Download Physics 11 - Course Assessment Assignment Hand in the last two

Physics 11 - Course Assessment Assignment
Hand in the last two pages only.
Lesson 1: Mathematics in Physics
Objectives:
In this section you will be reviewing:
 Measurement & Uncertainty
 Unit Conversions
 Scientific Notation
 Algebraic Equations & Manipulating Formulas
 Trigonometric Functions
Physics is the branch of science that studies the physical world. Physicists study the nature of matter and energy
and how they are related and interact. In this unit we will be looking at the motion of objects. Kinematics is the
description of how objects move and dynamics deals with force and why objects move as they do. Physics
often uses mathematics as it language. For this reason we will need to spend some time reviewing the
mathematical tools you will need throughout this course. Let’s begin…
PART A: Measurement & Uncertainty
Quantitative measurement is a part of science. However, all measured quantities have some degree of error or
uncertainty. When taking a measurement, all the digits that are certain are recorded plus a digit that estimates
the fraction of the smallest division on the measurement scale. For example:
By lining up the object with the scale on the ruler, we can see that it is longer than 9 cm but shorter than 10 cm.
Therefore, we can record with certainty that the object measures between 9 and 10 cm. We can also see that the
object is greater than 9.5 cm and less than 9.7 cm. It looks pretty close to 9.6 cm, but where uncertainty falls
into play is whether or not the object falls exactly on 9.6 cm, just above or just below. It could be 9.59 cm or
9.61 cm. If it was 9.58 cm or 9.62 cm it probably would appear to not line up with the 9.6 cm line, therefore
your limit of accuracy is about 0.02 cm. It would be hard to distinguish measurements more precisely than that.
Therefore, you should record your answer to two hundreds of a centimetre, which in this example is 9.60 cm. It
could be 9.59 cm long or 9.61 cm, which is why the last number recorded (the hundredths place in this case) is
uncertain.
You should not record the answer as 9.6 cm or 9.600 cm. Mathematically, these three numbers are the same, but
experimentally they are not. 9.6 cm is less precise than 9.60 cm. 9.60 cm shows that we know the length
approximately to the nearest hundredth of a centimetre. We cannot estimate visually the length to the nearest
thousandth of a centimetre and therefore we cannot record our answer as 9.600 cm.
Precision is the degree of exactness to which the measurement of a quantity can be reproduced. A precise
instrument will give nearly the same measurement each time. Because the precision of all measuring devices is
limited, the number of digits that are valid for any measurement is also limited. Range is used to record the
precision of a series of measurements (trials) in an experiment (ie. 2.67 0.01). Accuracy is the extent to which
a measured or experimental value agrees with the standard value of the quantity. If a 500 g weight is placed on a
scale we would expect the scale to read 500 g. If it does not, the scale is inaccurate. Digits that indicate an
instrument’s degree of accuracy are called significant digits. Significant digits include all numbers that are
certain and one that is uncertain.
When doing calculations, we need to know the number of significant digits. To determine significant digits,
begin by counting from left to right, beginning with the first non-zero digit and ending with the digit that
occupies the decimal place denoting the precision of the measurement.
RULES:





Any of the digits 1-9 is a significant digit (163.5 has four significant digits)
Leading zeros (place holders) are not significant (0.063 has two significant digits)
Trailing zeros to the right of the decimal are significant because they indicate the accuracy of the
measurement (0.140 has three significant digits)
Zeros should not be added unless they are significant, since each zero indicates a greater degree of accuracy
Precision Rule: an answer obtained by adding or subtracting measured values has a precision equal to the
least precise value used, or the value taken to the least number of decimal places.
Certainty Rule: an answer obtained by multiplying or dividing measured values has a certainty equal to the
least certain value used, or the value with the fewest significant digits.
Example #1: 0.024 89 x 6.94

x
0.024 89
6.94
0.172 736 6
4 significant digits
3 significant digits
Therefore, is recorded as 0.173
Example #2: 3.0 x 104 / 1.15 x 104
PART B: Unit Conversions
The International System of Units – the metric system – is usually referred to as SI. The table below shows
some common SI symbols, units and quantities. These are called SI base units. Sometimes SI units are
combined to measure other quantities. For example, speed can be measured in meters per second (m/s).
Unit
Quantity
Second
Minute
Hour
Gram
Meter
Joule
Watts
Liter
Pascal
degree Celcius
Mole
Time
Time
time
Mass
length
Energy, work
Power
Volume
pressure
temperature
Amount of substance
Symbol
s
min
h
g
m
J
W
L
Pa
o
C
mol
The next table shows all the SI prefixes (this table can also be found on the inside front cover of your textbook).
You can see that all the prefixes are related to each other by multiples of 1000. The SI prefixes may by
combined with the base units in the first table. For example: kilometers (km), milligram (mg), microliter (L).
Symbol
Factor
G
M
k
m

n
109
106
103
10-3
10-6
10-9
Prefix
Giga
Mega
Kilo
Milli
Micro
Nano
To convert units of measurement, all you need to do is multiply or divide by multiples of 1000. If you are
going from a smaller to a bigger unit you divide; if you are going from a bigger to a smaller unit you
multiply. For example, if I want to convert 35 km into meters, I am going from a bigger unit (km) to a smaller
one (m) so I would multiply by 103 or 1000 (35 km x 1000 = 35 000 m). If I want to convert 560 micrograms
into grams, I am going from a smaller unit (g ) to a bigger one (g) so I would divide by 10-6 or 1 000 000 (560
g / 1 000 000 = 0.00056 grams).
Example #1: Convert 3.2 hours into seconds.
? s  3.2hr 
60 min 60s

 11520s
1hr
1min
There is a table of other unit conversions on the inside front cover of the textbook you will
receive.
Example #2: Convert 7.2 ft into centimetres.
? cm  7.2 ft 
30.5cm
 219.6cm
1 ft
Example #3: Convert 14.5 ft/s into km/h.
? km / h  14.5 ft / s 
1mi / h
1km / h
x
 15.9km / h
1.47 ft / s 0.621mi / h
PART C: Scientific Notation
Scientific notation is a short-hand of writing numbers. It will not only save you time and writing, but actually
simplifies numbers that are very large or very small. In chemistry you will deal with both very large and very
small numbers as we deal with atoms and molecules.
Scientific Notation Rules & Steps:
 If a numerical value is less than one, a ‘0’ shall precede the decimal point. Example: 0.134 NOT
.134
 Long numbers are separated by as space in groups of three counted from either side of the
decimal point (no commas and not required with four-digit numbers). Example: 1 234.769 54
 Step 1: To change a regular number to scientific notation, move the decimal place
so that only one non-zero digit appears to its left.
 Step 2: Drop all non-significant zeros.
n
 Step 3: Multiply this number by 10 where ‘n’ equals the number of places the
decimal place has been moved (n is positive for moves to the left and negative for moves
to the right).
Example #1:
Speed of light
300 000 000 m/s = 3.0 x 108 m/s
Example #2:
Charge of an electron
0.000 000 000 000 000 000 159 C = 1.59 x 10-19 C
PART D: Algebraic Equations & Manipulating Formulas
Formulas are used a great deal to solve problems throughout this course. In order to solve for some unknowns,
manipulating formulas becomes very important. The manipulation of formulas, or equations, is the field of
algebra. An equation contains an equal sign, which indicates whatever is on either side of the equal sign must
have the same value. When solving for an unknown in an equation, use the following rules:


whatever you do to one side of an equation must also be done to the other side of the equation
to remove a term from one side of an equation, perform the opposite operation on both sides of the
equation
Example: In the following formula, solve for m2.
Fg 
Gm1m2
R2
In order to isolate m2, you must get rid of the other terms on the right side of the equation. The term, m 2, is
being multiplied by G and m1, therefore you need to divide these terms on both sides of the equation. The term,
m2, is also being divided by R2, therefore you must multiply by this term on both sides. Because this cancels out
all the terms except m2 on the right side, we do not need to rewrite them.
Fg R 2
 m2
Gm1
Generally, the isolated term is written on the left side of an equation or formula, therefore we should rewrite the
equation as:
Fg R 2
m2 
Gm1
PART E: Trigonometric Functions
When solving physics problems it is often useful to draw a diagram to help visualize and simplify the
information provided. With many of the situations encountered in this course, a right triangle results from this
practice. Since there are a few simple equations to determine the properties of any right triangle, this makes the
solving the problem much easier. A right triangle is any triangle with one angle equal to 90o (the right angle).
Hypotenuse
The right angle is indicated by a box in the corner. The longest side of the triangle, opposite the right angle, is
called the hypotenuse.
Trigonometric Ratios
Trigonometric functions help us find angles by using a ration of the length of the sides. These ratios are called
Sine (sin), Cosine (cos) and Tangent (tan). The Greek symbol theta (θ) is used to represent an unknown angle.
Sin θ = length of opposite side
length of hypotenuse
= opp
hyp
Cos θ = length of adjacent side
length of hypotenuse
= adj
hyp
Tan θ = length of opposite side
length of adjacent side
= opp
adj
SOH CAH TOA
Example: Find the length of side ‘x’ if θ = 30o.
y
2 cm
The hypotenuse is the side opposite the right angle, so its length
is 2 cm. The side opposite the angle θ is side ‘y’, and the side
adjacent to angle θ is side ‘x’. To solve for ‘x’ we need to use:
Cos θ = length of adjacent side
= adj
length of hypotenuse
hyp
Cos 30o =
θ
x
x
2cm
(Cos 30o)(2 cm) = x
(0.866)(2 cm) = x
1.73 cm = x
Therefore, side ‘x’ = 1.73 cm
When dealing with right triangles, the Pythagorean theorem is another useful formula to know. It states that ‘the
square of the hypotenuse is equal to the sum of the squares of the other two side’ or:
a2 + b2 = c2
Example: Billy-Bob walks 3 km north and 2 km west. How
far is he from his starting point?
2 km
c
3 km
a2 + b2 = c2
(3 km)2 + (2 km)2 = c2
9 km + 4 km= c2
13 km = c2
√13 km = √c2
3.6 km = c
?
a
b
Billy-Bob is 3.6 km from his starting point.
End of Lesson 1 …….
Physics 11 Assessment Assignment
ASSIGNMENT QUESTIONS:
Name:___________________________________
Show all work to achieve full marks.
TOTAL: 27 marks
1. Write the following numbers in scientific notation.
(3 marks)
a) 156.90
b) 12 000
c) 0.008 90
2. Expand the following numbers.
(3 marks)
a) 1.23 x 106
b) 2.5 x 10-3
c) 5.67 x 10-1
3. Give the number of significant digits in the following measurements.
(4 marks)
a) 2.9910 m
b) 0.00670 kg
c) 809 mL
d) 4.060 x 103g
4. Solve the following problems and give the answer in the correct number of significant digits.
Be sure to include appropriate units.
(6 marks)
a) 9.0 cm + 7.66 cm + 5.44 cm
b)
2.674m / s
2.0 s
c)
(2.68x102 m s)(2.3x103 m s)
(5.68x102 m)
5. Solve for ‘x’ in the following equations.
a)
3x 6 g

y
b
b) d 
c)
(3 marks)
t
x
2 x
y
c
6. Make the following conversions.
(4 marks)
a) 4008 g =
__________ kg
b) 23.9 km =
__________ m
c) 1 ½ hours =
__________ s
d) 20 m/s =
__________ km/h
7. What is the difference between precision and accuracy?
(2 marks)
8. A boat sails 12 km due North then 15 km due East. How far is the boat from its starting point?
(2 marks)
End of assignment…..