year 12 physics as 91171 (part 1 of 4) introduction to

12 Physics Craighead

Townshend 1

Year 12 Physics

AS 91171 (Part 1 of 4)

Introduction to Mechanics

2020

NAME: _______________________


Townshend 2

Solving simple physics problems

• Can identify the symbols and units for distance, time, velocity, force, energy and acceleration.

• Can solve simple physics problems by identifying variables, selecting and rearranging equations.

Show understanding of physics (Achieved)

For each of the following questions

I. Identify the subject of the question (what we need to find out)

II. Identify the values given

III. Write down the equation needed to solve the problem

IV. Rearrange the equation

V. Substitute in the values and solve the problem

Example

What is the distance travelled by a car that travels at an average speed of 30 m s-1 for 15

seconds?

Exercises

1. What is the force of gravity acting on a 6.0 kg brick?

2. What is the mass of an object that is accelerated at a rate of 1.5 m s-2 by a 10 N force?

3. What is the change in speed of a dog that accelerates at 3.0 m s-2 for 3.5 seconds?

4. What height above the ground is a 50 kg girl who has 340 J of gravitational potential

energy?

subject = d

v = 30 m s-1

t = 1.5 s

I. II.

III. IV. V.

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d v t =

1d 30 m s 15 s 450 m−= =


Townshend 3

Significant figures

Identify the least number of significant figures supplied by the values in the question. In question 4 the

least number of significant figures is 2 as the value 50 kg only has 2 significant figures. The final answer

to any question should always be written so it has the same number of significant figures as the value

with the least number of significant figures. In this case the answer will be written as 0.69 m.

5. Place the following numbers into the correct significant figure (sig. fig.) box below:

0.07, 12.0, 0.8, 1300, 9, 125, 0.032, 0.007, 0.4213

1 sig. fig. 2 sig. fig. 3 sig. fig. 4 sig. fig.

6. What is the force of gravity acting on a 56 kg boy?

7. What is the acceleration of a 800 kg car that has a net force of 340 N acting on it?

8. What is the average velocity of a bike that travels 80 meters in 5.5 seconds?

9. How long does it take for a jet accelerating at 32 m s-2 to go from standing still to 220 m s-1?

10. What distance does a girl cover if she runs at a constant speed of 220 m s-1 for 120 s?


Townshend 4

Quantities and units

• Can identify the expected unit of an answer by using the equation to multiply or divide units.

Physical Quantities and their standard units

Physical Quantity Quantity

Symbol

Standards Unit Name Unit

Symbol

Length d, l, h, x meter m

Mass m kilogram kg

Time T, t second s

Velocity v meters per second m s-1

Acceleration a Meters per second per second m s-2

Force F newton N

Energy E joule J

Power P watt W

Momentum p Kilogram meters per second kg m s-1

Torque τ torque N m

Deriving Units

Often the units for an unknown quantity are derived (worked out) from the quantities that were used to

calculate the unknown value. These derived units are often combinations of m, kg, and s. When we

derive units we use the same rules for multiplying and dividing exponents.

Example

11. Prove that the unit for v is ms-1 given that v=d/t

The exponents of unlike

quantities cannot be combined

Any value with an exponent of

0 equals 1

When any two identical quantities

are multiplied, the exponents of

the numbers are added.

Any value without an exponent

written has an exponent of 1.

When any quantity is divided into another, the exponent is equal

to multiplying by the negative exponent of the quantity.

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1x x=

1m m=

1 1 2m m m m m = =1 1 1 1x m x m x m = =

2 1 2 3m m m m m = = 11 1 0

11

m mm m m

m m

−= = = =

11 1 1

1

m mm s ms

s s

− −= = =


Townshend 5

12. Calculate the area for a rectangle 3.1 m long and 2.4 m wide. Prove that the unit for area is m2.

13. Derive the unit for acceleration.

What is a Jerk?

Velocity is also called the ‘first derivative’ of distance with respect to time. In this case, the change in

distance over time is calculated. Acceleration is the ‘second derivative’ of distance in respect to time.

This is calculated by the dividing the change in velocity by time. It so happens we can also calculate a

value for the change in acceleration over the change in time, this quantity is called a ‘jerk’ and is a ‘third

derivative’ of distance by time. We can also measure the change in Jerk over time and this ‘fourth

derivative’ is called a ‘jounce’. The quantities of jerk and jounce are often used to measure the

experience felt on rollercoasters and other amusement rides.

A highly reproducible experiment to demonstrate jerk is as follows: Brake a car, starting at a modest

speed, in two different ways:

• apply a constant, modest force on the pedal till the car comes to a halt, only then release the

pedal;

• apply the same, constant, modest force on the pedal, but just before the halt, reduce the force

on the pedal, optimally releasing the pedal fully, exactly when the car stops.

The reason for the by-far, bigger jerk in the first way to brake, is a discontinuity of the acceleration,

which is initially at a constant value, due to the constant force on the pedal, then drops to zero

immediately when the wheels stop rotating. Note that there would be no jerk if the car started to move

backwards with the same acceleration. Every experienced driver knows how to start and how to stop

braking with low jerk.

Example

14. Write the equations that we would use to calculate the Jerk and jounce of a moving object. Show, by

proof, the units for Jerk and jounce.


Townshend 6

Multipliers and Standard form

• Can Identify and use the prefixes M, k, m, μ, η and ρ to convert the magnitude of numbers.

• Can present answer in appropriate format using standard form and multiplier prefixes.

Standard prefix multipliers

prefix symbol Standard form Multiplier

number

Example

giga G x 109 x 1000 000 000 8 Gbytes

8 x 109 bytes

mega M x 106 x 1000 000 15 MTon

15 x 106 ton

kilo k x 103 x 1000 85 km

85 x 103 m

milli m x 10-3 x 0.001 2.7 mg

2.7 x 10-3 g

micro μ x 10-6 x 0.000001 7.9 μF

7.9 x 10-6 F

nano n x 10-9 x 0.000000001 112 nm

112 x 10-9 m

pico p x 10-12 x 0.000000000001 32 pHz

32 x 10-12 Hz

Exercise

15. Draw lines to connect the prefix, symbol, standard form and number for the multipliers.

prefix symbol Standard form number

giga G x 103 x 0.000000000001

killo M x 10-9 x 0.000000001

mega k x 10-3 x 0.000001

micro m x 109 x 0.001

milli μ x 10-12 x 1000

pico n x 106 x 1000 000

nano p x 10-6 x 1000 000 000


Townshend 7

Exercise

16. Convert each of the following into their standard unit. Use the examples from the table as help.

a. Wavelength of red light = 630 nm =

b. Distance from Earth to Sun = 149.6 Gm =

c. Velocity of Moon relative to Earth = 1.022 km s-1 =

d. Time of a Year = 31.6 Ms =

e. Diameter of carbon atom = 70 pm =

f. Width of human hair = 100 µm =

g. Speed of light = 300 Mm s-1 =

h. Mass of the Blue Whale = 190 Mg =

Standard form

Before any calculation is carried out, all given quantities need to be converted into the standard units.

Exercise

17. Convert each of the following numbers into standard form.

a. Mass of the Blue Whale = 190,000,000 g =

b. Wavelength of red light = 0.000000630 m =

c. Distance from Earth to Sun = 149600000000 m =

d. Velocity of Moon relative to Earth = 1022 m s-1 =

e. Time of a Year = 31600000 s =

f. Diameter of carbon atom = 0.000000000070 m =

g. Width of human hair = 0.000100 m =

h. Speed of light = 300 Mm s-1 =

The decimal point is

moved until it is to the

immediate right of the

first non-zero number.

The decimal was moved three places to the right so

the exponent in the standard form becomes -3.

The decimal point is

moved until it is to the

immediate right of the

first non-zero number.

The decimal was moved four places to the left so

the exponent in the standard form becomes 4.

30.00123 1.23 10 m m−=

456700 5.67 10 s s=


Townshend 8

Exercise

Complete each of the following steps for the following questions.

I. Convert each quantity into standard SI units

II. Write the number in standard form

III. Cary out the calculation

IV. Write the answer in standard form

V. Write answer using prefix

18. The Saturn V rocket, used to launch the Apollo moon missions, had a thrust of 34.0 MN and a mass

of 2.29 Gg. What was the acceleration of this rocket as it left the ground?

Physical

Quantity

Value with

multiplier

Prefix

multiplier

Value in

standard units

Standard

form

force, F 34.0 MN x 106 34.0 x 106 N 3.4 x 107 N

mass, m 2.29 Gg x 109 2.29 x 106 kg 2.29 x 106 kg

acceleration, a

19. The fastest snail travels at a top speed of 13 mm s-1. How long would it take

a snail to complete a lap of the ‘Levels’ race track, 2.4 km, traveling at top

speed?

Physical

Quantity

Value with

multiplier

Prefix

multiplier

Value in

standard units

Standard

form


Townshend 9

20. In the middle of summer in South Canterbury, grass can grow up to 11 mm

a day. How fast is the grass growing in SI units? How much will the grass

grow in 10 minutes?

Physical

Quantity

Value with

multiplier

Prefix multiplier Value in

standard units

Standard form

21. If it takes the grass 2.0 hours for the grass to reach its maximum growing rate of 11 mm per day,

what was the acceleration of the tip of the grass blades?


Townshend 10

Scalar and Vector quantities

• Can describe the difference between distance and displacement.

• Can identify scalar and vector quantities.

Distance is how far an object has travelled in meters. Displacement, is the shortest distance and the

direction of an object from its origin.

For instance, if you drive from Timaru to Greymouth, the distance of your journey could be 350 km.

This is a scalar quantity, as only a magnitude is given. If we draw an arrow starting at Timaru and

finishing at Greymouth, this arrow is called a vector. The length of this arrow represents the magnitude

of the displacement (220 km) and the angle from North (1°) represents its direction.

Displacement has both a magnitude and a direction so it is a vector quantity.

Velocity, Force and Acceleration are also vector quantities. Much of the work done in this Mechanics

topic involves calculations using vector quantities

Scalar Vector

distance displacement

speed velocity

acceleration

force

mass

time

tail

tip

The direction of the vector is often written as a

bearing. That is the angle that is measured

clockwise from 0°/360° angle(North).


Townshend 11

22. A student walks 10.0 m East along a path. She then turns to the South and walks another 10.0 m.

What distance did she travelled?

23. A girl walks 80 m South, 50 m East, then 50 m North? What distance did she travel? What is her

displacement?

A

B

10.0 m

10.0 m


Townshend 12


Townshend 13


Townshend 14

Adding vectors on one dimension

• Can add vectors in one dimension.

If the calculations involve vectors acting in one dimension; right/left, backwards/forwards, up and down

we assign one direction positive and the other negative and then carry out the calculation using linear

algebra. However, if the vectors involved interact in two dimensions, then we need to use trigonometry

to solve the problem.

• Two velocities acting on one object – add the two velocities (vobject 1 + vobject 2)

• Two separate objects – find the difference (vobject 1 - vobject 2)

Evaluate the final answer using common sense.

Exercise

24. A truck is travelling at 10.0 m s-1. A girl sprints off the back of the

deck at 3.5 m s-1. What is her velocity relative to the ground?

25. A traveller walks 3.0 m s-1 against the direction of a baggage conveyor

that is moving at 2.5 m s-1. What is her velocity relative to a bag on

the conveyor coming towards her?

26. A boy runs at 7.5 m s-1 up a down escalator that is travelling at 3.5

m s-1. What is his velocity relative to a man standing on a flight of

stairs beside the escalator?

10.0 m s-1 3.5 m


Townshend 15

27. What is his velocity relative to a girl standing on the up escalator that is travelling at 3.5 m s-1?

Adding vectors in two dimension

• Can add vectors in two dimensions.

Example

Velocity has both magnitude and direction. There are two methods to

calculate the magnitude and the angle of the resultant vector.

A football is kicked up-field at a constant speed of 12.0 m s-1. A cross

field wind blows at 6.0 m s-1. What is the velocity of the ball relative to

the ground?

Method 1: Draw the vectors to scale “tip to tail”. Draw

the resultant vector with its tail starting from the tail of

the first vector and its tip meeting the tip of the second

vector. Measure the length of the vector with a ruler and

the angle between the resultant vector and the initial

vector.

Method 2: Measure the length of the resultant vector

using Pythagoras’s theorem 2 2 2a b c+ = and the angle

the of resultant vector using tano

a = .

𝑎2 + 𝑏2 = 𝑐2

𝑐 = √𝑎2 + 𝑏2

𝑐 = √(12.0 𝑚 𝑠−1)2 + (6.0 𝑚 𝑠−1)2

𝑐 = 13.416 𝑚 𝑠−1 = 13 𝑚 𝑠−1

𝑡𝑎𝑛 𝜃 =𝑜

𝑎=

6.0 𝑚 𝑠−1

12.0 𝑚 𝑠−1

𝜃 = 𝑡𝑎𝑛−1(0.5)

𝜃 = 26. 6∘

The ball travels at 13 ms-1 at an angle of 27°.

6.0 m s-1 12.0 m s-1

12.0 m s-1

6.0 m s-1

resultant

Θ


Townshend 16


Townshend 17

Exercise

28. An aeroplane heads south at 80 m s-1. There is a westerly wind of 15

m s-1. What is the resulting velocity (direction and magnitude) of the

aeroplane?

29. A girl paddles a kayak at 5.0 m s-1 at 90⁰ from a river bank. The

current of the water flows at 3.0 m s-1. What is the girl’s velocity? If

the river was 20 m wide, how far down the river was the girl when

she reached the opposite shore?


Townshend 18

30. A pilot flies an aeroplane through the air northeast at 80 m s-1. There

is a 20 m s-1 nor’wester blowing. What is the velocity (magnitude

and direction) of the aeroplane relative to the ground.

31. A girl wishes to paddle a kayak at right angles to a river bank. The

current of the water flows at 1.0 m s-1? The girl can paddle at

3.5 m s-1. At what angle does the girl have to paddle in reach the

opposite shore? * More difficult question


Townshend 19

• Can work out the resultant vector by adding two vectors.

• Can work out the resultant vector by subtracting vectors.

To travel from Timaru to Christchurch, an aeroplane needs to travel

north east. The pilot wishes the plane to travel at 80 m s-1 relative to

the ground, and there is a 20 m s-1 nor’wester blowing? What is the

velocity (magnitude and direction) that the aeroplane has to head in?

Draw the initial vector. Draw the resultant vector originating from the

same place as the initial vector. The missing vector is

the vector that would add tip to tail to the initial vector

to produce the resultant vector.

𝑎2 + 𝑏2 = 𝑐2

𝑐 = √𝑎2 + 𝑏2

𝑐 = √(80 𝑚 𝑠−1)2 + (20 𝑚 𝑠−1)2

𝑐 = 82.46 𝑚 𝑠−1 = 82 𝑚 𝑠−1

𝒕𝒂𝒏 𝜽 =𝒐

𝒂=

𝟖𝟎 𝒎 𝒔−𝟏

𝟐𝟎 𝒎 𝒔−𝟏

𝜽 = 𝒕𝒂𝒏−𝟏 (𝟖𝟎

𝟐𝟎)

𝜽 = 𝟕𝟓. 𝟗𝟔∘ = 𝟕𝟔°

76°-45°=31°

Ground

speed

80 m s-1

wind

20 m s-1

resultant

80 m s-

1

20 m s-1

resultant


Townshend 20

32. A Captain of a ferry wishes to sail directly across the Amazon river.

The river is 8.0 km wide and flows at 0.61 m s-1. What is the average

velocity (speed and direction) the ferry must sail in order to cross the

river in 30 min?

33. A girl wishes to paddle a kayak at right angles to a river bank. The

current of the water flows at 1.0 m s-1? The girl can paddle at 3.5 m

s-1. At what angle does the girl have to paddle to reach the opposite

shore? * More difficult question


Townshend 21

Definitions

Magnitude, direction, displacement, multiplier, value, quantity, vector, standard form, deriving,

significant figures, initial, unit, velocity, direction, trigonometry rearranging, scalar

Key Word Definition The digits of a number used to express the accuracy, beginning from first nonzero

number.

Algebraic manipulation used to isolate the subject of a problem on the left hand side of an equation.

A physical property that can be quantified by measurement.

The number of a measured quantity.

The standard measurement for a quantity, given so measured results are reproducible.

Algebra used to calculate the units of a quantity..

Quantities where only a magnitude is given.

Quantity where the magnitude and direction are given.

The size of a quantity, represented by a number.

The values of a vector represented by an angle or bearing.

The product of the addition of two vectors.

The start.

Using the properties of triangles are used to solve problems.

Also called Scientific Notation. A convenient way to write down very large and very small numbers.

Both the direction and the magnitude in meters of an object from its initial point.

This quantity has both speed and direction.

A value written before a unit that represents how much larger or smaller the unit is than the unit written.


Townshend 22

End of topic – Practice Test

1. Measure the mass of your pen, record the mass in standard units using

standard form.

2. Imagine you are walking at 2.25 m s-1 and you throw a pen to your right at

5.00 m s-1. Assuming no friction, what is the velocity of the pen with

respect to the direction you are walking as it moves through the air?

3. Momentum is a physical quantity that represents an objects ability to keep moving. It has the

symbol, p and can be calculated using the equation below. Calculate and derive the unit for the

momentum of this pen.

4. Unfortunately another classmate has also thrown their pen and it is traveling towards you as you are

walking at a velocity of 5.75 m s-1. What is the velocity of the classmate’s pen relative to you?

5. During this experiment you walked 10 m North then 5.0 m East and then 7.0

m South. Calculate your distance and displacement during this

experiment.

Feedback/feedforward

p m v=


Townshend 23


Townshend 24

year 12 physics as 91171 (part 1 of 4) introduction to

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