Physics for Engineering
First Year Physics online publication
Table of Contents
- Introduction to physics
- Chapter 01: Converting Units
- Kinematics, vectors and scalars
- Straight line and projectile motion
- Force and motion
- Rotational motion and gravitation
- Work, energy and power
- Elasticity, stress and strain
- Fluids
- Thermal properties and heat
- Electrostatics: electric forces and fields
- Electrostatics: energy
- Direct current circuits
- Magnetism and electromagnetism
- Waves, light and optics
- Nuclear physics
Chapter 01: Converting Units
INTRODUCTION
Keen observation is essential in any scientific endeavour. Very often, observation goes hand in hand with performing measurements. All measurements have units in which the measurement is displayed. If we measuring time, these units could be hours, minutes, seconds or even fractions of a second such as picosecond or nanosecond.[br][br]Units play an important role in science, as they define a given value. Without a unit, the value of a measurement is meaningless. Your weight cannot be 75. Your mass has to be 75 kilogram (or 75 kg) for the value to have meaning. [br][br]Unit conversion is the process of changing from one unit to another. For example instead of saying you weigh 75 kg, we could convert your weight to grams. Then you would weigh 75 000 grams (or 75 000 g). This was an easy unit conversion. What if we wanted to convert a speed of 30 miles per hour to metres per second?
THEY GOT NUMBER RIGHT, BUT UNIT WRONG
In 1983, an Air Canada flight ran out of fuel above the town Gimli in Manitoba, Canada. The plane is reported to have been Air Canada's first aircraft to use metric measurements instead of imperial measurements. The plane's onboard fuel guage was not working, so the ground crew used measuring "dipsticks" to check how much fuel the plane required during refuelling. They got the measurement number correct, but assumed that they were referring to pounds (lbs) of fuel instead of kilograms (kg) of fuel. 1 lbs equals roughly 0.5 kg. This meant they they only half-filled the tank before take-off. Luckily the pilot was able to glide the plane safely onto the Gimli runway, giving the plane the nickname "Gimli Glider".
The Gimli Glider
CONVERTING FROM ONE UNIT TO ANOTHER
[list=1][*][color=#0000ff]Compare the two units[/color] and make sure that they both measure the same thing. You cannot convert 2 inches to kilograms! The one units measures length while the other measures time. If you are asked to convert 2 inches to centimetres, this can be done since both are units of length.[/*][*][color=#0000ff]Look up the conversion factor[/color] before you do the math. If for example you need to convert 2,3 inches to centimetre, you need to know that 1 inch = 2,54 centimetres (or 1 in = 2,54 cm). [br][/*][*][color=#0000ff]Write the conversion factor as a fraction[/color]. For example we know there are 2,54 cm in every 1 in. Written as a fraction this would be 2,54 cm / 1 in. We read this as 2,54 centimeters per inch.[/*][*][color=#0000ff]Set up a multiplication problem[/color], using your original number and the conversion factor. Multiplying these two numbers together will give you your answer. (2,3 in) [b]x ([/b]2,54 cm / 1 in) = ?[/*][*][color=#0000ff]Solve the multiplication problem[/color]. It's important to keep track of your units while doing so. [/*][/list][list][*][i][color=#ff0000][size=85]Notice, the inches cancel out, leaving only centimetres in the answer.[/size][/color][/i][/*][*][i][color=#ff0000][size=85][math]\frac{2,3in}{1}\times\frac{2,54cm}{1in}=5,84cm[/math][i][color=#ff0000][size=85][/size][/color][/i][/size][/color][/i][/*][/list]
CONVERT THE FOLLOWING
1. Convert 5,120 g to kg[br][br]2. Convert 15 kl to ml[br][br]3. Convert 245 mm to m
ENGINEERING AND SCIENTIFIC NOTATION
[u][color=#0000ff]Engineering notation[/color][br][/u][br]Engineering notation is a version of scientific notation in which the exponent of ten must be divisible by 3. Only the following unit prefixes are allowed. [i][size=85](Note, they are all multiples of 3).[br][br][table][tr][td]Exponent (10[sup]n[/sup])[/td][td]Prefix [/td][td]Symbol [/td][/tr][tr][td]12[/td][td]tera[/td][td]T[/td][/tr][tr][td]9[/td][td]giga[/td][td]G[/td][/tr][tr][td]6[/td][td]mega[/td][td]M[/td][/tr][tr][td]3[/td][td]kilo[/td][td]k[/td][/tr][tr][td]-3[/td][td]milli[/td][td]m[/td][/tr][tr][td]-6[/td][td]micro[/td][td][math]\mu[/math][/td][/tr][tr][td]-9[/td][td]nano[/td][td]n[/td][/tr][tr][td]-12[/td][td]pico[/td][td]p[/td][/tr][tr][td][br][/td][td][/td][td][/td][/tr][/table][code][/code][br][/size][/i]Examples:[br][list][*]40 000 000 000 m = 40 x 10[sup]9 [/sup]m = 40 Gm[/*][*]-0,540 N = -540 10[sup]-3[/sup] N = -540 mN[/*][*]2,456 x 10[sup]11[/sup] m[sup]2[/sup] = 0,2456 x 10[sup]12[/sup] m[sup]2[/sup] = 0,246 Tm[sup]2[/sup][/*][/list][u][br][/u][color=#0000ff][br]Scientific notation[/color][br][br]