# Lab 2 - Measurement of Mass, Length, and Time.pdf - LAB 2...

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2-1 LAB 2: Measurement of Mass, Length, and Time Consider the following statement: “Beer costs ten.” Ten what? If we’re talking about a beer for ten dollars, it’s a little steep. Ten Euros, it’s a lot steep. Ten pesos? Pass. The problem is compounded when we realize the amount of beer is also unknown. If we settle on \$10, questions remain about this deal if it’s for a single draw, a can, a case or a keg. Anything that can be counted has a unit . “1 six-pack costs ten dollars .” Without a unit, measured values are meaningless. After all, the point of a measurement is to tell us how much of something we have. Different systems of units exist around the world. You are probably most familiar with the English System of feet for distance and pounds for force. The metric system or MKS (meter, kilogram, seconds) is another system used globally for science and is part of the International System (SI) of units. Four fundamental units length, time, mass and charge are not the only physical quantities, but they are the most basic. Velocity (m/s), Acceleration (m/s 2 ), Force (N or kg m/s 2 ), Energy (J or kg m 2 /s 2 ) are real physical quantities , but they are made (derived) from relationships between the most basic units. Because the units for these derived quantities can sometimes get to be large and cumbersome, we give them special names like Newtons (N) or Joules (J). Anytime you must perform a calculation, *always* include the units in your work and break them down to their most basic forms if necessary to cancel any out. Units in calculations can always signal when something might be wrong, such as a velocity that comes out in hours per miles because we performed the calculation upside down! Most of the time when reporting measurements we will do so in standard units (m, kg, s). If measurements are small, they will often be recorded in smaller units (cm, mm, g, etc.). It is important to know how the metric prefixes modify the base units, and to be able to convert them accordingly. Prefix Modification to Base Unit Example pico- (p) × 10 -12 or ÷ 1 trillion 0.3pF = 3 × 10 -13 F nano- (n) × 10 -9 or ÷ 1 billion 532nm = 5.32 × 10 -7 m micro- or “mu”) × 10 -6 or ÷ 1 million 3.6 μ m = 3.6 × 10 -6 m milli- (m) × 10 -3 or ÷ 1,000 256ms = 0.256s centi- (c) × 10 -2 or ÷ 100 2.5cm = 0.025m kilo- (k) × 10 3 or × 1,000 78.5g = 0.0785kg mega- (M) × 10 6 or × 1 million 500MJ = 5 × 10 8 J giga- (G) × 10 9 or × 1 billion 8.21GW = 8.21 × 10 9 W tera- (T) × 10 12 or × 1 trillion 2TB = 2 × 10 12 B Special Note: Even though kg are not the base unit, in SI the “kg” is the standard unit. It is a mystery.
2-2 Unit Conversions All systems have something in common: they measure the same physical quantities, but the standard “amount” may vary from system to system. Because different units of distance still measure distance , you can easily convert from one system to another if you know the conversion factor (an “exchange rate”) between systems. Consider a conversion of 1 ft to cm knowing 1 in = 2.54 cm 1 ft 12 in 2.54 cm = 30.48 cm ft in In the conversion above, begin with the amount needing conversion. Because we don’t know the conversion factor from cm to ft, we will need to use a second