Ch.1&2: Measurement and Motion

Making a measurement Units: describes the relative size or nature of a measurement (always follows a number) Standard: something everyone can agree Accuracy vs Precision: right value vs repeatable

The scientific standard for measurement

Solving A Measurement Problem Get into groups of two Have one person obtain two paper clips of different sizes Follow the instructions on the lab sheet Answer the questions at the end

Math and Physics  Prefixes are used to change SI units by powers of 10, as shown in the table below (page 6).

Converting units Prefixes are added to the names of SI base units to represent quantities that are larger or smaller than the base units. Kilo – k Hecto – h Deka – da BASE Deci – d Centi – c Milli – m K ing H enry D ied B y D rinking C hocolate M ilk Dimensional Analysis: Conversion factors – equation that always equals one (ex. 1cm/0.01m) *Multiply the conversion factor so that units you do not want cancel and the unit that you do want ends up on top. EX. 6.98m/min = ___km/hr

Graphing Exercise Pie Graph (Exhaled Air) –Nitrogen 78% –Oxygen 16% –Carbon Monoxide 4% –Other 2% Bar Graph (Hours of sleep) –Average number of hours of sleep on a given night –Use results from board Line Graph (Driving Accidents per Time of Day) –Midnight – 3am13.1 –3am – 6am8.1 –6am – 9am9.7 –9am – noon9.7 –Noon – 3pm13.1 –3pm – 6pm16.0 –6pm – 9pm15.4 –9pm – midnight14.1

Graphing Data Independent variable – factor that is changed or manipulated during the experiment Dependent variable – factor that depends on the independent variable. Ex – line graph – which is which?? Linear relationship – line of best fit is a straight line; y = mx+b Quadratic (nonlinear) relationship – one variable depends on the square of another; y = ax 2 +bx+c Inverse relationship – one variable depends on the inverse of the other; y = a/x

GETTING IT STRAIGHT Materials: –Pieces of PVC, wire, wood –Ruler –Electronic balance Procedures: –Acquire each different size of PVC, wire, or wood –Measure their length or area based on their shape –Record those values in the chart (be sure to use the proper units) –Answer the questions at the end

Fill-in the spaces below Small (cm or cm 2 ) small mass (g) Large (cm or cm 2 ) Large mass (g) Medium (cm or cm 2 ) Predict mass (g) PVC WIRE WOOD

Questions 1)Measure the mass of the medium piece. Did it match your predicted value? 2)What are your sources of error for this lab? 3)Did those errors affect your results? Explain. 4)How would you describe the relationship between mass and size: linear, quadratic, or inversely proportional? Explain.

What is motion? Obvious answer: when something is moving So, how do you tell something is moving? Answer: Frame of reference (reference frame): –A mathematical/physical construction that defines a given situation (defines the zero point of the variable) Coordinate system: tells location of zero point of the variable and the direction the values of the variable increase.  Position: defines where an object is  Distance: length traveled from a given position  Displacement: total distance traveled from a position So how do you tell distance from displacement ?

Distance and Displacement Distance –length traveled from a given position –Always positive –Not dependent on direction of motion Displacement –total distance traveled from a position –Can be positive or negative –Dependent on direction of motion

Vectors and Scalars vectorsQuantities that have both magnitude (size) and direction, are called vectors (graphically represented by arrows). scalarsQuantities that are just numbers without any direction, are called scalars. To add vectors graphically, the length of a vector should be proportional to the magnitude. So it is important to make an accurate drawing.

resultant The vector that represents the sum of the other two vectors is called the resultant. The resultant always points from the tail of the first vector to the tip of the last vector. Vectors and Scalars

Measuring distance (in meters, m) Distance interval is defined as: The i is initial and the f is final, but are relative to your reference frame (your choice)  (Greek letter “delta”) stands for “change in” or final - initial

Measuring time (in seconds, s) Time interval is defined as: The i is initial and the f is final, but are relative to your reference frame (your choice)  (Greek letter “delta”) stands for “change in” or final - initial

SPEED Speed is distance traveled in a certain time There are three basic types of speed: –instantaneous: speed at one specific time –constant: unchanging speed –average: speed averaged over a period of time Can be calculated by equation or graph Always positive (scalar)

SPEED EQUATION v = d / t v : speed (meters per second, m/s) d : distance (meters, m) t : time (seconds, s)

VELOCITY vs. SPEED Speed or velocity can be found by taking the slope of a position-time graph Velocity is a vector– must have magnitude and direction  Speed is the magnitude of velocity.

USING A GRAPH Simply read the distance and time off the position-time graph Divide the distance and time to get the instantaneous speed Average velocity would be subtracting two distances and dividing by the subtraction of their corresponding times, or v =  d /  t

SLOW FLYER LAB Materials: –five pieces of paper Objective: –design and build a paper airplane to travel the slowest possible speed Each group will get four official tests and one official throw. The plane must be made of one page only, the other pages are for testing ideas.

DESIGN A SLOW FLYER Get in groups of 2 Each group will receive five sheets of paper –four will be for testing –one for the actual plane (if you need it) Plane must be able to fly at least 3 m horizontally Throw plane and measure time We will determine the winner using our speed equation (remember: SLOW flyer)

Instantaneous Velocity Vectors Objective –Practice using vectors Materials –String –Masses –Graph paper (optional) Procedures –Turn to page 46 –Follow steps outlined –Answer the questions

The graph describes the motion of a student riding his skateboard along a smooth, pedestrian-free sidewalk. What is his average velocity? What is his average speed?

Section IV: Graphing 1)Plot the following data on a Position-Time graph. 2)Show me on the graph how you would find the average speed of the car between 1 and 2 s. 3)What was the average speed between 1 and 2 s? 4)What was the average speed between 2 and 3 s? Time (s) Position (m)

HW Answers – Ch.1&2 p ). quadratic; y=ax 2 +bx+c 46). inverse; linear; quadratic 50). g/cm 3 or kg/m 3 ; derived unit 51). cm; mm; m; km 67) m; 6.2x m; 2.1x10 4 m; 2.3x10 -5 m; 2.14x10 -4 m; 5.7x10 -8 m 69). 0.31mg, 1021  g, kg, 11.6 mg 83). A. 80g; B. 260g; C. 400g b). A. 36cm 3 ; B. 11cm 3 ; C. 7cm 3 c). The slope represents increased mass of each cm 3 of the substance. d). y-intercept is (0,0)- when v= 0cm 3, the mass=0 P ). 20m 50) x m 51) m 53). 1.8 min or 108 s 57). car A:150km, car B:170km; b). car A:1.6hr, car B:1.4hr 63. Varied possibilities

Tri-Race Lab Objective –Find instantaneous, average, and constant velocity of car Materials –Lego Kits –Stop watch –Ruler Procedures –Build a free rolling car –Roll down ramp –Find average speed at end (2m). –Find instantaneous speed every 0.5m. –Show your work!