Motion in One Dimension Reminder: Homework due on Wed, August 29 Converting Units Order of magnitude 2.1 Reference Frame 2.2 average Velocity

Reading Significant Figures Nonzero Digits are always significant Zeros between significant figures are significant. Examples: 409.8 s 0.058700 cm 950.0X 101 mL

Answer In 409.8 s : all four digits are significant In 0.058700 cm: the two zeros on the left are not significant, they are used to place a decimal point, the numbers 5,8,7 are significant, and so are the two final zeros. In 950.0 X 101 ml: the final zero is significant since it comes after the decimal point. The zero at its left is also significant since it comes between two other significant digits, so the results is four significant figures.

Adding Significant Figures 67.9 g + 0.002 g + 3.51 g = ? Sum (or difference) can’t be more precise than least precise quantity Answer: 71.4 g When you add or subtract you keep the decimal place of the least precise value.

Multiplying Significant Figures Distance = velocity x time Velocity = 65.4mph Time = 4.2 hours Distance=274.7 or 275 or 2.7x102 miles When you multiply (or divide) you keep the number of significant figures that are equal to the quantity with the smallest number of significant figures.

Importance of Units The 165 million dollars Mars Polar Lander Units help you figure out equations Speed in mph Density in kg/m3 Units help you determine the correct solution www.nasa.gov

Units, Standards, and the SI System Quantity Unit Standard Length Meter Length of the path traveled by light in 1/299,792,458 second Time Second Time required for 9,192,631,770 periods of radiation emitted by cesium atoms Mass Kilogram Platinum cylinder in International Bureau of Weights and Measures, in Paris

Units, Standards, and the SI System Figure 1-5. Caption: Some lengths: (a) viruses (about 10-7 m long) attacking a cell; (b) Mt. Everest’s height is on the order of 104 m (8850 m, to be precise).

Units, Standards, and the SI System

Units, Standards, and the SI System

Units, Standards, and the SI System We will be working in the SI system, in which the basic units are kilograms, meters, and seconds. Quantities not in the table are derived quantities, expressed in terms of the base units. Other systems: cgs; units are centimeters, grams, and seconds. British engineering system has force instead of mass as one of its basic quantities, which are feet, pounds, and seconds.

Converting units Problem 11.(I) Write the following as full (decimal) numbers with standard units: (a) 286.6 mm, (b) 35mV, (c) 760 mg, (d) 60.0 ps, (e) 22.5 fm, (f) 2.50 gigavolts.

1yd=3ft and 1m=3.28ft Converting units Problem 15. (II) What is the conversion factor between (a) ft2 and yd2 (b) m2 and ft2 1yd=3ft and 1m=3.28ft

Converting units Write this in miles/s and miles/hour 30.0 km/h =? 1 km = 0.6214 miles 1 mile=1.6093km How many Us dollars is in 220 Canadian dollars? $220 Canadian Dollars = ? 1 US dollar = 1.31 Canadian dollar

Converting units

Question 1 atm = 1.013 x105 Pa = 14.70 lb/in2 If you want to convert 0.46 atm to Pa you should Multiply 0.46 atm by 14.70 lb/in2 Multiply 0.46 atm by 1.013 x105 Pa Divide 0.46 atm by 14.70 lb/in2 Divide 0.46 atm by 1.013 x105 Pa 16

Converting units Multiplying by 1 leaves a quantity unchanged. “1” can be represented as Choose form for ‘1’ for which units match.

Prefixes Prefixes correspond to powers of 10 Each prefix has a specific name Each prefix has a specific abbreviation

Prefixes The prefixes can be used with any base units They are multipliers of the base unit Examples: 1 mm = 10-3 m 1 mg = 10-3 g

Fundamental and Derived Quantities In mechanics, three fundamental or base quantities are used Length Mass Time Will also use derived quantities These are other quantities that can be expressed as a mathematical combination of fundamental quantities

Density Density is an example of a derived quantity It is defined as mass per unit volume Units are kg/m3

Order of Magnitude: Rapid Estimating A quick way to estimate a calculated quantity is to round off all numbers to one significant figure and then calculate. Your result should at least be the right order of magnitude; this can be expressed by rounding it off to the nearest power of 10. Diagrams are also very useful in making estimations.

Order of Magnitude: Rapid Estimating Example 1-6: Thickness of a page. Estimate the thickness of a page of your textbook. (Hint: you don’t need one of these!) Figure 1-8. Caption: Example 1–6. Micrometer used for measuring small thicknesses. Answer: Measure the thickness of 100 pages. You should find that the thickness of a single page is about 6 x 10-2 mm.

Chapter 2: Kinematics in one Dimension Coordinate Axis In Physics we draw a set of coordinate axis to represent a frame of reference. In one dimensional axis coordinate, the position of an object is given by its x or y. y -x x o -y

Position on a line Reference point (origin) position Distance Direction The position of Charlotte in reference to Fort Mill ( Fort Mill is the origin) Symbol for position: x SI units: meters, m

Displacement on a line Change of position is called Displacement: xf xi Displacement is a vector quantity It has magnitude and direction

Displacement Defined as the change in position during some time interval Represented as x SI units are meters (m) x can be positive or negative Different than distance – the length of a path followed by a particle. Displacement has both a magnitude and a direction so it is a vector.

Example Mary walks 4 meters East, 2 meters South, 4 meters West, and finally 2 meters North. The entire motion lasted for 24 seconds. Determine the displacement and distance Mary travelled.

Vectors and Scalars Vector quantities need both a magnitude (size or numerical value) and direction to completely describe them Will use + and - signs to indicate vector directions Scalars quantities are completely described by magnitude only

Average Speed Average speed =distance traveled/ time elapsed Example: if a car travels 300 kilometer (km) in 2 hours (h), its average speed is 150km/h. Not to confuse with average velocity. Average speed is a scalar

Average Velocity The average velocity is rate at which the displacement occurs The SI units are m/s Is also the slope of the line in the position – time graph

Average Velocity, cont Gives no details about the motion Gives the result of the motion It can be positive or negative It depends on the sign of the displacement It can be interpreted graphically It will be the slope of the position-time graph

Not to Confuse Speed is a number : a scalar Velocity is a vector : with a magnitude and a direction