PHY 2048 Fall 2009 LECTURE 1 Units & Calculations
POWERS OF TEN 1 10 100 1,000 10,000 100,000 1,000,000 = 101 = 102 = 103 = 104 = 105 = 106 1 0.1 0.01 0.001 0.0001 0.00001 0.000001 = 10-1 = 10-2 = 10-3 = 10-4 = 10-5 = 10-6
Wright the following numbers in scientific notation: 45100 = 4.5 x 104 310,000,000,000 = 3.1 x 1011 0.001000 = 1.0 x 10-3 0.0000000000012 = 1.2 x 10 -12
What number is 510-5107 5 0.5 50 500 None of the above
500 x 6000 = (5x102) x (6x103) = 30 x 105 = 3x106 6000 ÷ 500 = (6 x 103) ÷ (5x102) = 60 ÷ 5 =12 0.005 x 0.000006 = (5x10-3) x (6x10-6) = 30x10-9=3x10-8 0.003 ÷ 0.000006 = (3x10-3) ÷ (6x10-6) = 0.5x103 = 5x102 =500
There are questions like "how fast", "how far", or "how much" which, when answered, we must supply a unit of measurement: How fast: 50 How far: 30 How much: 8 miles per hour miles pounds Because of this, numbers in science will always have "units". These units are just as important as the numbers when communicating observations. Never write a number without its units.
1 mile = 1760 yards 1 yard = 3 feet 1 foot = 12 inches The British System of Measurement is commonly used as the day to day system in the United States. We are familiar with this system: we know about pounds, feet, and gallons. However, the British system is an impossible system to do conversions between units since the relations between units have no pattern (they are arbitrary). 1 mile = 1760 yards 1 yard = 3 feet 1 foot = 12 inches
1 centimeter = 10 millimeters The International System of measurement (abbreviated SI) is commonly called the metric system in the United States. The relation between units are multiples of ten. All science measurements are made using this system. 1 kilometer = 1000 meters 1 meter = 100 centimeters 1 centimeter = 10 millimeters
Relation between SI and British systems metric British approximate relation m yd 1 yd = 0.9 m m mile 1 mile = 1600 m mm in 1 in = 25 mm liter quart 1 quart = 1 liter liter gallon 1 gallon = 3.8 liters g lb 1 lb = 450 g
1 lb on earth has a mass of 0.45 kg 1 meter = 3.3 ft = 39 inches 1 cm = 0.39 inches 1km = 0.62 miles 1 ft = 30 cm 1 inch = 2.5 cm 1 mile = 1.6 km 1 kg weights 2.2 lb on earth 1 lb on earth has a mass of 0.45 kg Celsius temperature =5 x (Fahrenheit temperature – 32) / 9 Fahrenheit temperature = 32 + (9 x Celsius temperature) / 5
Using wrong units caused trouble as recently as September 1999, when a probe launched by NASA was lost in the atmosphere of Mars because the engineers who built the engines were working in British units and the scientists who were controlling the engines were working in SI units. This lets us emphasize that units are part of every result.
In physics, there are three basic quantities that are the basis for everything: Length, Time, Mass We understand all these quantities from experience but we find very hard to define!
International System of Units (abbreviated SI from Système Internationale) Quantity unit symbol Length meter m Time second s Mass kilogram Kg The meter, second, and kilogram are called base units in SI Other units are expressed in terms of them
Common prefixes in SI Prefixes are standard letters that are attached in front of a unit and make it a multiple of some power of 10. the prefix is read and multiplies the unit by μ micro 10-6 m milli 10-3 c centi 10-2 K kilo 103 M mega 106 G giga 109
Common Prefixes Power Prefix Abbreviation 1015 peta P 1012 tera T 109 giga G 106 mega M 103 kilo k 102 hecto h 101 deka da 10–1 deci d 10–2 centi c 10–3 milli m 10–6 micro 10–9 nano n 10–12 pico p 10–15 femto f
Mass is the quantity of matter in an object Mass is the quantity of matter in an object. It is also the measure of the inertia that an object exhibits in response to any effort made to start it, stop it, or change its state of motion in any way. Demo with hammer+lead+wood here.
To compare the inertia, or mass, of two objects, accelerate them side-by-side. The one that requires the most force is the one with the larger mass.
International System of Units Quantity unit symbol
International System of Units Quantity unit symbol Length meter m
International System of Units Quantity unit symbol Length meter m Time second s
International System of Units Quantity unit symbol Length meter m Time second s Mass kilogram Kg
International System of Units (abbreviated SI from Système Internationale) Quantity unit symbol Length meter m Time second s Mass kilogram Kg The meter, second, and kilogram are called base units in SI Other units are expressed in terms of them
Dimensions of Some Common Physical Quantities Quantity Dimension Distance [L] Area [L2] Volume [L3] Velocity [L]/[T] Acceleration [L]/[T2] Energy [M][L2]/[T2]
If a distance d has units of meters, and a time T has units of seconds, does the quantity T + d make sense physically? What about the quantity d/T ?
The quantity T + d does not make sense physically, because it adds together variables that have different physical dimensions. The quantity d / T does make sense, however; it could represent the distance d traveled by an object in the time T.
Which of the following equations is dimensionally consistent Which of the following equations is dimensionally consistent? (a) v = at, (b) v = ½ at2 (c) t = a/v, (d) v2 = 2ax
To find a speed requires measurements of length and time.
Average speed is distance traveled divided by the time used. average speed = distance/time v = d/t
What is the unit of speed in SI? Quantity unit symbol Speed=length/time
International System of Units Quantity unit symbol Length meter m Time second s Mass kilogram Kg Speed meter/sec m/s
Photographs can be used to measure motion. ANIMATED: one mouse click brings up the last sentence. While the camera’s shutter was open, both the runners and the camera moved to blur this photo.
The real speed at any moment is called instantaneous speed.
(final speed – initial speed) Galileo was the first to analyze motion in terms of measurements and mathematics. He described acceleration, which is the rate of change of speed. (final speed – initial speed) acceleration = ______________________ time required
Galileo did experiments to convince others that the acceleration caused by gravity would be the same for all freely falling objects if there was no air to retard their motion. He dropped two heavy metal balls together from the leaning tower in Pisa, Italy. Although one weighed far more than the other, they reached the ground almost at the same time. ANIMATED: One mouse clicks bring the last paragraph in.
A tennis ball and a golf ball dropped side-by-side in air A tennis ball and a golf ball dropped side-by-side in air. The tennis ball is affected more by the air’s resistance than the golf ball. The larger the object is, and the faster it is falling, the greater the air’s resistance to its motion, as skydivers all know… Tennis ball and golf ball falling side-by-side in air; the tennis ball lags.
Skydivers depend on air to retard their downward acceleration. Terminal speed in this position average 120 mph (about 50 m/s). Skydivers depend on air to retard their downward acceleration.
When most of the air is removed from a container, feathers and apples fall almost side-by-side, their speeds changing at almost the same rate. If all the air were removed, they would accelerate downward at exactly the same rate. Notice here that the vacuum is only partial, point out the top and bottom images and show that the feather is being left behind…
In a vacuum the feather and apple would fall exactly together if released at the same time. The positions here simulate a strobe photo.
International System of Units Quantity unit symbol Length meter m Time second s Mass kilogram Kg Speed meter/sec m/s Acceleration meter/sec2 m/s2
Here two heavy balls begin “free fall” at the same time. The red one is dropped, so it moves straight downward. The yellow ball is given some speed in the horizontal direction as it is released. ANIMATED: Two mouse clicks. (The next two slides appear with a mouse click with almost the same figure but different text, making this one seem animated.)
A Vector and Its Scalar Components The vector ŕ is defined by its length (1.50m) and its direction angle(25o) measured counterclockwise from the positive X axis.
A Vector and Its Scalar Components Alternatively, the vector ŕ can be defined by its X component, rx=1.36m, and its Y component, ry=0.634m.
A Vector Whose x and y Components Are Positive
Vector Angle
Vector Angle
Adding Several Vectors
Identical Vectors A at Different Locations
A + B = B + A
A + B = B + A
Graphical Addition of Vectors
Component Addition of Vectors
Component Addition of Vectors
Vector Subtraction
Vector Subtraction D= A – B Dx= Ax – Bx Dy= Ay - By
Unit Vectors The unit vectors x and ŷ points in the positive x and y directions, respectively.
Vector Components
Multiplying a Vector by a Scalar