PHYS 115PHYS 115Principles of Physics IPrinciples of Physics I

Dr. Robert KayeDr. Robert Kaye

What kinds of things will we talk about?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?What kinds of things will we talk about?

• Mechanics also includes description of Mechanics also includes description of solidssolids, , fluidsfluids, and , and gassesgasses– Blood pressure measurementsBlood pressure measurements– How hot-air balloons workHow hot-air balloons work– Why some insects can walk on waterWhy some insects can walk on water

• Field of Field of thermodynamicsthermodynamics– How refrigerators workHow refrigerators work– Why water pipes sometimes burst in the winterWhy water pipes sometimes burst in the winter– Why it is warmer on average in Seattle, WA than Why it is warmer on average in Seattle, WA than

Delaware, OH in the winterDelaware, 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:

• 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!

Symbol Prefix Factor of 10

n nano 10–9

micro 10–6

m milli 10–3

c centi 10–2

k kilo 103

M mega 106

Examples:

1 s = 10–6 s

1 cm = 10–2 m

1 Mg = 106 g

Example Problem #1.22

Solution (details given in class):

9.2 nm/s

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.

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 = r2

= 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 sUncertainty 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

• Plane Polar coordinate system

(4 m,2 m)

(1 m,4 m) points labeled by (x,y) coordinates

y (m)

x (m)O

y (m)

x (m)O

(5.7 m,450)r

points labeled by (r coordinates

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

• The “trig” functions relating sides a, b, c to angle are:– sin = b / c , cos = a / c , tan = b / a

– Remember (crazy) word “SOHCAHTOA” !• Pythagorean Theorem: a2 + b2 = c2

• sin–1(0.5) yields angle whose sine is 0.5 ( = 30°)

900

a

b c

Trigonometry Interactive

Example Problem #1.42

Solution (details given in class):

2.33 m

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?

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