Measurement in Physics

Mark LesmeisterPearland ISD

Mini-lab: Indirect measurements In this lab, you will complete 3 lab

stations involving indirect measurement.

You will work in pairs at each station. You will only have two minutes at each

lab station, so work quickly and efficiently.

When I give the word, switch to the next lab station.

Mini-Lab Results Grp. 1 Grp. 2 Grp. 3 Grp. 4 Grp. 5

Mass of 1 note (direct) (g)

Mass of 1 note (indir.) (g)

Thickness of 1 page (cm)

Time for 1 heartbeat(s)

Objectives

List SI units and the quantities they describe.

Use scientific notation. Distinguish accuracy and precision. Use significant figures.

Dimension In physics, dimension refers to the type of

quantity being measured. For example:

Both the height of a building and the distance from here to Dallas have the dimension of length, though they are usually measured in different units.

A football player’s age in years and the number of seconds he takes to run 40 yards are both measurements of the time dimension.

Measurement in Experiments

SI Base Units of Measurements

Dimension Unit Symbol

length meter m

time second sec or s

mass kilogram kg

current ampere A

temperature kelvin K

Measurement in Experiments

SI Base Units of Measurements

unit symbol

luminous intensity

candela cd

amount of a substance

mole mol

All other units are called derived units because they are based on combinations of two or more of the SI base units.

Measurement in ExperimentsCommon Numerical Prefixes

10-18 atto- a 101 deka- da

10-15 femto-

f 103 kilo- k

10-12 pico- p 106 mega-

M

10-9 nano- n 109 giga- G

10-6 micro-

µ 1012 tera- T

10-3 milli- m 1015 peta- P

10-2 centi- c 1018 exa- E

10-1 deci- d

Converting metric prefixes

Determine the units of the known and unknown quantity.

Write an equation between the two.

Write the equation as a fraction equaling 1.

Multiply the known by this fraction.

Practice with metric prefixes A typical radio wave has a period

of 1 s. Express this period in seconds.

A human hair is approximately 50 m in diameter. Express this diameter in meters.

The distance between the sun and the Earth is about 1.5 x 1011 m. Express this distance in kilometers.

Sample Problem 2 Determine the units

of the known and unknown quantity.

Write an equation between the two.

Write the equation as a fraction, with the unknown on top.

Multiply the known by this fraction.

meters (m) and m

10-6 m = 1 m

m 1

m 01 -6

m 10 5 m 10 50

m 1

m 10 1 m 50

5-6-

-6

Sample Problem 3 Determine the units

of the known and unknown quantity.

Write an equation between the two.

Write the equation as a fraction, with the unknown on top.

Multiply the known by this fraction.

meters (m) and km

1000 m = 1 km

m 1000

km 1

km 10 5.1

m 1000

km 1 m 10 .51

8

11

Problem Set 1A: Problem 1

Problem Set 1A: Problem 2

Problem Set 1A: Problem 3

Problem Set 1A: Problem 4

Problem Set 1A: Problem 5

Problem Set 1A: Problem 6

Problem Set 1A: Problem 7

Problem Set 1A: Problem 8

Problem Set 1A: Problem 9

Problem Set 1A: Problem 10

Metric conversion practice: #1 What are the units of

the unknown? What is the value of

the known? Write an equation

between the known and unknown.

Make a fraction with the unknown units on top.

Multiply the known by the fraction.

ml 37854120 l

1 l = 1000 ml

l 1

ml 1000

ll

l

ll

m10 3.854,120 m 000,120,854,37

1

m 1000 37854120

10

Metric conversion practice: #3 What are the units of

the unknown? What is the value of

the known? Write an equation

between the known and unknown.

Make a fraction with the unknown units on top.

Multiply the known by the fraction.

km 3000 m

1 km = 1000 m

km 30001

km 1m 3000

m

m 1000

km 1

Answers: Metric conversion #2

90,760 ms = 9.0760 x 104 ms

100,000 cm =1 x 105 cm

#4 0.020 ks 0.1 km

# 5 739 m

#6 3033 m

#7 6.250 A

#8 62,400 cm

Discovery Lab: Accuracy and Precision

Please complete the Accuracy and Precision Mini-lab handout that you picked up on the way into class.

Accuracy and Precision

accuracy – how close a measured value is to the true or accepted value of the quantity being measured

precision – the degree of exactness with which a measurement is made and stated

Accurate, Precise, or Both The following students measure the density of

a piece of lead three times.The density of lead is actually 11.34 g/cm3. Considering all of the results,which person’s results were accurate? Which were precise? Were any both accurate and precise? a. Rachel: 11.32 g/cm3, 11.35 g/cm3, 11.33 g/cm3 b. Daniel: 11.43 g/cm3, 11.44 g/cm3, 11.42 g/cm3 c. Leah: 11.55 g/cm3, 11.34 g/cm3, 11.04 g/cm3

Significant Figures or Digits

One way to express the precision of a measurement is to use significant figures or digits.

Significant figures or digits are those digits in a measurement that are known with certainty plus the first digit that is uncertain.

They are also called sig figs or sig digs.

Rules for Determining Significant Figures All nonzero digits are significant. Zeroes between other nonzero digits are

significant. Zeroes in front of nonzero digits are not

significant; they are placeholders. Zeroes at the end of a number and to the

right of the decimal point are significant. Zeroes at the end of a number but to the

left of the decimal are not significant, but are important as placeholders, unless you are told they are measured.

How many significant digits?

3.0025 .0008 .0430 4500

Rules for calculations with significant figures

In addition or subtraction, the answer should have the same number of digits to the right of the decimal as the measurement with the smallest number of digits to the right of the decimal.

In multiplication and division, the final answer should have the same number of significant figures as the measurement with the fewest number of significant figures.

Compute using sig figs.

72.4 +36.73 80.1 + 23 26 x .0258 15.3 / 1.1

Rules for Rounding

Leave the number alone when the digit following the last significant figure is 0, 1, 2, 3, or 4.

Round up when the digit following the last significant figure is 5, 6, 7, 8, or 9

Special Rules for RoundingThe Symmetric Rounding Rule

This rule is sometimes followed when the digit following the last significant figure is 5. This rule says to round to the nearest even number. This rule is often used to reduce average error due to rounding since the numbers are sometimes rounded up and sometimes rounded down.

Your text uses this rule.