LESSON 2

PHYS 1100 LESSON 2 FOR
TUESDAY, AUGUST 03, 2010

I Introduction

II Logistics: Seating, Syllabus, etc.

Here are two additional resources that may help in solving physics problems (solutions are here)

www.cramster.com

www.wolframalpha.com

III Review of Lesson 1: Measurements, Ch 1
Units – metric (mks; also known as SIU)
Meters for length
Length / Distance / Displacement, “x”
Kilograms for mass
Mass; 1kg = 2.2 lbs at sea level
Seconds for time
Time; second; 3600 sec = 1 hour
Coordinates: 3D: x, y, z
Speed: v = Dx/Dt; D = “change of” or
(x2 – x1) / (t2 – t1)
Velocity = speed with a vector
Acceleration = Dv / Dt or (v2 – v1) / (t2 – t1) ; often a vector
Scientific Notation:
5,617 = 5.617 x 103 or 5.617 x 10^3 or 5.617 E3
Significant Figures: 5,617 x 27 = 151,659 ? NO! 150,000 or 1.5 x 105
Estimating (ball parking; educated guessing): 5,617 x 321 = (5.6 x 3) x 105 = 16.8 x 105 = 1.68 x 106 for a guess. Exact is 1,803,057 = 1.80 x 106
Trigonometry: Create a right triangle inside a “unit” circle of radius r = 1. Then the x-component will be r cosine(θ) and the y-component will be r sine(θ) . However, since r = 1, we realize that the x-component will almost always be cosθ while the y-component will almost always be sinθ. Plus, sinθ / cosθ = y/x = tangent of the angle, or, tanθ.

IV Lesson 2: Vector Physics/Motion, Ch 2



Vectors
Virtual arrow: magnitude (size) and direction

heads, tails

adding vectors ≠ adding algebraically



adding vectors

align the head of one vector with the tail of another; never put 2 tails together, or 2 heads

together: →→ is

okay; NOT →←

and NOT ←→

→↑ is okay; but ↑→ is not okay; and →↑ is not okay
A vector usually has an arrow (→) above it: , or a “hat” or “carrot” (^) above it:

Pythagoras (576 BC – 495 BC)














KISMIE
Velocity, acceleration, force, momentum, or any number of other concepts can be represented as vectors
Components: see above; the x-component of vector A+B is A; the y-component is B.
If a vector is not directly along the x-axis or along the y-axis, it can be broken down into its x- and y- components
Acceleration vector, along an inclined plane: a = g sin θ, where θ is the angle shown:









Projectile Motion





















Range, height, angle (above)



Circular motion
v = 2pr/P Э 2pr = c (circumference); r = radius; P = period, in seconds, to make one trip around the circle; and P = 1/n, Э n = the frequency in cycles per second (Hz).

v2/r = 4p2r/P2, but since P = (1/n), then P2 = (1/ n)2, or (1/P2) = n2


So, v2/r = 4p2rn2 which can be written as v2/r = (2pn)2 r

And, in circular motion, a = v2/r =
(2pn)2 r, “centripetal acceleration”
However, 2pn = w in rad/sec, thus a = w2r



If part of a circle, say, s, is the arc, AB, then we can say that for small “s” that r sin θ = s, and if it’s even smaller, then r θ = s

because for small θ, sin θ° = θr where the angle, θ, is measured in radians, not degrees. 360° = 2p radians, so 1 radian = 57.3°.

Since v = dist/time, then v = s/t = r θ/t but is another way of writing w, so v = wr and v2/r = w2r = a, “acceleration”


V Laboratory Exercise 2: Density of Water


VI Conclusion
Finish Homework 1 Problems until end of period: HWK Assignment 1: Read Chapters* 1-4 and do Problems 1, 3, 9, 13, 19, 25, 29, 31, and 39 on pp 15-16; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, 53, 63, 65 and 71 on pp 48-54; Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, and 53 on pp 76-80; and Problems 1, 3, 9, 13, 19, 25, 29, 31, 39, and 53 on pp 103-107. (due 5/6)
Prepare for Test 1 (review and problems)