Transcript Intro

PHYS 115
Principles of Physics I
Dr. Robert Kaye
What kinds of things will we talk about?
• Field of mechanics (“classical” mechanics or
“Newtonian” mechanics)
– How do roller coasters work? How do airplanes fly?
How do satellites orbit the Earth?
• Mechanics provides answers to these and many
other questions about the world around us
• Provides physical theories and mathematical
engine to:
– Understand observed phenomena
– Predict future behavior
• 2 general areas of mechanics:
– Kinematics: Study of objects in motion
– Dynamics: Study of how forces produce motion
What kinds of things will we talk about?
• Mechanics also includes description of solids,
fluids, and gasses
– Blood pressure measurements
– How hot-air balloons work
– Why some insects can walk on water
• Field of thermodynamics
– How refrigerators work
– Why water pipes sometimes burst in the winter
– Why it is warmer on average in Seattle, WA than
Delaware, OH in the winter
Standards and Units
• Physics utilizes experimental observations and
measurements – need units to quote results
• Most common system of units is International
System (or SI), i.e. “metric” system – but be aware of
British System (used in the U.S.)
• SI unit standards:
– Time: second (s), defined in terms of cesium “atomic clock”
– Length: meter (m), defined in terms of distance
traveled by light in a vacuum
– Mass: kilogram (kg) = 1000 grams (g), defined
by mass of a specific platinum–iridium alloy
cylinder kept in France
• Note that standard of length in British
system (common in U.S.) is the inch
(1 in. = 2.54 cm)
Standards and Units
• Factor of 10 multiples of units are given by standard
prefixes:
Symbol
Prefix
Factor of 10
Examples:
1 ms = 10–6 s
1 cm = 10–2 m
1 Mg = 106 g
m
m
nano
micro
milli
10–9
10–6
10–3
c
k
M
centi
kilo
mega
10–2
103
106
n
• Remember to carry units throughout entire
calculation
 d = vt = (5 m/s) (2 s) = 10 m
• Treat units as algebraic characters
• Great way to convert from one set of units to
another!
Example Problem #1.22
Suppose your hair grows at the rate of 1/32
inch per day. Find the rate at which it grows in
nanometers per second. Because the
distance between atoms in a molecule is on
the order of 0.1 nm, your answer suggests
how rapidly atoms are assembled in this
protein synthesis.
Solution (details given in class):
9.2 nm/s
Significant Figures (# of meaningful digits)
• When multiplying or dividing numbers, result
should have same # of sig. figs. as the
number with the fewest sig. figs.
 A = pr2
 p = 3.141592654…(10 sig. figs.)
 r = 2.53 cm (3 sig. figs.)
 A = 20.1 cm2 (3 sig. figs.)
 Use scientific notation if numbers get too big or
small
• When adding or subtracting numbers, look at
location of decimal point:
16.71 s + 5.2 s = 21.9 s
Uncertainty is in the tenth digit
CQ1: Use the rules for significant figures to
find the answer to the addition problem:
21.4 + 15 + 17.17 + 4.003 =
A) 57.573
B) 57.57
C) 57.6
D) 58
E) 60
Uncertainties
• All measurements have uncertainties (amount
depends on measuring device)
– Uncertainties indicate the likely maximum difference
between measured and true value
• Example: Measuring the diameter of a quarter
– Using a ruler, you may get d = 2.40  0.05 cm
• Min. value you would likely get is dmin = 2.35 cm
• Max. value you would likely get is dmax = 2.45 cm
– Using a micrometer, you may get
d = 2.405  0.001 cm
• dmin = 2.404 cm
• dmax = 2.406 cm
Order-of-magnitude calculations
• Sometimes we wish to obtain a numerical
result that is accurate only to a factor of 10
for estimation purposes
• Example: Estimate the number of marbles
that could fill an Olympic-size swimming pool
• “Order-of-magnitude” calculations (“Fermi
problems”)
• Usually require some preliminary
assumptions
• Symbol “~” stands for “on the order of”
• “Three orders of magnitude” stands for factor
of 1000 (103)
CQ2: What is the approximate number of
breaths a person takes over a period of
70 years?
A) 3 × 106 breaths
B) 3 × 107 breaths
C) 3 × 108 breaths
D) 3 × 109 breaths
E) 3 × 1010 breaths
Coordinate systems
• Many times in physics we wish to describe
positions in space, or make measurements with
respect to a reference point
• Coordinates are used for this purpose
– Positions along a line requires only one coordinate
– Positions along a plane require two coordinates
– Positions in space require three coordinates
• Coordinate systems are a way to keep track of and
map coordinates. They consist of:
– A fixed reference point called the origin (“Checkpoint
Charlie” or “home base”) having coordinates (0,0) in 2–D
– A set of specified axes with appropriate scale and labels
– Directions on how to label coordinates in the system
Coordinate systems
• Cartesian (or Rectangular) coordinate system
y (m)
(1 m,4 m)
(4 m,2 m)
points labeled by
(x,y) coordinates
x (m)
O
• Plane Polar coordinate system
y (m)
(5.7 m,450)
r
points labeled by
(r,q) coordinates
q
O
x (m)
Trigonometry Review
• Trigonometry deals with the special properties of right
triangles, particularly with the relationships between
the lengths of their sides and the interior angles
c
b
900
Trigonometry
Interactive
q
a
• The “trig” functions relating sides a, b, c to angle q are:
– sinq = b / c , cosq = a / c , tanq = b / a
– Remember (crazy) word “SOHCAHTOA” !
• Pythagorean Theorem: a2 + b2 = c2
• sin–1(0.5) yields angle whose sine is 0.5 (q = 30°)
Example Problem #1.42
A ladder 9.00 m long leans against the side of
a building. If the ladder is inclined at an angle
of 75.0° to the horizontal, what is the
horizontal distance from the bottom of the
ladder to the building?
Solution (details given in class):
2.33 m
CQ3: At a horizontal distance of 45 m
from a tree, the angle of elevation to the
top of the tree is 26°. How tall is the tree?
A) 22 m
B) 31 m
C) 45 m
D) 16 m
E) 11 m