It is stored in food, fuels and batteries, and is released as other forms of energy
during chemical reactions.
Mechanical Energy -- Energy of the moving parts of a machine. Also refers to movements in humans
Heat Energy -- a form of energy that is transferred by a difference in temperature
What is Power
Power is the work done in a unit of time. In other words, power is a measure of how quickly work can be
done. The unit of power is the Watt = 1 Joule/ 1 second.
One common unit of energy is the kilowatt-hour (kWh). If we are using one kW of power, a kWh of energy
will last one hour.
Calculating Work, Energy and Power
WORK = W=Fd
Because energy is the capacity to do work , we measure energy and work in the same units
( joules).
POWER (P) is the rate of energy generation (or absorption) over time:P = E/t
Power's SI unit of measurement is the Watt, representing the generation or absorption of energy at the
rate of 1 Joule/sec. Power's unit of measurement in the English system is the horsepower, which is
equivalent to 735.7 Watts.”
Write 3 questions you have about the ideas in this passage.
Create definitions in your own words for work energy and power.
38
The flying ball and the weight lifter
Imagine someone hitting a ball straight up with a cricket bat,
assuming no energy is lost through air friction the kinetic energy it
has when it leaves the bat will all be turned into gravitational potential
energy when it arrives at its peak.
Draw force diagrams which show your understanding of the forces
acting on the ball throughout its journey then try the problems below.
39
NCEA Questions
Question 1 2004
(a) The ball left the bat with an initial speed of 20 m s–1. The mass of
the ball is 160 g (0.16 kg). Use the formula Ek = 1–2 mv2 to find
the initial kinetic energy of the ball.
Kinetic energy =
J
(b) Assuming that the energy is conserved throughout the upward
flight of the ball, calculate the maximum height reached by the
ball.
Maximum height reached =
(unit)
(c) How much work was done on the ball as it was rising?
40
Question 2 2007
The athlete lifts a 100 kg set of weights above his head, so that the
height is changed by 1.5 m.
(a) Using the formula Fw = mg, calculate the weight force of the
weights.
Weight =
N
(b) Calculate the work done by the athlete to lift the weights to the
new height of 1.5 m above its original position. Give an
appropriate unit.
Work =
(
)
unit
(c) Describe the major energy change that occurs when the athlete
drops the weights from the new height.
(d) If it took the lifter 1.2 seconds to lift the weights how powerful is
he?
41