PHYSICS AND MEASUREMENT

FUNDAMENTAL QUANTITIES

SI units:Time – secondMass – KilogramLength – meter

TIME

Before 1967, a second was defined as (1/60)(1/60)(1/24) of a mean solar day. As this is based on the rotation of Earth, it is not universal.

Redefined as 9,192,631,770 times the period of vibration of radiation from the cesium-133 atom making use of the high precision atomic clock.

MASS

Defined by the mass of a specific platinum-iridium alloy cylinder kept at the International Bureau of Weights and Measures in France.

Established in 1887Duplicate at the National Institute of Standards and Technology in Gaithersburg, MD.

LENGTH

A meter is the distance traveled by light in a vacuum during a time of 1/299,792,458 second. (1983)

Originally defined as one ten-millionth of the distance from the equator to the North Pole along a longitudinal line that passes through Paris. (1799, earth-based)

Until 1960, distance between to marks on a specific platinum-iridium bar.

Between 1960-1970, defined as 1,650,763.73 wavelengths of orange-red light emitted from a krypton-86 lamp.

PERCENT ERROR

Percent error is a way of comparing a calculation or a measurement to an exact, known value.

STANDARD DEVIATION

The standard deviation is one number that is used to express how far (on average) the data points are from the mean value of the data set. 

ADDING AND SUBTRACTINGWITH STANDARD DEVIATION

Addition

1. Add the principal numbers.

2. Add the standard deviations

() + () = ( + ) ()

Subtraction

3. Subtract the principal numbers.

4. Add the standard deviations

() - () = ( - ) ()

MULTIPLYING AND DIVIDING WITH STANDARD DEVIATION

Multiplication

1. Multiply the principal numbers

2. Determine the fractional uncertainty (FUN) of each principal number.

and

3. Add the fractional uncertainties to get total FUN.

FUN (total) = FUN (x) + FUN (y)

4. Multiply total FUN by the principal result to get the total uncertainty.

EXAMPLE CALCULATION

Suppose in a lab situation that you would like to calculate the velocity of an object with standard deviation. The displacement of the cart based on your measurements is (1.57 +/- 0.07) meters and the cart’s time to travel this distance is (0.68 +/- 0.02) seconds.

To calculate velocity:

To get your principle avg velocity, divide your principle numbers.

EXAMPLE CALCULATION CONT…

To get your standard deviation, First find your fractional uncertainty for each value (essentially your

percent uncertainty, in decimal form) and

Next, add your fractional uncertainties to get total uncertainty

Finally, multiple your total fractional uncertainty to your principle number to get your total standard deviation.

So…