Scientific

Measurement Units Measurements and Mathematics Topic 1 Evaluating

Experimental Designs Graphing Data Scalar and

Vector Quantities Solving Equations

While Using Algebra Tools for

Measurement Uncertainty in

Measurement Before Adding/Subtracting/Multiplying/Dividing values, they must have the same units.

After Adding/Subtracting sum or difference is rounded to the same decimal point value as the least sensitive measurement.

When Multiplying/Dividing values, the answer is rounded to the same number of SigFigs as the lowest value SigFigs in the given.

ex. (200.0cm)(2.6cm)=520cm²

*The product can only have 2 SigFigs, since 2.6 is the smallest value of SigFigs. Add, Subtract, Multiply, Divide with measured values Digits that are known with certainty plus the one digit whose value has been estimated are called Significant Digits.

Non-zero numbers are always significant.

The following rules apply in order to the zeroes in a measured value

1)Zeroes before a non-zero are not Significant. (0.002) 1SigFig.

2)Zeroes between non-zero digits are Significant. (0.706) 3SigFigs

3)Zeroes that appear after a nonzero digit are significant only if

a)followed by a decimal.

ex. (40s) 1SigFig.

(40.s) 2SigFigs

b)appear right of the decimal point.

ex. (37.0cm) 3SigFigs

(4.100m) 4SigFigs Significant Digits Every measurement has an experimental uncertainty

Uncertainty comes from:

1)Limitation of the measuring Instrument

2)Skill of the person using the instrument

3)Number of Measurements made

If several measurements are made and are nearly identical, the measurements are Precise.

If the measurements are very close to the accepted value found in a handbook, the measurement is Accurate. Uncertainty in Measurements Sample Problem 1 A block is displaced a vertical distance of 0.75 meter as it slides down a 3.00 meter long plane inclined to the horizontal.

(a) Calculate the horizontal displacement

of the block.

(b) Calculate the angle the plane makes

with the horizontal.

Sin θ = a/c

Cos θ = b/c

Tan θ = a/b

- Knowing the length of any two sides of a right

triangle is enough to figure out the length of

the third side using the Pythagorean theorem.

The Pythagorean theorem uses the

formula: c2 = a2 + b2 Tools for Measurement b = √c2 - a2

b = √(3.00m) - (0.75m)

b = 2.0m

sin = a÷c

sin = (0.75m) ÷ (3.00m) = .25

= 14.5° Given:

a = 0.75m

c = 3.00m

b = ?

= ?

c2= a2+ b2

b = √c2-a2

sin = a÷c Measuring an Angle

- A common unit for measuring angles is

degree (°). The protractor is an instrument

used for measuring angles in degrees

Trigonometry

- Is the branch of mathematics that treats the relationships

between angles and sides of triangles. Basic trigonometric

relationships are used to solve some types of physics

problems

- Important ratios of the sides of a right triangle in terms

of angle θ include the following: Measuring Length

Length is commonly measured in the Metric System

with the unit being meters (m). Occasionally centimeters

are more appropriate

Measuring Mass

- Mass is the amount of matter an object contains, it can be

measured with an electronic balance or a triple-beam balance

- A mass determined in grams can be converted to kilograms (kg)

by dividing by 1000

Measuring Time

- Elapsed time can be measured with a clock or a stopwatch.

because most events measured in physics occurs quickly,

the unit for time is measured by seconds (s)

Measuring Force

- A force is a push or pull on a mass. Forces are measured

with a spring scale, being measured in Newtons (N).

- Newtons is a derived unit from Kg*m/s2

Tools for Measurement 2 4 5 Units - A unit is a standard quantity that you can use to compare

other quantities to.

- For example centimeters and inches are both units and they can be

compared because 10 centimeters equals one inch

- All measurements must have a standard quantity. - The SI system contains universally accepted units for

scientific measurements.

- There are 7 fundamental units in Physics

-Derived units are combinations of 2 or more

fundamental units. The SI System What is a Unit? Symbols for Units and Quantities - SI units are symbolized with letters. But be

careful because some of the unit symbols are

also used to symbolize formulas.

- For example: A can be ampere

or area. SI Prefixes - SI prefixes are prefixes combined

with SI base units to form new units that are larger or smaller than the base units by a multiple or sub multiple of

10. - For example a 1000 meters can become 1 km Or 0.01 meter can be expressed as 1 centimeter

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