Using the Metric System A. Why do scientists use the metric system? The metric system was developed in France in 1795 - used in all scientific work because it has been recognized as the world wide system of measurement since 1960. SI system is from the French for Le Systeme International d’Unites. The metric system is used in all scientific work because it is easy to use. The metric system is based upon multiples of ten. Conversions are made by simply moving the decimal point.

What is the basic unit of length? The meter – a little longer than a yard

A millimeter – There are 1,000 millimeters in a meter What do scientists use to measure the length of an object smaller than a yard? A centimeter – one hundredth of a meter, so there are 100 centimeters in a meter A millimeter – There are 1,000 millimeters in a meter

How do scientists measure long distances? The kilometer – There are 1,000 meters in a kilometer

Which measurement to USE?

Base Units (Fundamental Units) QUANTITY NAME SYMBOL _______________________________________________ Length meter m ----------------------------------------------------------------------------- Mass gram g ------------------------------------------------------------------------------- Time second s Temperature Kelvin k -------------------------------------------------------------------------------- Volume(liquid)__________liter_____________L________________

SI Prefixes Prefix Symbol Multiplication Factor Term Micro u (0.000 001) one millionth Milli m (0.001) one thousandth Centi c (0.01) one hundredth Deci d (0.1) one tenth One Unit 1 one Deka dk 10 ten Hecto h 100 one hundred Kilo k 1000 one thousand Mega M 1 000 000 one million

Metric Units Used In This Class QUANTITY NAME SYMBOL Length meter m centimeter cm millimeter mm kilometer km Mass gram g kilogram kg centigram cg milligram mg Volume liter (liquid) L (l) milliliter (liquid) mL (ml) cubic centimeter (solid) cm3

Derived Units Base Units – independent of other units-measure Derived Units – combination of base units-calculated Examples density  g/L mass / volume (grams per liter) volume  m x m x m = meters cubed Velocity  m/s (meters per second

SCIENTIFIC NOTATION Scientific Notation: Easy way to express very large or small numbers A.0 x 10x A – number with one non-zero digit before decimal x -exponent- whole number that expresses the number decimal places if x is (-) then it is a smaller if x is (+) than it is larger

PRACTICE Convert to Normal Convert to SN 2.3 x 1023 m 3,400,000, 3.4 x 10-5 cm .0000000456

Multiplying Calculating in Scientific notation Multiple the numbers Add the exponents (2.0 x 104) (4.0 x 103) = 8.0 x 107

Dividing 9.0 x 107 3.0 x 102 3.0 x 105 divide the numbers subtract the denominator exponent from the numerator exponent 9.0 x 107 3.0 x 102 3.0 x 105

Add Add or subtract get the exponents of all # to be the same calculate as stated make sure the final answer is in correct scientific notation form 7.0 x 10 4 + 3.0 x 10 3 = 7. 0 x 104 + .3 x 104 = 7.3 x 104 70,000 + 3,000 = 73000= 7.3 x104

subtract 7.0 x 10 4 - 3.0 x 10 3 = 7.0x 104 – .30 x 104 = 6.7 x 104 70,000 - 3 000 =67,000

PRACTICE Add: 2.3 x 103 cm + 3.4 x 105 cm Subtract: Multiply: : 2.3 x 103 cm X 3.4 x 105 cm   Divide: : 2.3 x 103 cm / 3.4 x 105 cm

Significant figures http://www.youtube.com/watch?v=puvE8hF6zrY

Using Significant Figures (Digits) value determined by the instrument of measurement plus one estimated digit reflects the precision of an instrument example – if an instrument gives a length value to the tenth place – you would estimate the value to the hundredths place

Mathematical Operations Involving Significant Figures Multiplication and Division The answer must have the same number of significant figures as the measurement with the fewest significant figures.

Making Unit Conversions Make conversions by moving the decimal point to the left or the right using: “ king henry died unit drinking chocolate milk” Examples 10.0 cm = __________m 34.5 mL = __________L 28.7 mg = __________kg

Factor label method / Dimensional analysis Use equalities to problem solve converting units. quantity desired = quantity given x conversion factor (equality) A-given unit B-desired unit C-given unit  A x B C B C must equal 1 use equality sheet

Equalities You Need To Know 1 km = 1000 m 1 m = 100 cm 1 m = 1000 mm 1L = 1000 mL 1kg = 1000g 1 g = 100cg 1 g = 1000 mg

ENGLISH TO METRIC 1 inch=2.5 centimeters 1 gal=3.8 liters 1lb= 4.4 Newtons 1qt = .94 Liters 1 ft = .30 meters 12 in = .30 meters 1 mi = 1.6 Km

Four-step approach When using the Factor-Label Method it is helpful to follow a four-step approach in solving problems: 1.What is question – How many sec in 56 min 2. What are the equalities- 1 min = 60 sec 3. Set up problem (bridges) 56 min 60 sec 1 min 4. Solve the math problem -multiple everything on top and bottom then divide 56 x 60 / 1

Motion Describing and Measuring Motion How do you recognize motion? An object is in motion when its distance from another object is changing Movement depends on your point of view

Distance We all know what the distance between two objects is... So what is it? What is distance? What is length? ALSO - you can't use the words "distance" or "length" in your definition; that would be cheating.

Distance As you can see from your efforts, it is impossible to define distance. Distance is a fundamental part of nature. It is so fundamental that it's impossible to define. Everyone knows what distance is, but no one can really say what it is. However, distances can be compared.

Distance We can compare the distance between two objects to the distance between two other objects. For convenience, we create standard distances so that we can easily make comparisons... and tell someone else about them. This doesn't define distance, but it allows us to work with it.

Distance We'll be using meter as our standard for measuring distance. The symbol for distance is "d". And the unit for the meter is "m“. d = 0.2 m

Distance Activity Work in partners create a difference in position between you and a partner. Use a meter stick to determine the distance between you and your partner.( position A) Now move to a different position. Measure the difference in your position now. ( Position B) make note of the distance you have traveled?

Time Similarly, everyone knows what time is... But try defining it; what is time? Remember you can't use the word "time" or an equivalent to the word "time", in your definition.

Time Like distance, time is a fundamental aspect of nature. It is so fundamental that it's impossible to define. Everyone knows what time is, but no one can really say what it is... However, like distances, times can be compared.

Time We can say that in the time it took to run around the track, the second hand of my watch went around once...so my run took 60 seconds. When we compare the time between two events to the time between two other events, we are measuring time. This doesn't define time, but it allows us to work with it.

Time We will be using the second as our standard for measuring time. The symbol for time is "t" The unit for a second is "s". t = 10s click here for a "minute physics" on measuring time and distance

Time Activity Repeat previous distance activity Use a timer – use seconds as the unit Determine the time it took to go from position A to position B Draw a diagram of your activity List the known information- Distance: between position A to position B Time: it took to go from A to B

How do scientists calculate speed? Speed – the distance the object travels in one unit of time Rate – tells you the amount of something that occurs or changes in one unit of time Speed = distance time

Speed The units of speed can be seen by substituting the units for distance and time into the equation s = d t meters second m s We read this unit as "meters per second"

SPEED = Distance / time Use the information from the previous two activities to calculate your speed. Use these steps 1. draw a diagram 2. list known and unknown data 3. write the formula you will use 4. plug in data 5. solve the problem using the correct units

A car travels at a constant speed of 10m/s. This means the car: increases its speed by 10m every second. c B decreases its speed by 10m every second. C moves with an acceleration of 10 meters every second. c c D moves 10 meters every second.

2 A rabbit runs a distance of 60 meters in 20 s; what is the speed of the rabbit?

How can you calculate the distance an object has moved? Rearrange the speed formula Speed = distance/time Distance = Speed x Time

Rearrange the following formula Speed =distance time Find-distance: what you do to one side you do to the other time x speed = distance x time distance=time x speed Find- time: what you do to one side you do to the other distance= time x speed speed speed Time =distance speed

3 A car travels at a speed of 40 m/s for 4.0 s; what is the distance traveled by the car?

4 You travel at a speed of 20m/s for 6.0s; what distance have you moved?

5 An airplane on a runway can cover 500 m in 10 s; what is the airplane's average speed?

Solve for time:

6 You travel at a constant speed of 20 m/s; how much time does it take you to travel a distance of 120m?

7 You travel at a constant speed of 30m/s; how much time does it take you to travel a distance of 150m?

Graphing graph – a visual representation of data that reveals a pattern Bar- comparison of different items that vary by one factor Circle – depicts parts of a whole Line graph- depicts the intersection of data for 2 variables Independent variable- factor you change Dependent variable – the factor that is changed when independent variable changes

Graphing Creating a graph- must have the following points Title graph Independent variable – on the X axis – horizontal- abscissa Dependent variable – on Y axis – vertical- ordinate Must label the axis and use units Plot points Scale – use the whole graph Draw a best fit line- do not necessarily connect the dots and it could be a curved line.

Interpreting a graph Run X2 –X1 Slope- rise Y2 –Y1 relationship direct – a positive slope inverse- a negative slope equation for a line – y = mx + b m-slope b – y intercept extrapolate-points outside the measured values- dotted line interpolate- points not plotted within the measured values-dotted line

WORK ON GRAPHING EXERCISES Graphical analysis – click and go

What is average speed? Most objects do not move at constant speeds for very long To find average speed divide the total distance by the total time Car trip

How do you graph motion? You can show the motion of an object on a line graph in which you plot distance against time Time is along the x-axis independent variable and distance on the y-axis dependent variable

How do you interpret motion graphs? A straight line indicates a constant speed The steepness depends on how quickly or slowly the object is moving The faster the motion the steeper the slope

Bulldozer Lab

Average Speed Return to Table of Contents

Average Speed The speed we have been calculating is a constant speed over a short period of time. Another name for this is instantaneous speed. If a trip has multiple parts, each part must be treated separately. In this case, we can calculate the average speed for a total trip. Determine the average speed by finding the total distance you traveled and dividing that by the total time it took you to travel that distance.

Distance and Time Intervals In physics we use subscripts in order to avoid any confusion with different distances and time intervals. For example: if an object makes a multiple trip that has three parts we present them as d1, d2, d3 and the corresponding time intervals t1, t2, t3.

Average Speed & Non-Uniform Motion The following pattern of steps will help us to find the average speed: Find the total distance dtotal = d1+ d2+ d3 Find the total time ttotal = t1 + t2 + t3 Use the average speed formula savg = dtotal ttotal

Average Speed - Example 1 You ride your bike home from school by way of your friend’s house. It takes you 7 minutes (420 s) to travel the 2500 m to his house. You spend 10 minutes there, before traveling 3500 m to your house in 9 minutes (540 s). What was your average speed for this trip? To keep things clear, we can use a table to keep track of the information...

Example 1 - Step 1 Write the given information in the table below: You ride your bike home from school by way of your friend’s house. It takes you 7 minutes (420 s) to travel the 2500 m to his house. You spend 10 minutes there, before traveling 3500 m to your house in 9 minutes (540 s). What was your average speed for this trip? Segment Distance Time Speed (m) (s) (m/s) I II III Total /Avg.

Example 1 - Step 2 Next, use the given information to find the total distance and total time Segment Distance Time Speed (m) (s) (m/s) I 2500m 420 s II 0 m 600 s III 3500m 540 s Total /Avg. You ride your bike home from school by way of your friend’s house. It takes you 7 minutes (420 s) to travel the 2500 m to his house. You spend 10 minutes there, before traveling 3500 m to your house in 9 minutes (540 s). What was your average speed for this trip?

Example 1 - Step 2 Next, use the given information to find the total distance and total time Segment Distance Time Speed (m) (s) (m/s) I 2500m 420 s II 0 m 600 s III 3500m 540 s Total /Avg. 6000m 1560s You ride your bike home from school by way of your friend’s house. It takes you 7 minutes (420 s) to travel the 2500 m to his house. You spend 10 minutes there, before traveling 3500 m to your house in 9 minutes (540 s). What was your average speed for this trip?

Example 1 - Step 3 Next use total distance and time to find average speed. You ride your bike home from school by way of your friend’s house. It takes you 7 minutes (420 s) to travel the 2500 m to his house. You spend 10 minutes there, before traveling 3500 m to your house in 9 minutes (540 s). What was your average speed for this trip? Segment Distance Time Speed (m) (s) (m/s) I 2500m 420 s II 0 m 600 s III 3500m 540 s Total /Avg. 6000m 1560s

Example 1 - Solution Next use total distance and time to find average speed. Segment Distance Time Speed (m) (s) (m/s) I 2500m 420 s II 0 m 600 s III 3500m 540 s Total /Avg. 6000m 1560s m/s You ride your bike home from school by way of your friend’s house. It takes you 7 minutes (420 s) to travel the 2500 m to his house. You spend 10 minutes there, before traveling 3500 m to your house in 9 minutes (540 s). What was your average speed for this trip?

Example 2 Segment Distance Time Speed (m) (s) (m/s) I II III Total /Avg. You run a distance of 210 m at a speed of 7 m/s. You then jog a distance of 200 m in a time of 40s. Finally, you run for 25s at a speed of 6 m/s. What was the average speed of your total run?

Example 2 - Reflection Segment Distance Time Speed (m) (s) (m/s) I 210 30 7 m/s II 200 40 5 m/s III 150 25 6 m/s Total /Avg. 560 95 5.89 m/s What happens when you take the 'average' (arithmetic mean) of the speed for each leg of the trip? Is it the same as the average speed? Why do you think this happens?

Position and Reference Frames Return to Table of Contents

Position and Reference Frames Speed, distance and time didn't require us to define where we started and where we ended up. They just measure how far we traveled and how long it took to travel that far. However, much of physics is about knowing where something is and how its position changes with time. To define position we have to use a reference frame.

Position and Reference Frames A reference frame lets us define where an object is located, relative to other objects. For instance, we can use a map to compare the location of different cities, or a globe to compare the location of different continents. However, not every reference frame is appropriate for every problem.

Reference Frame Activity Send a volunteer out of the classroom to wait for further instructions. Place an object somewhere in your classroom. Write specific directions for someone to be able to locate the object Write them in a way that allows you to hand them to someone who can then follow them to the object. Test your directions out on your classmate, (who is hopefully still in the hallway!) Remember: you can't tell them the name of something your object is near, just how they have to move to get to it. For instance 'walk to the SmartBoard' is not a specific direction.

Reference Frame Activity - Reflection In your groups, make a list of the things you needed to include in your directions in order to successfully locate the object in the room. As a class, discuss your findings.

Results - Reference Frames You probably found that you needed: A starting point (an origin) A set of directions (for instance left-right, forward-backward, up-down) A unit of measure (to dictate how far to go in each direction)

Results - Reference Frames In this course, we'll usually: Define the origin as a location labeled "zero" Create three perpendicular axes : x, y and z for direction Use the meter as our unit of measure

The Axis In this course, we will be solving problems in one-dimension. Typically, we use the x-axis for that direction. +x will usually be to the right -x would then be to the left We could define it the opposite way, but unless specified otherwise, this is what we'll assume. We also can think about compass directions in terms of positive and negative. For example, North would be positive and South negative. The symbol for position is "x". +x - x

All of the following are examples of positive direction except: 8 All of the following are examples of positive direction except: A to the right B north C west D up

Displacement Return to Table of Contents

Displacement Now that we understand how to define position, we can talk about a change in position; a displacement. The symbol for "change" is the Greek letter "delta" "Δ". So "Δx" means the change in x or the change in position

Displacement -x +y -y +x Displacement describes how far you are from where you started, regardless of how you got there.

Displacement +y For instance, if you drive 60 miles from Pennsylvania to New Jersey... -x x0 +x (In physics, we label the starting position x0) -y

Displacement and then 20 miles back toward Pennsylvania. -x +y -y +x and then 20 miles back toward Pennsylvania. x0 xf (We also label the final position xf )

Δx = Xf - Xo Displacement You have traveled: a distance of 80 miles, and a displacement of 40 miles, since that is how far you are from where you started -x +y -y +x x0 xf we can calculate displacement with the following formula: Δx = Xf - Xo

Displacement Measurements of distance can only be positive values (magnitudes) since it is impossible to travel a negative distance. Imagine trying to measure a negative length with a meter stick...

Displacement However, displacement can be positive or negative since you can end up to the right or left of where you started. xo xf -x +y -y +x xf xo -x +y -y +x Displacement is positive. Displacement is negative.

Which of the following are vectors? Scalars? Vectors and Scalars Scalar - a quantity that has only a magnitude (number or value) Vector - a quantity that has both a magnitude and a direction Which of the following are vectors? Scalars? Quantity Vector Scalar Time Distance Displacement Speed

How far your ending point is from your starting point is known as: 9 How far your ending point is from your starting point is known as: A distance B displacement C a positive integer D a negative integer

10 A car travels 60m to the right and then 30m to the left. What distance has the car traveled? +x - x

11 You travel 60m to the right and then 30m to the left. What is the magnitude (and direction) of your displacement? +x - x

12 Starting from the origin, a car travels 4km east and then 7 km west. What is the total distance traveled? A 3 km B -3 km C 7 km D 11 km

13 Starting from the origin, a car travels 4km east and then 7 km west. What is the net displacement from the original point? A 3 km west B 3 km east C 7 km west D 11 km east

14 You run around a 400m track. At the end of your run, what is the distance that you traveled?

15 You run around a 400m track. At the end of your run, what is the displacement you traveled?

Which of the following is a vector quantity? 16 Which of the following is a vector quantity? c A time B velocity C distance c D speed

Average Velocity Return to Table of Contents

What is Velocity? Speed in a given direction When you know the speed and direction of an object’s motion, you know the velocity of the object Example 15 km/hour westward

Average Velocity Speed is defined as the ratio of distance and time d Average speed = distance traveled time elapsed Similarly, velocity is defined as the ratio of displacement and time Average velocity = time elapsed displacement Δx Δt v =

Average Velocity Speeds are always positive, since speed is the ratio of distance and time; both of which are always positive. s = d t Average speed = distance traveled time elapsed But velocity can be positive or negative, since velocity is the ratio of displacement and time; and displacement can be negative or positive. Average velocity = time elapsed displacement Δx Δt v = Usually, right is positive and left is negative.

17 Average velocity is defined as change in ______ over a period of ______. cc A distance, time c B distance, space c C displacement, time c D displacement, space

18 Velocity is a vector. c True c False

19 You travel 60 meters to the right in 20 s; what is your average velocity?

20 You travel 60 meters to the left in 20 s; what is your average velocity?

21 You travel 60 meters to the left in 20 s and then you travel 60 meters to the right in 30 s; what is your average velocity?

22 You travel 60 meters to the left in 20 s and then you travel 60 meters to the right in 30 s; what is your average speed?

25 You travel 160 meters in 60 s; what is your average speed?

DOT DIAGRAM GO TO PHYSICS CLASSROOM TO PRACTICE DOT DIAGRAM EXAMPLES. Ticker Tape Diagrams- dot diagram The distance between dots on a ticker tape represents the object's position change during that time interval. A large distance between dots indicates that the object was moving fast during that time interval. A small distance between dots means the object was moving slow during that time interval. Ticker tapes for a fast- and slow-moving object are depicted below.

Dot diagram-

Instantaneous Velocity Return to Table of Contents

Instantaneous Velocity Sometimes the average velocity is all we need to know about an object's motion. For example: A race along a straight line is really a competition to see whose average velocity is the greatest. The prize goes to the competitor who can cover the displacement in the shortest time interval. But the average velocity of a moving object can't tell us how fast the object moves at any given point during the interval Δt.

Instantaneous Velocity Average velocity is defined as change in position over time. This tells us the 'average' velocity for a given length or span of time. If we want to know the speed or velocity of an object at a specific point in time (with this radar gun for example), we want to know the instantaneous velocity... Watch what happens when we look for the instantaneous velocity by reducing the amount of time we take to measure displacement. Instantaneous Velocity- velocity of an object at a specific point in time

Instantaneous Velocity Displacement Time 100m 10 s Velocity In an experiment, an object travels at a constant velocity. Find the magnitude of the velocity using the data above.

Instantaneous Velocity 10 m 1 s Displacement Time Velocity 100m 10 s 10 m/s What happens if we measure the distance traveled in the same experiment for only one second? What is the velocity?

Instantaneous Velocity Displacement Time Velocity 100m 10 s 10 m/s 10 m 1 s 10 m/s 0.001m 0.0001 s What happens if we measure the distance traveled in the same experiment for a really small time interval? What is the velocity?

Instantaneous Velocity Displacement Time Velocity 100 m 10 s 10 m/s 10 m 1 s 1.0 m 0.10 s 0.10 m 0.010 s 0.010 m 0.0010 s 0.0010 m 0.00010 s 0.00010 m 0.000010 s Since we need time to measure velocity, we can't know the exact velocity "at" a particular time... but if we imagine a really small value of time and the distance traveled, we can estimate the instantaneous velocity.

Instantaneous Velocity To describe the motion in greater detail, we need to define the velocity at any specific instant of time or specific point along the path. Such a velocity is called instantaneous velocity. Note that the word instant has somewhat different meaning in physics than in everyday language. Instant is not necessarily something that is finished quickly. We may use the phrase "It lasted just an instant" to refer to something that lasted for a very short time interval.

Instantaneous Velocity In physics an instant has no duration at all; it refers to a single value of time. One of the most common examples we can use to understand instantaneous velocity is driving a car and taking a quick look on the speedometer. At this point, we see the instantaneous value of the velocity.

Instantaneous Velocity The instantaneous velocity is the same as the magnitude of the average velocity as the time interval becomes very very short. Δx Δt as Δt 0 close to zero v =

Instantaneous Velocity These graphs show (a) constant velocity and (b) varying velocity. (a) When the velocity of a moving object is a constant the instantaneous velocity is the same as the average. v (m/s) t (s) v (m/s) t (s) (b) When the velocity of a moving object changes its instantaneous velocity is different from the average velocity.

MOTION GRAPHS Slow, Rightward(+) Constant Velocity Fast, Rightward(+) Constant Velocity

Constant velocity to Speeding up Positive Velocity Positive Velocity Changing Velocity (acceleration)

Slowing down Slow, Leftward(-) Constant Velocity Fast, Leftward(-) Constant Velocity

Velocity time graphs CONSTANT VELOCITY Calculate distance using v=d/t for 3 and 5 secs

Position time graph Constant Velocity Calculate velocity using v=d/t for 3 and 5 secs

Constant Positive Velocity Observe that the object below moves with a constant velocity in the positive direction. The dot diagram shows that each consecutive dot is the same distance apart (i.e., a constant velocity). The position-time graph shows that the slope is both constant (meaning a constant velocity) and positive (meaning a positive velocity). The velocity-time graph shows a horizontal line with zero slope (meaning that there is zero acceleration); the line is located in the positive region of the graph (corresponding to a positive velocity). The acceleration-time graph shows a horizontal line at the zero mark (meaning zero acceleration).   http://www.physicsclassroom.com/mmedia/kinema/cpv.gif

Velocity Graphing Activity The graph below shows velocity versus time. How do you know the velocity is constant? v (m/s) t (s)

Velocity Graphing Activity The graph below shows velocity versus time. When is the velocity increasing? Decreasing? Constant? v (m/s) t (s)

TEST