PHYS 115 Principles of Physics I

1. PHYS 115Principles of Physics I Dr. Robert Kaye

2. 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

3. 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

4. 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)

5. Standards and Units Examples: 1 ms = 10–6 s 1 cm = 10–2 m 1 Mg = 106 g • 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!

6. 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

7. 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

8. CQ1: Use the rules for significant figures to find the answer to the addition problem:21.4 + 15 + 17.17 + 4.003 = • 57.573 • 57.57 • 57.6 • 58 • 60

9. 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 getd = 2.40  0.05 cm • Min. value you would likely get isdmin = 2.35 cm • Max. value you would likely get isdmax = 2.45 cm • Using a micrometer, you may getd = 2.405  0.001 cm • dmin = 2.404 cm • dmax = 2.406 cm

10. 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)

11. CQ2: What is the approximate number of breaths a person takes over a period of 70 years? • 3 × 106 breaths • 3 × 107 breaths • 3 × 108 breaths • 3 × 109 breaths • 3 × 1010 breaths

12. 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

13. y (m) y (m) x (m) x (m) O O Coordinate systems points labeled by (x,y) coordinates (1 m,4 m) • Cartesian (or Rectangular) coordinate system • Plane Polar coordinate system (4 m,2 m) (5.7 m,450) points labeled by (r,q)coordinates r q

14. 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 sidesa, b, cto angleqare: • 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°) c Trigonometry Interactive b q 900 a

15. 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

16. 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? • 22 m • 31 m • 45 m • 16 m • 11 m