Harry Ainlay2006

Harry Ainlay 2006

Science 10 Physics

Kinematics, Dynamics and Energy

Kinematics

The study of how objects move. By measuring the changes in distance and time we can explain and predict the movement of many objects.

Dynamics

The study of why objects move. The study of forces and their net effect on an object.

Energy

One of the most basic laws of the universe, the law of conservation of energy, is used to examine the behaviour of systems in motion. We will look at the

relationship between energy, force, mass, distance and time. We will examine the many changes in energy that take place. Some of these changes in energy are very efficient and some are not. We will conclude our study of energy by looking at historical and social issues surrounding the conversion of energy.

Unit 1 The Language of Physics – Unit Analysis

In Physics you will be using the mks system of measurement (mks stands for metre, kilogram, second). All the other units you use will be derived from these fundamental units. These fundamental units are from the S.I. (System

International) which is a standardised world system. A metre is a measure of length, a kilogram is a measure of mass, a second is a unit of time.

1. Fill in the blanks for mass and time in the table.

Pref x

Symbo

l Fractio

n Distance Mass Time

micro  1/1 000 000

or (10^-6) m g s

milli m ^{1/1 000}

or (10^-3)

centi c ^1/100

or (10^-2)

deci d ^(10-1)

or 1/10

BASE UNIT

metre (m) gram (g) second (s)

kilo k ¹⁰⁰⁰

or (10³)

mega M ^{1 000 000}

or (10⁶)

giga G ^{1 000 000}

000 or (10⁹)

Physics – Unit Conversion

A very useful method for converting one unit to an equivalent unit is called the factor-label method of unit conversion.

1000m = 1 km 1 min = 60 s 1 h = 60 min 1km 1000m 60 s 1 min 60min 1 h

Example 1

To convert 80 millilitres to litres, frst choose the factor. Since 1L = 1000mL, 1L = 1

1000mL

Use this factor for your conversion as follows.

80 mL x 1L = 0.08 L (Note: mL cancel) 1000 mL

A: Convert the following to metres, kilograms, and seconds (mks) units.

1) 327 cm x 1 m = 3.27 m 100 cm

2) 2 833 mm 2.833 m 3) 123 g 0.123 kg

4) 49.39 cm 0.4939m 5) 984 ms 0.984 s

6) 4.880 km 4880 m

7) 239.039 s 0.000239039s

8) 39.384 g 0.000000039384 kg

B: Make the requested changes in the units.

1) 93.3 kg x 1000 g x 1000 mg = 93 300 000 mg 1 kg 1 g

2) 2 984 m = 2.984 km

3) 9.835 m = 9835 mm

4) 928 cg = 9.28 g

5) 0.123 mm = 0.0123 cm

6) 9 823 mm = 0.009823km

7) 2.093 km = 2093000 mm

8) 0.372m = 37.2 cm

C: Make the required change in the following units of time.

1) 30 min. 0.50 h

2) 11.5 h 41400 s

3)15 h 0.0017 a

4) 53 ms 0.053 s

5) 12 ks 3.3 h

6) 1200 s 0.3333 h

Activity

1. Using a metre stick measure the width of the desk in:

millimetres centimetre s

decimetres metres

2. Using the balance determine the mass of a can of pop in:

grams milligrams kilograms

3. Using a stop watch time the fall of a ball from the ceiling to the floor in:

seconds minutes hours

milliseconds

Carry out the following conversions using the factor-label method.

1. How many seconds in a year?

2. Convert 36 km/h to cm/s.

1000 cm/s

3. Convert 50 g/d to kg/a.

18.25 kg/a

4. Convert 450 m/s to km/h.

1620 km/h

5. Convert 85 cm/min to m/s.

0.014 m/s

6. Convert the speed of light, 3.0 x 108 m/s to km/d 2.592 x 10¹⁰ km/d

Physics – Accuracy and Precision

Accuracy: A comparison between two numbers, one predicted (a.k.a “accepted”) the other measured (usually by you).

% value 100

predicted

value measured -

value predicted difference

%  x

e.g.: M = 9.85 m/s² %diff. = P = 9.81 m/s²

Signifcant digits: A way to communicate precision

We use signifcant digits to communicate precision in physics data and

calculations. It is important because almost all calculations involve measurements with varying degrees of precision.

e.g.1: Numbers of signifcant digits

Line AB is measured with the following degree of precision:

Precision is measured in signifcant digits and the following rules apply:

 All zeros following a whole number are signifcant (e.g. 43 000 = 5 sig.

digs)

 All digits are signifcant except preceding zeros (e.g. 0.004 3 = 2 sig. digs) Further examples: 123 456 has 6 signifcant digits

123.00 has 5 signifcant digits 120 007 has 6 signifcant digits

0.000 123 has 3 signifcant digits

1) State the number of signifcant digits in these measurements.

a) 3405 m (4) e) 120 cm (3) i) 54.00 g (4) b) 0.042 s (2) f) 100 004 km (6) j) 100.5 cm (4) c) 0.000 56 km/h (2) g) 0.240 7 cm (4) k) 500.05 mm (5)

d) 0.002 0 g/d (2) h) 1.003 5 m/s (5) l) 54 000 a (5)

A B

17 cm 17.2 cm 17.24 cm

2 SD’s 3 SD’s

4 SD’s

Rule #1: When adding or subtracting data with varying degrees of precision, round the fnal answer using the least precise decimal place

Rule #2: When multiplying or dividing using data with varying degrees of precision, round the fnal answer using the least precise number of signifcant digits

2) Carry out the following calculations using signifcant digits.

a) 10.0 x 5.3 = 53 (only 2 sig digs) f) 25 x 1.5 = 38

b) 0.10 x 122 = 12 g) 0.000 2 x 2500 = 0.5

c) 50.5 x 0.62 = 31 h) 12.25 x 8.0 = 98

d) 100 / 45 = 2.2 i) 2230 / 3.00 = 743

e) 0.5 / 24.5 = 0.02 j) 46.5 /10.01= 4.65

Physics - Scientifc Notation

In Science you will often deal with very large or very small numbers (as you may have noticed on the previous page). To be able to express these without a lot of zeros physicists use scientific notation.

Scientifc notation is always written:

a 10 ^b

· The coefficient tells you how signifcant (# of sig digs) the number is.

 The coefficient must be a number equal to or greater than 1 and less than 10.

· The exponent tells you where the decimal is.

- A zero or a positive exponent tells you that the number is greater than one. The decimal is to the right of the frst number.

e.g. 1.23 x 104 = 12 300 units (move decimal 4 spaces right) - A negative exponent tells you that the number is less than one. The decimal is to the left of the frst number.

e.g. 1.23 x 10-6 = 0.000 001 23 units (move decimal 6 spaces left)

Example 1

To express 5 904 in scientifc notation, move the decimal three places to the left (5.904) and add x 10³:

5 904 m = 5.904 × 10³ m Example 2

To express 0.000 072 mm in scientifc notation, move the decimal 5 places to the right( 000 07.2 or 7.2) and multiply by 10^-5:

0.000 072 mm = 7.2 × 10^-5 mm

Physics - Scientifc Notation

Practice: Express the following in scientifc notation with three signifcant digits.

1) 29 840 km = 2.98 x 10⁴ km 6) 12 098 329 kg = 1.21 x 10⁷ kg

2) 0.000 019 982 g = 2.00 x 10^-5g 7) 0.000 398 5 mm = 3.99 x 10^-4 mm

3) 5 092 348 985 people = 5.09 x 10⁹ people 8) 0.000 034 434 s

= 3.44 x 10^-5 s

4) 44 123 km = 4.41 x 10⁴ km 9) 7 680 m = 7.68 x 10³ m

5) 18 345 000 s = 1.83 x 10⁷ s 10) 0.000 003 00 mm

=

EXERCISES

1. Express the following in scientifc notation. (Assume 4 sig dig accuracy) a. 40 000 000 m = 4.00 x 10⁷

b. 0.000 086 254 m = 8.63 x 10^-5

c. 0.000 000 005 125 6 m = 5.13 x 10^-9

2. A rectangle is measured and found to be 24 cm long and 21 cm wide.

Calculate the area of the rectangle and express in scientifc notation with correct number of sig digs. (5.0 x 10² cm²)

3. The light year is the distance travelled by light in one year. Express a light year in metre/year. (One light year = 3.0 × 10⁸ m/s x 365 d/a x 24 h/d x 3 600 s/h.) (9.5 x 10¹⁵ m)

4. The highest g force ever to be endured by a human being was 1 764 m/s². In 1977 David Purley crashed his race car from a speed of 173 km/h. The car

stopped in a distance of 66 cm. Mr. Purley suffered 29 fractures, 3

dislocations and 6 heart stoppages. Express all numerical values to one sig dig using scientifc notation. (2 x 10³, 2 x 10², 7 x 10¹, 3 x 10¹, 3, 6)

5. Human beings have travelled at increasingly faster speeds. The fastest anyone has ever gone was the crew of the command capsule of Apollo 10.

Thomas P. Stafford, Eugene Cernan and John Watts reached a speed of 39 889 km/h on May 26, 1969. Express this speed in 2 sig digs. (4.0 X 10⁴ km/h)

Topic 2 :Kinematics - the study of motion

Kinematics is the study of motion. In this unit we will be using measurements of distance and time to describe the motion of

1. an object that is at rest (it does not move)

2. an object that is moving at a constant speed (uniform motion) 3. an object that is speeding up or accelerating at a constant rate.

(accelerated motion) Speed/velocity:

We are going to calculate speed/velocity of objects in this class. Speed is calculated from distance and time data.

The formulas below show the relationship between distance (d), speed or velocity (v) and time (t).

in time change

distance in

change

 velocity

t v d



 

d vt  ^{t d}

 v

Example 1:

You have measured the distance from the street corner to your house to be 0.33 km. When a car comes around the corner, you time it to your house. It takes 40 seconds to arrive at your house. How fast is the car going in km/h?

t = 40 s ; d = 0.33 km ; v = ?

Note: You frst need to convert seconds to hours so that you can substitute

appropriately into the formula. There are 60 seconds in a minute and 60 minutes in an hour. Therefore, there are 3600 seconds in an hour.

s h s h

time 0.011

3600 40  1 

 v = d/t

v = 0.33 km/0.011 h v = 0.33/0.011 x km/h

v = 29.7 km/h = 30 km/h (2 sig digs)

The car coming toward your house was traveling at 30 km/h.

Notice that the unit we get in the answer is a correct unit for velocity, which should give you some confdence that you have done the mathematics correctly.

Kinematics - Constant Velocity Problems

Use your velocity, distance and time equations to complete the table below. Pay attention to significant digits and units and show all of your work.

Distance Speed Time Formula and Work

1 _______

km 30.0 km/h 0.25 h

7.5 km

2 _______

km 550 km/h 0.750 h

413 km 3 _______

km 120 km/h 90 s

3.0 km

4 0.750 m ________m/s 0.12 s

6.3 m/s

5 0.25 km _______

km/h 30 s

30 km/h

6 85 cm ________ m/s 325 ms

2.6 m/s

7 60.0 m 15.0 m/s ________ s

4.00 s 8 3.5 m 0.130 m/s ________ s

2.7 s 9 3.00 km 20.0 m/s

150 s or 0.0417 h (4.17 x 10² h)

Kinematics – Practice Problems

1. Sam walks 13 km in 2.0 h. What is his speed in km/h and in m/s? (6.5 km/h, 1.8 m/s)

2. An athlete runs 100 m in 12.20 s. What is her speed in m/s and in km/h?

(8.20m/s, 29.5 km/h)

3. A bullet is shot from a rifle with a speed of 320.0 m/s. How long will it take for the bullet to strike a target 3240.0 m away? What is the speed of the bullet in km/h? (10.13 s, 1152 km/h)

4. On a baseball diamond, the distance from home plate to the pitcher’s mound is 18.5 m. If the pitcher is capable of throwing a ball at 38.5 m/s, how much time does it take the ball to reach home plate? (0.481 s)

5. A high-speed French train takes 2 h and 15 min to travel from Paris to Lyons, a distance of 450 km. What is the average speed of the train? (200 km/h)

6. A cyclist rides at an average speed of 20.0 km/h for 3 h 15 min. How far does he travel? (65.0 km)

Kinematics - Graphing

Physicists graph numerical information for several reasons.

1) Graphs communicate the relationship between two variables (manipulated and responding) as a shape.

2) They can also extrapolate the data; that is scientists can look at a trend and predict what might have happened before or what will happen after the observed time span.

3) Finally scientist can infer a mathematical relationship between the two variables.

Discuss and List other important graphical knowledge:

10 rules of graphing

Kinematics - Graphing

Graph the following data and determine the slope of the graphs.:

1. Distance travelled by a car over 25 minutes.

Time Elapsed

(min)

Distance Travelled

(km)

0.0 0.0

2.0 1.8

4.0 4.2

6.0 6.1

8.0 7.8

10.0 10.1

2. Distance travelled by a remote controlled car in 10 s. intervals.

Time Elapsed

(s)

Distance Travelled (m)

0.0 0.0

10 4.0

20 12.0

30 17.0

40 21.0

50 26.0

60 34.0

70 40.0

80 43.0

90 52.0

3. Running data of two cross-country runners.

Time Elapsed

(s)

Bill’s Distance

(km) Distance

Travelled (km)

0 0.0 0.0

2 0.3 0.3

4 0.6 0.5

6 0.8 0.6

8 1.1 0.9

10 1.4 1.0

12 1.6 1.2

14 1.8 1.5

16 2.1 1.6

18 2.5 1.9

20 2.8 2.1

1.0 km/min

0.58 m/s

#1 - 0.14 km/s #2 – 0.105 km/s

Kinematics - Graphing Constant Velocity

Example 1: Distance/time graph

Consider a car, driving at 60 km/h from Edmonton to Red Deer, 150 km south of Edmonton.

Time

(min) 0 10 20 30 40 50 60 70 80 90 10 0 11

0 12 0 13

0 14 0 15

0 Distanc

e (km) 0 10 20 30 40 50 60 70 80 90 10 0 11

0 12 0 13

0 14 0 15

0

Use the grid to graph the

above data. Give a title and label the axes.

Again this graph can tell us a number of things.

a) By interpolating we could tell that the car went ____65___ km in 65 minutes.

b) By extrapolating we could tell that the car went ____180___ km in 3 hours.

c) The slope of the graph can tell us the velocity of the car: _______1.0_____

km/min.

Consider the same car from example 1, driving at 60 km/h from Edmonton to Red Deer, 150 km south of Edmonton.

We could generate velocity/time data for that trip:

Time(s) 0 10 20 30 40 50 60 70 80 90 10 0 11

0 12 0 13

0 14 0 15

0 Velocity

(m/s) 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60 60

Use the grid to graph

the data from the table.

Title the graph and label the axes.

Slope = 0 m/s/s

a) The area under the graph communicates how far it has travelled.

Area = Height x Base

Area = velocity x time = v x t = distance = (m/s) x (s) = m

= 60 m/s x 150 s

= 9000 m

Kinematics – Uniform Velocity Problems

1. In the 1988 Summer Olympics Florence Griffith-Joyner won the 100-m race in 10.54 s.

a) What was her average velocity during that race? (9.49 m/s)

b) She also won the 200-m race in 21.34 s. What was her average velocity in this race? (9.37 m/s)

c) Which race did she run fastest? Why? 100m. Faster avg velocity 2. Study the distance/time graph for the frst 12 s of a run by Michael.

a) How far has he travelled in the frst 3.0 s? (8-9 m)

b) What is his average velocity during the frst 5.0 s? (3.0 m/s) c) How far did he travel during the 5 – 10 second interval? (0 m)

d) How does the slope of the second segment compare with the frst? (flat)

e) What does the slope tell you about velocity? (Steeper slope = faster speed)

f) What was his average velocity during the interval from 5.0 to 10 s? (0 m/s)

g) What was his average velocity during the frst 10 s? (1.5 m/s)

Distance vs. Time Graph of Micheal Running

0 5 10 15 20 25

D i s t a n c e (m)

5 10 15

Time (s)

h) Why was his average velocity lower than for the frst 5 s? (stopped for 5 s)

i) What was his average velocity for the period from 10 s to 12 s? (5 m/s)

j) How far did he travel in the frst 12 s of this sprint? (25 m)

k) What was his average velocity for the entire 12 s? (2.1 m/s)

3. In the adjacent graph, a radio-controlled car travelling through a speed trap is clocked and the velocity is plotted on this graph.

a) What is the instantaneous velocity of the car at 3.0 s, 6.0 s and 12 s?

(9m/s, 3m/s, 0m/s)

b) If distance is the product of velocity and time, how far did the car travel in the frst 1.0 s? (9m)

c) How far has it gone in the frst 5.0 s? (45m)

d) How did you calculate this distance? (bxh)

e) Show how that distance is represented on the graph by shading it in with diagonal lines.

f) From the graph, how does the distance travelled during the period from 5.0 s to 10 s compare with the frst interval? (less distance – 15m)

g) How far does the car travel in the period from 10 s to 15 s? (0m)

Velocity/Time Graph

0 2 4 6 8 10

V e l o c I t y (m/s)

5 10 15

Time (s) 0

h) What is the total distance travelled in the 15 s period? (60m)

i) Calculate, from the total distance travelled, the average velocity for the trip. (4m/s)

4. Using the data from the above graph,

· construct a distance/time graph on the adjacent grid. Your graph should show three segments having different slopes.

· (eg. If a car is travelling at 10.0 m/s, it will travel 10 m in the frst s, after 2 s it will have travelled a total of 20 m and so on).

a) From the graph, what is the total distance travelled in 15 s? (60m)

b) What does the slope of the interval from 10 s to 15 s tell you? (slower speed)

c) Write a generalisation that describes the relationship between velocity and slope.

(as slope increases, velocity increases)

5. Andrea throws out a runner at home plate from her position at shortstop, a distance of 48.3 m, in 1.84 s. With what speed did she throw the ball? (26.3 m/s)

6. What is the speed of a skier who travels 1200 m down a hill in 60.0 s? (20.0 m/s)

7. A spacecraft travels 100 m,

500 m, 1400 m and 3000 m, during first to fourth seconds after launch, respectively.

a) Calculate the average speed at

the end of each second. (100m/s, 300m/s, 667m/s, 1250m/s) b) Construct a distance/time graph

on the right for that period.

(Total distance travelled please!)

8. Doug Weight drives a hockey puck into the goal at a speed of 34.8 m/s. From a distance of 60.0 m, how long will it take to reach the net? (1.72 s)

9. A police officer sees the flash of a gun in the hands of an armoured car robber 125 m away. If the bullet travels at a speed of 585 m/s, how much time does she have to duck? (0.214 s)

Challenge questions

10. You have to meet your parents in Banff, 400 km away. If your parents leave 0.50 h before you and travel at a constant speed of 100 km/h, how fast will you have to drive to get there at the same time as your parents? (114 km/h) – took them 4 h to get there. You need to get there in 3.5 h

11. In a similar situation, you leave 0.50 h after your parents on a trip to Red Deer (100 km away). If they travel an average of 100 km/h, how fast will you have to travel to arrive at the same time? (200km/h) – you need to get there in 0.5 h to arrive at the same time. It will take them 1 h to get there.

Acceleration

Acceleration is the change of velocity during time. Uniformly accelerated motion can be found using:

Where:

a is acceleration (m/s²)

vfis final (second) velocity (m/s) vi is initial (first) velocity (m/s)

tis change in time (the time it takes to change velocity) (s) vave is average velocity (m/s)

N.B., Final and initial do not have to be actually start and stops. They may simply be two velocities during an object’s motion.

Graphing non-uniform velocity (acceleration):

Free-Fall

When an object is allowed to fall with only the earth’s gravitational field exerting a force on it, it is said to be in free-fall and accelerates at a rate of 9.81 m/s², ignoring effects due to air resistance.

Air resistance may be ignored if two conditions are met: the object

• has a low surface area-to-mass ratio.

• falls for only a short time (or distance).

Unless it is otherwise stated, air resistance is typically ignored.

fi

- v v a v

t t

  



 

 

t v

slope = acceleration area under graph = displacement

t a

area under graph = change in velocity

t d

1. A racecar travelling north accelerates uniformly from 43.2 m/s to 68.7 m/s. The car required 2.0 s to travel between these two velocities. Calculate the car’s acceleration. [13 m/s², north]

2. A Boeing 767 starts from rest and lifts-off from the runway at a speed of 75 m/s. Determine the magnitude of its acceleration in m/s² if it accelerated for 24.1 s. [3.1 m/s²]

3. A racquetball is moving towards a player at 3.0 m/s. It is hit so it continues in the same direction but with a speed of 5.0 m/s. Calculate the ball’s acceleration during contact if the ball was in contact with the racquet for 0.60 s. [3.3 m/s²]

4. A racquetball is moving towards a player at 3.0 m/s. It is hit so it changes its direction giving it a speed of 5.0 m/s, opposite of its original direction. Calculate the ball’s acceleration during contact if the ball was in contact with the racquet for 0.60 s. [13 m/s²]

5. A car is travelling north at 3.0 m/s when it accelerated for 0.80 s to the north at 2.5 m/s². Calculate the car’s final velocity. [5.0 m/s, north]

6. Sketch the graph shape of a displacement-time graph and a velocity-time graph for a uniformly accelerating object starting from rest.

7. A rock is dropped from Edmonton’s High Level Bridge and takes 3.02 s to reach the water directly below. Calculate the height of the bridge above the water (neglect air resistance). [45 m]

8. A pen is dropped from a height of 9.50 m above the ground; at what speed will it be travelling just before it reaches the ground? (13.6 m/s)

9. An object is dropped from the roof of a building. If the object takes 2.5 s to reach the ground, what was the velocity of the object just before it reached the ground? (25 m/s down)

t t

d v

Dynamics - Forces and Motion F = ma

E.g. If you apply a force of 1.0 N to an object that has a mass of 1.0 kg, the acceleration will be 1.0 m/s².

2 2 1.0 0

. 1 0 . 1 0 . 1

0 . 1

s m kg

s kg m

kg N m

a F  







1. What will be the acceleration of a 1.0 kg mass, if a force of 5.0 N is applied?

2. How does increasing the force affect the acceleration of the object?

3. What force is required to accelerate a 2.5 kg mass at 2.0 m/s²?

4. How does the mass affect the acceleration if the net force is kept constant?

5. What is the mass of an object accelerated at 0.981 m/s² with a force of 2000 N?

6. A net force of 25 N is applied to a 10 kg mass. What will the acceleration rate be for this object?

7. An athlete exerts a force of 30.0 N on a shot-put, giving it an acceleration of 12.00 m/s². What is the mass of the shot-put?

8. SuperMouse steals a large piece of Edam cheese by rolling across the floor with a force of 15.0 N. If the cheese has a mass of 5.00 kg, with what acceleration does the cheese move? (3.00 m/s²)

9. A net force acting on a 4.0 kg mass gives it an acceleration of 2.4 m/s². How large is the force?

10. A large lead ball is struck with a force of 850 N, giving it an acceleration of 75.83 m/s². What is the mass of the ball?

Dynamics - Force due to Gravity

F

= m g

E.g. If your teacher has a mass of 75 kg, their mass would be:

F

= m g = (75.0 kg)(9.81 m/s

) = 736 N

1. Andrea reports her mass as 40.0 kg. What is her weight? (392 N)

2. What is the force of gravity on a 4.5 kg block of concrete?

3. What is the mass of an object that is pulled down by a force of gravity of 167 N at the Earth's surface?

4. The force of gravity on a 250 kg spacecraft on the moon is 408 N. What is the gravitational feld strength there?

5. What is the weight in Newtons of a 5.0 kg mass?

6. a. A stone weighs 96 N. What is its mass?

b. At what rate, is the stone accelerated straight up if a 108 N force is applied to it in that direction?

7. An 8.0 kg mass weighs 78.4 N. What is the acceleration of gravity on this object?

8. In space travel astronauts talk about acceleration in numbers of g's. This is a multiple of the acceleration of gravity on Earth. 4 g's would be 4 x 9.81 m/s² or 39 m/s². When a fghter pilot experiences 7 g's (s)he blacks out. What is his acceleration in that case?

Physics – Energy

Everything seems to depend on energy. From the time you get up you think in terms of energy. Do you have the energy to go to school today? Do you need to eat right away? Do you have the energy to walk all the way to the bus stop or do you need a ride? Do you have the energy to make it up the stairs? Perhaps it is too cold and you are loosing too much energy?

It takes energy to get up, to move, to warm up and we get all of that energy by eating food. To generate the vast quantities of electricity our society uses we burn huge amounts of fossil fuel. Then we use the electricity to heat, beat, bake, clean and cool. Our life is full of energy conversions.

Forms of Energy -chemical potential -electrical potential -potential gravitational -kinetic

-thermal (movement of particles) -nuclear potential

-radiant (light or thermal) -electromagnetic

The total amount of matter and energy that was created at the beginning of our universe has not changed although a substantial amount of the matter has been changed to light and heat (as well as x-rays, gamma rays, microwaves and radio waves) in the hearts of millions of suns. Scientists realise that matter can be converted into energy but the reverse process does not usually take place.

Once the energy is created it can only change forms. It can not disappear and so we say that energy must be conserved. (Law of Conservation of Energy).

Ultimately all forms of energy are converted to heat energy and scientists

speculate that after no more matter can be converted into energy, and after all of that energy has changed to heat energy the universe will die a 'heat death'.

Energy - As Work

Background: Most of us already realise that work and energy are closely

related. When we say "I have not got the energy to do all of that work!"

we realise that it requires ENERGY to do WORK. So what is work?

Definition:Work (W) is the result of applying a force (F) through a distance (d).

W = Fd the units for work are Joules (J)

Remember also that we can derive information by graphing.

The area under the line is:

Forc

e x distan

ce = work

done

(N) (m) (J)

Work In = Energy Out

Summary: from previous unit: W = F x d (basic formula)

F = m x a Fg = m x g

W = F x d or W = F x d

W = m x a x d W = m x g x h

Force (N)

Distance (m) Area = F x d

Energy – Work Practice

1. How much work is done if you have to apply a 10 N force to move a block 1.0 m?

10 J

2. How much work is done if you apply a force of 10 N to move a block 100 m?

1.0 x 10³ J

3. If you do 1750 J of work applying a force of 150 N to a block, how far will you move the block?

11.7 m

4. How much work is done by a boy pushing a car with a force of 800 N for a distance of 200 m?

1.60 x 10⁵ J

5. A force of 20 N was used to push a box along the floor for a distance of 8.0 m.

How much work was done?

1.6 x 10² J

6. A boy on a bicycle drags a wagon full of newspapers at a constant speed of 0.80 m/s for 30 min using a force of 40 N. How much work has he done?

d=vt d = 1440m W=Fd 5.8 x 10⁴ J

7. A small motor does 520 J of work to move a toy car 260 m, what force did it exert on the car?

2.00N

Energy - Potential Gravitational Energy

1. A parent has lifted their 17 kg baby 1.8 m above the ground. Find the potential energy the child possesses.

(3.0x10² J)

2. A 1.2 kg falcon has gained an altitude of 875 m. What is her potential energy now?

(1.0 x 104 J)

3. On a Ferris wheel ride Bill has attained a height of 53 m. Find Bill's potential energy if his mass is 75 kg.

(39 kJ)

4. A 580kg satellite circles the Earth at an altitude of 120km. What is its potential energy?

(683 MJ)

5. Flight 723 has a mass of 3.7 x 105kg and cruises at an altitude of 12km.

Determine the potential energy.

(4.4 x 104MJ)

6. A 0.00030 kg flea can jump to a height of 0.75 m. How much potential energy does it have at the top of its jump? (2.2 x 10-3 J)

7. 16 m above the ground a 325 g pear is hanging on a branch. Find its potential energy. (51 J)

8. Swinging on a swing Beth attains a height of 3.95 m. What is her potential energy if her mass is 53 kg? (2.1 kJ)

9. Find the potential energy of the top sheet of paper on a pile 3.5 cm high if one sheet weighs 1.2 g. (4.1 x 10-4 J)

10. A 415 mg ant has made it 82 cm up a tree. Find the potential energy. (3.3 x 10-3 J)

Energy – Potential Energy

1. To raise an object a distance of 10 m, you apply a force of 150 N.

a) How much work is done on the object?

b) What is its potential energy at that time?

2. An object with a mass of 35 kg is 1.0 m above the ground.

a) What is its potential energy?

3. What amount of work can it do when it strikes the ground.

4. A pile driver is used to sink heavy piles (sort of like power poles) into the ground upon which bridge trestles are built for example. The pile driver is a large crane that raises a weight (the hammer) and then lets it drop onto the top of the pile. If the 'hammer' has a mass of 500 kg, and the crane raises it 10 m each time before it drops it onto the pile, calculate:

a) The potential energy of the hammer before it is dropped.

b) The work done by the crane in raising the hammer.

c)The work done on the pile by the hammer each time it is dropped.

d) If it strikes the pile 100 times, the total work done on the pile.

5. What is the gravitational potential energy of a 56.1 kg person standing on the roof of a 10 story building relative to each of the following levels? (Assume each story is 2.50 m )

a) Ground level (First floor) b) Tenth floor

c) Sixth floor

6. A 15,000 kg airplane descends a vertical distance of 10.0 km over a horizontal distance of 80.0 km. What is the airplane's loss of potential energy?

7. A chair lift delivers a skier to the top of a mountain 300 m high. If the skier and gear has a mass of 80.0 kg,

a) What is the increase in potential energy that the lift gives to the skier?

b) How much work does the lift have to do to raise the skier by 300 m?

Energy - Kinetic Energy

Defnition: Energy of motion is called Kinetic Energy and is related to the speed something is moving.

E

= ½ mv

Ek = 1/2mv² m = 2Ek/v²

m v 2E^k



The mass must be in kilograms and the velocity in metres per second.

You can check that the units here are again, Joules.

J s

m Kg x s x m

Kg ₂

2 

s  m

e.g.: What happens to the kinetic energy of an object if the mass is increased 10 times?

e.g.: What happens to the kinetic energy if the velocity is increased 10 times?

1. Find the kinetic energy of a 2.50 kg bowling ball moving at 5.00 m/s. (31.3 J)

2. Determine the kinetic energy of a 85 kg football player running at a velocity of 8.2 m/s.

(2.9x10³J)

3. What is the kinetic energy of a 1000 g brick that is thrown with a velocity of 22 m/s.

(2.4x10²J)

4. What is the mass of a baseball thrown with a speed of 35.0 m/s and a kinetic energy of 2.30x10² J? (0.376 kg)

5. What is the velocity (in km/h) of a 1 750 kg car moving with 1.7x10⁵ J of energy?

(50 km/h)

6. A falling piano reaches a velocity of 120 km/h. Find the kinetic energy if the mass of the piano is 357 kg. (198 kJ)

7. If a 32.0 g bullet moves with 1.56 kJ of kinetic energy, what is its velocity? (312 m/s)

8. Find the kinetic energy of a 185g apple falling with a velocity of 25km/h. (4.5J)

9. What is the mass of a feather floating to the ground at 25 cm/s with a kinetic energy of 1.6 x 10-5J? (0.50g)

10. Determine the kinetic energy of a 0.025kg snail moving at 0.008km/h. (6 x 10- 8J)

Energy - Total Mechanical Energy

Definition:The total mechanical energy is the sum of the potential energy and the kinetic energy at any given time. The rule for any object that is in motion is that the total mechanical energy stays the same as long as there are no effects from friction.

E

= E

+ E

1. A 1.0 kg ball starts from rest in your hand and you accelerate it at a rate of 25 m/s² for 0.40 s. Calculate how fast the ball was going when it left your hand.

2. Using the principle of energy transformation, determine how high the ball went.

3. What was the speed of the ball half way back down?

Energy - Analyse Energy Conversions

A 20 kg sandbag is dropped from a hot air balloon from a height of 300 m.

Determine the potential and the kinetic energy at 20 m intervals for the whole way down and graph these below. Also graph total mechanical energy on the same graph (Use g = 10m/s²).

Mechanical Energy = Potential Energy + Kinetic Energy

height (m)

300 280 260 240 220 200 180 160 E

(J)

E

(J) E

(J) height (m)

140 120 100 80 60 40 20 0

E

(J)

E

(J)

E

(J)

Energy - Total Mechanical Energy

Example 2: This is one example of the Law of Conservation of Energy or the First Law of Thermodynamics. Some children go tobogganing on an icy hill. They start from rest at the top of the hill as shown in the diagram. The hill is on the left is 10 m high and the hill on the right is 5.0 m high. The toboggan and children have a combined mass of 90.0 kg. Ignoring friction, determine:

1. Their potential energy at their starting point. (8829J)

2. The total mechanical energy at their starting point. (8 829 J)

3. When they reach the bottom of the slope their total mechanical energy will be converted to kinetic energy.

Calculate their speed at this point.(14.0 m/s)

4. When they come up to the top of the other side of the dip, the total mechanical energy will still be the same as before but now they will have some potential energy and some kinetic energy. Calculate their potential energy. (4 415J)

5. Calculate their kinetic energy. (4415 J)

6. Calculate their speed. (9.9m/s)

7. They then run into a tree. How much work do they do on the tree? (4 415 J)

Energy - Total Mechanical Energy

Example 3: A student throws a 5.00 kg steel shot directly upwards so that it leaves his hand when it is 2.00 m above the ground. If its velocity is 15.0 m/s when it leaves his hand, calculate:

1. The shots potential energy in the students hand before he throws it.

2. The kinetic energy when it leaves his hand.

3. The minimum work done to accelerate it to 15.0 m/s

4. The total mechanical energy of the shot.

5. The height above his hand where it stops rising.

6. The height above the ground at that point.

7. The potential energy relative to the ground at that point.

8. The kinetic energy just before it strikes the ground.

9. The velocity with which it strikes the ground.

Physics - Other Types of Energy

Electrical energy is generated in a variety of familiar ways.

Batteries

Chemical potential energy is stored in a sealed container so that a chemical reaction starts only when power is demanded (a switch is turned on).

An alkaline cell uses this chemical reaction:

2MnO

+ 2 NH

Cl

+ Zn



Mn

O

+ 2NH

+ ZnCl

+ H

O

A car battery uses this chemical reaction:

PbO

+Pb

+ 2H

SO

 2PbSO

+ 2 H

O

Coal Burning Power Plants

Chemical energy stored in carbon from plant and animal remains is released through combustion. The heat energy is used to heat water to steam which in turn rotates an electric generator which produces electricity.

C

+ O

 CO

also produced are by-products of SO2(g) and NO2(g)

Nuclear Power Plants

Nuclear power plants release a huge amount of thermal energy (heat) as a result of a very complex nuclear reaction of them is shown below.

The heat is used to heat water…….you get the idea

92 235

0 1

56 141

36 92

0

31

U n Ba Kr  n

Hydrodynamic Power Plants

Are placed next to large body of stored water which has a lot of

potential gravitational energy and when released gains kinetic energy which in turn is used to rotate an electrical generator.

Solar Power

Light energy (electromagnetic energy) impact substances like silicon or other metalloids and release kinetic electrons - electric energy.

Or The solar energy is used to heat large quantities of water which turns to steam

Wind Power

Kinetic energy of moving air particles impacts on specially designed propellers, or turbines and turns an electric generator.

Geothermal Power

Water is injected into a volcanically active area of the Earth and the heat of the underlying mantle turns the water to steam which is used to turn a turbine (generator).

Tidal Power

Tides are really just very, very long water waves. The water at the crest of the wave has more potential energy (imparted by the Moon’s

rotation around the Earth) and the wave turns a stationary generator by moving past it.

Physics - Concept: Energy Efficiency

Energy efficiency is a measure of how much energy is converted into another (desirable) form. It is usually expressed as a percentage. Many processes are surprisingly inefficient, for example many cars are only 15% - 25% efficient and of course nothing can exceed 100%. So, does this mean that energy is lost? Not at all!

When we determine efficiency we consider any energy that is not useful to be lost energy. In the example of the automobile a lot of the energy is lost as heat, some as noise and a little as friction between tires and the road.

Energy efficiency is determined like your percentage on tests:

Percent = (Correct answers/ Total answers) x 100%

Efficiency = (Energy Out/ Energy In) x 100%

Physics - Practice: Electric Energy and Power

Electrical energy, like other forms of energy, is a measured in Joules. However, electrical energy is often looked at by the amount of power output (measured in Watts (J/s)) or kilo Watt hours (kWh).

1. If you use your television an average of 3.0h/day for a 30 day month, and its power rating is 200.0W, how much energy will it use during that period. Express your answer in Joules and kWh.

(6.48x10⁷J, 18kWh)

2. If electricity costs 6.0cents/kWh what will it cost to run your TV for that month?

($1.08)

3. How much would it cost to operate a block heater rated at 400W for a 30 day month if you used it 10.0h/day?

(120kWh= $7.20)

4. How fast could a 5.0kg object move if 1.5kWh of energy was transferred to it?

(1.5x10³m/s)

5. Determine the amount of energy needed to raise a 75kg mass to a height of 6.0m.

a) How many kWh are required?

b) How many Watts are needed if the mass is raised in 10.0s? (4.4x10³J, 1.2x10^-

3kWh, 4.4x10²W)

6. Determine the energy in kWh needed to raise a 3000kg elevator 50.0m in a high rise?

How long (in seconds) would a 5.0kW motor have to run to do this? (0.41kWh, 0.082h, 294s)

7. An air conditioner rated at 1500W runs for 48h one weekend. How many Joules of energy are used? (2.6x10⁸J, 72kWh)

8. A hydro power plant produces electricity by utilising the energy of 75.0 tons (1ton=1000kg) falling a distance of 45.0m every second. (3.3x10⁷J, 3.3x10⁷W) a) How much energy is produced?

b) How much power is produced?

9. How many kWh are required to drive a 2500kg car 50km on a level highway if the combined road and air resistance is 1725N. (8.6x10⁷J, 24kWh)

10. Cycling becomes more and more difficult the faster you go. For a 145kg bike and rider

a) calculate the kinetic energy at 20km/h (2.2x10³J)

b) determine the work that must be done to increase the speed from 5.0km/h to 10km/h

(419J) c) determine the work that must be done to increase the speed from 15km/h

to 20km/h

(979J) d) Why would it be difficult to increase ones velocity on a bike much beyond

50km/h?

e) A person in good shape can put out about 0.25 horse power (1 hp = 746W) Calculate the time it would take to go from 0km/h to 15km/h.

(1.69s)

11. Use unit analysis to demonstrate that work, kinetic energy, potential energy all have the same units.

12. Prove that Nm is a unit of energy.

13. Prove that Ws is a unit of energy.

Physics - Practice: Electric Energy and Efficiency

Challenge questions

1) On the construction site an electric crane is used to lift materials 63m to the 10^th floor. A 180 kW motor requires 2.0 minutes to lift a 10 500kg load of bricks 218m high. How efficient is the crane? (22.5%)

2) Burning 1.0kg of coal releases 33MJ of energy. This energy is converted into electricity with an efficiency of 18%. Determine the mass of coal that must be used to supply a city with 2.0MWh. (1.2x10³kg)

3) It takes a natural gas (methane) heater a considerable amount of time to heat a swimming pool. A 150 kW heater takes 28 hours to heat 110 000L (110 000 kg) of water by 8.00^oC. How efficient is it? (24.4%)

Kinematics - Constant Velocity Lab - Speed of Moving Cars pg. 1

Problem: To determine the speed of cars travelling up the hill by the school.

Design: By measuring the time it takes for cars to travel from the bridge up the hill, students will calculate the velocity of various vehicles.

Procedure: Each group will consist of a Starter/Stopper, a Recorder and several Timers.

Starter/

Stopper: Looks out for car and gives signal to timers to start timing Gives signal for timers to stop timing.

Timers: Use stopwatch to time cars.

Recorders: Records number of the car, car description, and times for the car to travel a measured distance from the bridge.

1. The whole team follows the teacher's instructions and positions themselves at one of the marks on the guardrail. These marks are at 400 m, 410 m and 420 m from the exit of the bridge below.

2. Starters/Stoppers give the signal to start timing when cars come out of the shadow of the girders of the bridge.

3. Starters/Stoppers give the signal to stop timing when car is directly across from their mark on the guardrail.

4. Recorders record time and data on the table.

5. Record time and data for 10 vehicles.

Data: Record your data on the data table provided. Do the calculations in class.

Graphing: Use the graph paper provided to construct a distance/ time graph.

Record the distance/time point of three cars for the trip up the hill.

#1 - shortest time ; #2 - average time ; #3 - longest time Connect each point with the origin (0,0) (See diagram below)

Draw a sloped line on your graph from the origin to the data points for each of the three cars. Identify on the graph, the car with the shortest, average, and longest time. There should be a total of three slopes on your graph.

Time (s) Distance (m)

Constant Velocity Lab - Speed of Moving Cars pg. 2

Data Collection

:

Group Members:

Distance:

No. 1 2 3 4 5 6 7 8 9 10

Descripti on

Time 1 (s)

Time 2 (s)

Time 3 (s)

Time 4 (s)

Average (s)

Speed

(m/s) ave.

(km/h)

Constant Velocity Lab - Speed of Moving Cars pg. 3

Graphing:

Constant Velocity Lab - Speed of Moving Cars pg. 4

Analysis:

All work must be done on a separate sheet of paper. Use sentences where required.

1. Using the velocity formula, calculate the speed of each of the three cars used in the graph.

2. Calculate the slope of the three cars using the slope formula (slope = rise/run)

3. From observing your graph, how can you tell which car was travelling the fastest?

4. Write a generalised statement about the relationship between slope and velocity.

5. The speed limit on that road is 50 km/h. What is this speed in m/s?

6. Calculate the time required to make the trip, travelling at the speed limit and construct another line on your graph showing the slope for the speed limit.

Hint: Keep the unadjusted value that appeared in your calculator from question 5 and use it in the formula for this question.

7. From your data, how many of the 10-15 cars were travelling at speeds greater than the speed limit?

8. If the speed limit was set according to the average speed of cars on that road, what would the speed limit be?

Extensions: (show all your work)

9. The winning time in the 100-m sprint in a recent Olympic games was about 10 s.

a) Find the winner's average speed in m/s.

b) If you can run 2/3 of her speed, would it be worthwhile for you to try and outrun a grizzly bear in Jasper Park? Note: A typical bear's running speed is 45 km/h.

10. When the spacecraft Mariner 4 started transmitting pictures of the surface of Mars to Earth it took the radio signals 12.0 min to arrive. Radio signals, like light, travel through empty space at 3.00 x 10⁸ m/s. How far was Mariner 4 from Earth when the picture transmission started?

11. A motorist travels the entire length of a 200 km highway in 2 hours. What was his average speed for the trip:

in km/h?

in m/s?

You and your friend Kim are hiking in Jasper Park when you encounter a grizzly bear. When he rears up on his hind feet (the bear, not Kim), you know that he is going to attack. Immediately, Kim starts tightening the laces on her shoes. You say, "Why are you doing that, you can't outrun a bear anyway?" Her response, "I'm not trying to outrun the bear, I only have to outrun you!"

0.00

1.2 0.0

0.00

0.050

0.00

0.100

0.00

2.4

0.00

1.2 1.20.00 0.00

24

0.00

24

0.00

Kinematics – Air Track Lab: Uniform Velocity & Acceleration pg.1

Problem: How does the motion of an object that is travelling at a uniform speed compare with one that is accelerating uniformly.

Design: Through the use of an ‘air track spark timer’, we will be able to determine the distance travelled by an air cart with relation to time. Upon evaluating these measurements we will be able to determine the uniform velocity and uniform acceleration.

Part 1: Uniform Motion

Data Collection: Label your ticker tape Uniform Motion.

Measure and record the distance for each dot.

Note: - Measure the total distance to each of the dots from your 0 mark and record the total time and total distance.

- Time and distance will both increase from 0.

- Do not measure distances between adjacent dots.

Analysis Complete the table for the columns for t, d, d and vav. Use d and

and Calculations: the spark timer interval (usually 0.050 s) to calculate vav for each set of dots.

Example:

- Find the sum of the velocity values in the v column, calculate the average velocity and enter this amount in a box at the bottom of the v column.

- Show one sample calculation for each calculation you have done.

Graphing: - You will construct two graphs for the data from Part 1.

- Set up your graph page so that you have the distance/time graph above the velocity/time graph. (The time values should

correspond for both graphs).

t (x 0.050s) d (cm) d (cm) vav (cm/s)

- A line of best ft is necessary for both graphs.

Kinematics – Air Track Lab: Uniform Velocity & Acceleration pg.2

Part 2: Uniform Acceleration

Design/Data

Collection : Repeat the procedure for a second set of data, with the following differences:

- From the velocity data calculate the change in velocity, v, and make a column on the table.

- From the v and time calculate the acceleration, and make an acceleration column on the table.

- Calculate the average acceleration and put this value in a box at the bottom of the acceleration column.

Graphing: You will need to construct three graphs for this part. If possible, you should construct all three graphs on the same page, one above the other.

1. Draw the displacement/time graph at the top, 2. the velocity/time graph in the middle,

3. and the acceleration/time graph at the bottom.

We are doing this so that you can see the relationship between the three types of data.

Analysis: 1. What is the general shape of the displacement graph in Part 1? How is it different from the displacement graph from Part 2?

2. What is the general shape of the velocity graph in Part 1?

How is it different from the velocity graph from part 2?

3. Which graph from Part 2 looks like the displacement graph from Part 1?

4. Which graph from Part 2 looks like the velocity graph from Part 1?

5. What is the acceleration of your puck in Part 2?

6. If you were to describe the "line of best ft" for each of your graphs in one word what would it be?

What to hand in….

- Problem

- Procedure (for part 1 and 2)

- Data Collection Table (for part 1 and 2)

- Graphs (total of 5) - Analysis

Energy - Energy Conversions/Conservation

The Pendulum:

Background: A pendulum is a simple energy conversion device. It changes potential energy to kinetic energy and back again.

Materials: Pendulum bobs String

Activity: Make pendulum and attach it to your desk or table.

Measure the distance from the floor to the bottom of the bob.

Swing the bob up and measure the new height.

Let the pendulum swing and answer the following questions.

Questions: Consider the illustration above.

1. At what points does the pendulum have the most Potential energy?

2. At what point does the pendulum have the greatest amount of kinetic energy?

Experimental design: Construct your own pendulum and determine the following:

1. The amount of potential energy at rest (point B).

2. The amount of potential energy at the point from which you release it (point A).

3. How much kinetic energy it has at the lowest point in the swing?

4. The velocity it should have at the bottom of the swing.

A

B

C

D