Introduction to Measurement & Vectors MIT C.P. PHYSICS Introduction to Measurement & Vectors

Science is based on measurements.

All measurements have: Units

Length Foot = Length of Hercules’s Foot Mile = 1000 Soldiers’ Paces

1790

SI Units Quantity Base Unit Symbol Length Meter m Mass Kilogram kg Volume Liter l Temperature Kelvin K Time Second s

Light travels in a vacuum during 1/299,792,458 of a second Meter 1 Meter Light travels in a vacuum during 1/299,792,458 of a second

Kilogram

A US cent weighs exactly 2.5 g, while the nickel weighs exactly 5 g. 2.5 grams 5.0 grams

Volume occupied by 1 kilogram of H2O Liter 1 Liter Volume occupied by 1 kilogram of H2O

All measurements have: Units Magnitude

Metric Prefixes Nano is derived from dwarf in Greek. Nano is a prefix meaning 10-9. (1 Nano-meter = 10-9 meter.) For example, 1 nanometer is approximately 100,000 times thinner than a human hair.

Powers of Ten

Powers of Ten

Very Large Measurements k (kilo) means “one thousand of” M (mega) means “one million of” G (giga) means “one billion of”

Very Small Measurements c (centi) means “a hundredth of” m (milli) means “a thousandth of” n (nano) means “a billionth of”

What is a “Nanometer”? A nanometer is to one inch as one inch is to 400 miles. Another way to visualize the size: the diameter of a quarter compared to the driving distance between Los Angeles and San Francisco. One nanometer equals a billionth of a meter.

What is “Nanotechnology”? The fundamental definition of Nanotechnology is that in a microenvironment that is within the dimension of one nanometer, the ability of man to understand and change nature shall be elevated to the atomic and molecular level Nanotechnology is a highly interdisciplinary field encompassing elements of colloidal science, physics, chemistry and biology.

Ceramic “Nano” Pores

How Small Am I? DNA Molecule Bacterium Red Blood Cell Carbon Buckyball Strand of Human Hair Red Blood Cell

How Small Am I? Strand of Human Hair 60,000 nanometers Bacterium Red Blood Cell 7,000 nanometers DNA Molecule 2 nanometers Carbon Buckyball (C60) 1 nanometer

How Many Nanometers?

Scientific notation is used to express very large or small numbers. 10,300,000,000,000,000,000,000 carbon atoms A carbon atom’s mass = 0.000,000,000,000,000,000,000,020 grams

Scientific Notation Scientific notation consists of a coefficient multiplied by 10 raised to an exponent. 10,300,000,000,000,000,000,000 = 1.03 x 10^22 = 1.03 E22 0.000,000,000,000,000,000,000,020 = 2.0 x 10^-23 = 2.0 E-23

All measurements have: Magnitude Units Uncertainty

Which One? Shooter 1 Shooter 2

Accuracy & Precision Accurate Precise Accuracy refers to the closeness of measurements to the correct or accepted value of the quantity measured. Precision refers to the closeness of a set of measurements of the same quantity made in the same way.

Lab: How Heavy is Papa Smurf

Lab: How Heavy is Papa Smurf Data Chart Mass (g) Displacement (cm)

Percent Error Observed Value-Accepted Value/Accepted Value x 100%

Sample Problem You complete a lab and you measured a force to be 90 Newtons. You should have measured 130 Newtons. What is your % error? Step 1: Observed – Accepted (Absolute Value) 40 Step 2: Error/Accepted 0.308 Step 3: Answer X 100% 30.8%

Significant Figures

Significant Figures

The numbers 1,2,3,4,5,6,7,8,9 are always significant! Significant Figures The numbers 1,2,3,4,5,6,7,8,9 are always significant! Rules for “0” Rule #1: Zeros between numbers are significant! 506 3 Significant Figures 10050 4 Significant Figures

Significant Figures Rule #2: Zeros to the right of a number are NOT significant unless the are to the left of a decimal point! 4830 3 Significant Figures 4830. 4 Significant Figures

Significant Figures Rule #3: Zeros to the right of a number & to the right of a decimal point are significant! 8.0 2 Significant Figures 16.40 4 Significant Figures

Significant Figures Rule #4: Zeros by themselves to the left or right of a decimal point are NOT significant! 0.06 1 Significant Figure 0.008 1 Significant Figure

Math with Significant Figures Multiply or divide as you normally would! Your answer can only have as many “Sig Fig’s” as the number with the fewest significant figures! 2,000.45 X 3,200 = 641440 Since 3,200 has only 2 “Sig Figs” 640,000

Power of the Graph! Chart Graph Organizes Data ☺ ☺ Displays Data ☺ ☺ Predicts Data ☺

Power of the Graph!

Power of the Graph!

Lab: Mr. G’s Cup Challenge

Lab: Mr. G’s Cup Challenge

Lab: Mr. G’s Cup Challenge

Lab: Mr. G’s Cup Challenge Data Chart Trial Setting Distance (cm) 1 2 3 Average 4

Proportional Relationships Direct Proportion Indirect Proportion

Vectors

Function of Vectors Magnitude Direction

Vector Interpretation Magnitude Scale: 1 cm = 50 km/hr Direction

Vector Interpretation

Vector Addition

Vector Addition

Lab: Vector Addition (Force Table)

Lab: Vector Addition ( Force Table) Each notch on the table = 10° Always have the ring over the hole Always have Vector A = 0 °

Lab: Vector Addition ( Force Table) Vector B Resultant Vector Trial # Force (N) Angle (°) 1 2 3 4 5 6 7 8 9 10

Vector Addition Head-to-Tail Method

Vector Addition Head-to-Tail Method

Vector Addition Head-to-Tail Method Step 1: Step 2:

Vector Addition Head-to-Tail Method

Vector Addition Head-to-Tail Method

Lab: Validating Force Table Lab

Lab: Validating Force Table Lab Observed Resultant Calculated Resultant Trial # Force (N) Angle (°) 1 2 3 4 5 6 7 8 9 10

Vector Addition Graphical Method

Vector Addition Graphical Method

Lab: Interactive Vector Addition

Lab: Interactive Vector Addition Resultant Vector Trial x y 1 2 3 4 5 6 7 8 9 10

Vector Addition Pythagorean Method

Vector Addition Pythagorean Method Step 1: Determine the Magnitude R = 15.6 N

Vector Addition Pythagorean Method Step 1: Determine the Direction Sin Θ = b/c Sin Θ = 11/15.6 Sin Θ = 0.7051 Θ = 45°

Friction Force that opposes motion. Resistance caused by 2 objects in contact with each other.

Increasing Friction Make surfaces rougher!

Increasing Friction Make surfaces wider!

Increasing Friction Increase weight!

High Friction

Low Friction

Lubricant

Friction between 2 nonmoving objects. Static Friction Friction between 2 nonmoving objects.

Static Friction

Coefficient Determination µ static = tan (angle of tilt) 

Lab: Coefficient of Static Friction

Lab: Coefficient of Static Friction Data Chart Footwear Type Angle of Elevation Coefficient of Static Friction

Sliding Friction Kinetic Friction

Friction between moving object(s). Sliding Friction Friction between moving object(s).

Sliding Friction

Coefficient Determination µ kinetic = Force/Normal A block of wood is shown sliding across a wooden table. Notice that the force of kinetic friction (fk) is equal to 40% of the normal force (FN).   The coefficient of kinetic friction would be 0.4. 

Coefficient Determination µ kinetic = Force/Normal As we compare the simulation of wood on wood to wood on asphalt, we find that the amount of friction on the block increased for the same amount of weight. The coefficient of kinetic friction would be 0.6! 

Comparing Coefficients µ kinetic = Force/Normal

Lab: Coefficient of Sliding Friction

Lab: Coefficient of Sliding Friction Data Chart Surface Type F(gravity) (N) F(applied) Coefficient Of Sliding Friction Plastic Sandpaper Cardboard Wood

Comparing Coefficients Coefficient of Friction Surfaces Static Friction Kinetic Friction Steel on steel (dry) 0.6 0.4 Steel on steel (greasy) 0.1 0.05 Teflon on steel 0.041 0.04 Brake lining on cast iron 0.3 Rubber tires on dry pavement 0.9 0.8 Metal on ice 0.022 0.02