Physics Einstein, atomic bombs, spacecraft, math Baseballs, roller coasters, toasters, rainbows, cats The study of the physical world, the most fundamental of the sciences. The behavior and structure of matter.

Hypothesis- a conjecture to be used as a basis for further investigation Theory- a synthesis of a large body of information that encompasses well-tested and verified hypotheses Fact- close agreement by many competent observers of the same phenomenon. Law- a concise statement about how nature behaves

The metric system The System Internationale, SI Standards of length, time, and mass Length: meter, m Mass: kilogram, kg Time: second, s Derived units: a combination of fundamental units, such as meter per second, m/s

Measurement uncertainties Precision: the degree of exactness, is limited by the divisions on the scale Accuracy: how well the measure agrees with an accepted standard.

Good measurements Parallax, the apparent shift in the position of an object when it is viewed from different angles.

Scientific Notation and Rounding 356,000,000, x x x 10 8 When moving the decimal point, the exponent changes: Left – LargerRight- Reduced

It’s 1500 miles to Fresno, California ….EXACTLY 1500 miles??? Which numerals are significantly important in the measurement of a quantity?

HOW DO YOU DETERMINE THE NUMBER OF SIGNIFICANT FIGURES? Is the decimal point present or absent? Decimal present (Pacific) Decimal absent (Atlantic)

P If decimal is P resent,  count from the left  start counting at the first non-zero number  count that number and all digits to the right of it If decimal is A A bsent,  count from the right  start counting at the first non-zero number  count that number and all digits to the left of it (3) 2,500 (2)

The rules for Significant Digits 1.All non-zero digits are significant. 2.Zeros between non-zero number are significant. 3.If a decimal is present, zeros that follow non- zero numbers are significant. Examples: ? Put in scientific notation!

Conversion Equivalents 3600 seconds = 1 hour 60 seconds = 1 minute 60 minutes = 1 hour 1000 meters = 1 kilometer 100 centimeters = 1 meter 1 kilometer = miles 1 meter = 1000 millimeters 1 mile = 5280 feet 2.54 cm = 1 in

Unit Conversions

Converting Inches to centimeters 10.0 in We start by writing down the number and the unit

Converting Inches to centimeters 10.0 in 1 in 2.54 cm Our conversion factor for this is 1 in = 2.54 cm. Since we want to convert to cm, it goes on the top.

Converting Inches to centimeters 10.0 in 1 in 2.54 cm Now we cancel and collect units. The inches cancel out, leaving us with cm – the unit we are converting to.

Converting Inches to centimeters 10.0 in 1 in 2.54 cm = 25.4 cm Since the unit is correct, all that is left to do is the arithmetic... The Answer

Even though we have two different numbers and two different units, they represent the exact same length. You can check this by looking at a ruler – find the 10 in mark and directly across at the cm side. What number do you find?

A more complex conversion km to m hr s In order to work physics problems, we need to be able to convert kilometers per hour into meters per second. We can do both conversions at once using the same method as in the previous conversion.

80 km hr A more complex conversion km to m hr s Step 1 – Write down the number and the unit!

80 km hr 1 hr 3600 s A more complex conversion km to m hr s First we’ll convert time. Our conversion factor is 1 hour = 3600 sec. Since we want hours to cancel out, we put it on the top.

80 km hr 1 hr 3600 s 1000 m 1 km A more complex conversion km to m hr s Next we convert our distance from kilometers to meters. The conversion factor is 1 km = 1000 m. Since we want to get rid of km, this time it goes on the bottom.

80 km hr 1 hr 3600 s 1000 m 1 km = A more complex conversion km to m hr s Now comes the important step – cancel and collect units. If you have chosen the correct conversion factors, you should only be left with the units you want to convert to. m s

80 km hr 1 hr 3600 s 1000 m 1 km = 80,000 m 3600 s A more complex conversion km to m hr s Since the unit is correct, we can now do the math – simply multiply all the numbers on the top and bottom, then divide the two.

80 km hr 1 hr 3600 s 1000 m 1 km = 80,000 m 3600 s = 22 m s A more complex conversion km to m hr s The Answer!!

80 km/hr and 22 m/s are both velocities. A car that is moving at a velocity of 80 km/hr is traveling the exact same velocity as a car traveling at 22 m/s.

Graphing Data Independent axis: the x-axis- horizontal Dependent axis: the y-axis- vertical The y values depend on the x values

A clever way to remember what goes on which axis when graphing: Dependent Result Y-axis Manipulated Independent X-axis

Graphing Data Linear relationship, y = mx + b Inverse relationship y = b/x, b = rational number Quadratic relationship y = bx 2

Questions 1-4 choose from A, B, C, or D) A. hypothesis B. fact C. law D. theory 1. A close agreement by competent observers who make a series of observations of the same phenomena 2. A synthesis of a large body of information that encompasses well- tested and verified hypotheses about certain aspects of the natural world. 3. A concise statement about how nature behaves found to be experimentally valid over a wide range of observed phenomena 4. A conjecture that accounts for a set of facts and can be used as a basis for further investigation 5. The SI standard unit for distance measurements A. Centimeter B. Millimeter C. Meter D. Kilometer 6. The SI standard unit for mass: A. Centigram B. Milligram C. Gram D. Kilogram 7. The SI standard unit for time: A. Second B. Hour C. Day D. Year

(Questions 8-10 choose answer A, B, or C from below) A. Parallax B. Precision C. Accuracy 8. Limited by the smallest division on the measuring device scale. 9. How much the measurement agrees with an accepted standard. 10. Results from a change in the viewer’s position 11. How many significant figures? A. 213 B C D E Put in scientific notation: A B C Match graphs: A. Linear B. Inverse C. Quadratic 12 3

Linear Motion Position- the location of an object relative to a reference point. We often use the letter x to represent position. (“x marks the spot” Sometimes we also use “d”, when position is some measured distance, d, from a reference point. Reference point- the point from which measurements are made.

Distance- how far something moves. Displacement – how far something moves in a given direction. ( It’s only concerned about where you started and where you stopped, not what you did in between.) For example: if you take a trip all the way around the world and end up right back where you started, you traveled a great distance, but your displacement was zero!

Rate- a quantity divided by time- how much something is changing in a certain amount of time Speed- the rate at which position changes- “how fast?” Example: 60 miles per hour- the position of a car will change 60 miles in one hour. We will use m/s most often.

Average speed = total distance covered ÷ time interval Instantaneous speed- the speed at any instant

 - “delta”- a symbol that means “the change in” the change in position,  x Change in time,  t Change in velocity,  v The change in a value is the difference between the final value and the original value- “final minus original”  velocity = final velocity – original velocity Example: a car was moving at 18 m/s and then sped up to 22 m/s. What was  v ?  v = 22 m/s - 18 m/s = 4 m/s

SOLVING PHYSICS PROBLEMS Using the GUESS method GWrite down all the GIVENS and assign them a variable UWrite down all the UNKNOWNS and assign them a variable EFind the appropriate EQUATION SSUBSTITUTE the appropriate values in the equation. SSOLVE for the unknown in the equation.

Example using the Guess Method Example: a car was moving at 9 m/s and then sped up to 10 m/s. What was  v ? GIVENS –Initial velocity = 9 m/s –Final velocity = 10 m/s UNKNOWN  v EQUATION  v = final velocity – initial velocity SUBSTITUTE  v = 10 m/s – 9 m/s SOLVE  v = 10 m/s – 9 m/s = 1m/s

Speed and Velocity In physics, speed and velocity are not the same! Speed is “how fast”, Velocity is “how fast and in what direction”. Example: 10 m/s is a speed, 10 m/s north is a velocity

“uniform” means “constant, unchanging” At a uniform speed, the distance traveled is given by Distance = speed x time At uniform velocity, the displacement is given by Displacement = velocity x time d = vt

Examples How far will you go while traveling at 23 m/s for 12 seconds? v = 23 m/s t = 12 s d = ? d = vt = 23 m/s x 12 s = 276 m

How long will it take to travel a distance of 240 km traveling at 12 m/s? Convert 240 km to meters first! 240 km x = m Rearrange the equation d = vt to solve for t t = d ÷ v = m ÷ 12 m/s = s

How far, in meters, will you go while traveling at 70 km/h for 18 seconds? Convert to the 70 km/h to m/s first, then calculate the distance. 70 = 19.4 m/s d = vt = 19.4 m/s x 18 s = 349 m

Acceleration Acceleration: the rate at which velocity changes Acceleration = Unit:

Remember, velocity is how fast (speed) AND in what direction. If either speed OR direction changes, the velocity has changed, which means that there is an acceleration!

Constant velocity means that neither the speed nor the direction of motion can change. A race car driving around a circular path at a constant 80 mi/h has a constant speed but not a constant velocity since its direction is changing.

An object accelerates when its speed OR its direction changes! So……

How to tell if you accelerated too quickly from a red light.

Positive Away Negative Toward

Positive or Negative? Choose a direction for + and – then stick with it! Going forward, speeding up Going forward, slowing down Going backward, speeding up Going backward, slowing down pos posnegneg negpos VelocityAcceleration

KEY WORDS “stops” The final velocity is zero, v f = 0 “at rest” The original velocity is zero, v o = 0 v O = original velocity v f = final velocity

Sample problems: An Indy 500 race car’s velocity increases from +4.0 m/s to 36 m/s over a 4.0 s time interval. What is its average acceleration?

The race car in the previous problem slows from +36 m/s to +15 m/s over 3.0 s. What is its average acceleration.

A car is coasting backwards downhill at a speed of 3.0 m/s when the driver gets the engine started. After 2.5 s, the car is moving uphill at 4.5 m/s. Assuming that uphill is the positive direction, what is the car’s average acceleration?