Motion in One Dimension Reminder: Homework due Wednesday at the beginning of class Sig. figs Converting Units Order of magnitude 2.1 Reference Frame 2.2 average Velocity

Significant Figures Scientific notation is commonly used in physics; it allows the number of significant figures to be clearly shown. Much of physics involves approximations; these can affect the precision of a measurement also.

Reading Significant Figures Nonzero Digits are always significant Zeros between significant figures are significant. Examples: s cm 950.0X 10 1 mL

Answer In s : all four digits are significant In 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 X 10 1 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 g 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 2.7x10 2 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 The 165 million dollars Mars Polar Lander Units help you figure out equations: Speed in m/s Density in kg/m 3 Units help you determine the correct solution

Units, Standards, and the SI System QuantityUnitStandard LengthMeterLength of the path traveled by light in 1/299,792,458 second TimeSecondTime required for 9,192,631,770 periods of radiation emitted by cesium atoms MassKilogramPlatinum cylinder in International Bureau of Weights and Measures, in Paris

Order of Magnitude Viruses Mt Everest’s Height=8850m

Order of Magnitude

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 1. Multiplying by 1 leaves a quantity unchanged. 2. “1” can be represented as 3. Choose form for ‘1’ for which units match.

Converting units 1. You're stopped by police for speeding 30.0 km/h over the speed limit on an Ontario highway. What is the speed in mph? 2. That'll be a $180 fine, plus a $35 victim surcharge and a $5 court fee ($220 in all) should you decide to plead guilty and settle out of court. (in Canadian Dollars). What is the fine in US dollars?

Converting units km/h =? 1 km = miles 2. $220 Canadian Dollars = ? 1 US dollar = 0.97 Canadian dollar

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 = m  1 mg = 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/m 3

Question 1 atm = x10 5 Pa = lb/in 2 If you want to convert 0.46 atm to Pa you should A. Multiply 0.46 atm by lb/in 2 B. Multiply 0.46 atm by x10 5 Pa C. Divide 0.46 atm by lb/in 2 D. Divide 0.46 atm by x10 5 Pa

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!)

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. o x y -y -x

Position on a line 1.Reference point (origin) 2.Distance 3.Direction Symbol for position: x SI units: meters, m

Displacement on a line xfxf xixi Change of position is called Displacement: 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.