Introduction to Physics Physics 114 Eyres

Transcription

1 What is Physics? Introduction to Physics Collecting and analyzing experimental data Making explanations and experimentally testing them Creating different representations of physical processes Finding mathematical relations between different variables Testing those relations in new experiments Module 1 1 Module 1 Lab Outcomes: The practice (doing) of physics 1 Develop a Testable Question: Draft an interesting, testable question Make Observations (sometimes referred to as doing the experiment ): Design and communicate all the operational details necessary to carry out the experiment 3 Analyze Information and Drawing Conclusions: Organize and analyze observations so that conclusions might be generated that speak to the purpose of the experiment 4 Communicate Results: Present the results of an experiment following appropriate guidelines Physics: First Things Representing Physics Particle model and Motion diagrams (dots) Coordinate systems What is the Quantity & what? Position, Time, velocity, etc Direct (simple measurement) and indirect (calculated) Metric, US, small or large? Using units: Unit analysis and conversion Reporting the Measured Quantity Type if measurement How many digits? Best Value +/- Uncertainty Module 1 3 Module 1 4 Representing Motion: It is relative Introduction: Representing Physics Motion is a change in an object's position relative to a given observer during a certain change in time Without identifying the observer, it is impossible to say whether the object of interest moved Physicists say motion is relative, meaning that the motion of any object of interest depends on the point of view of the observer The reference frames is what we use to make the observer s point of view clear Module 1 5 1

2 Reference frames require: An object of reference (or a point on an object if the object is large) A coordinate system with a scale for measuring distance A clock to measure time Coordinate System Establish the coordinate system ruler A number line with an indication showing positive side It is your choice whether left, right, up, down, or along a slope is positive The x=0 (or y=0) location is identified Again it can be any place your choose x=0 Position Establish the coordinate system ruler Read the position from the ruler Don t forget the units and direction x= -10 x=0 x=+10 Negative Positions Positive Positions Displacement A displacement is a change in position A vector so it has direction Only defined by the start position and end position Any motion in between makes no difference Direction can be specified by an angle or by a sign Sign depends on the coordinate system Module 1 10 Example: Displacement-1 If an object is initially at x=-4 and later at x=+, then the object is moving to the right on this coordinate system The change in position (displacement) is positive on this coordinate system Example: Displacement- If an object is initially at x=+4 and later at x=-, then the object is moving to the right on this coordinate system The change in position (displacement) is negative on this coordinate system Initial position Final position Initial position Final position x= -4 m x=- m x=0 x= + m x=+4 m x= +4 m x= + m x=0 x=- m x=-4 m = = +4 = 6 Notice that the change in position is positive The velocity is also positive This is the same motion as the previous slide, yet the sign of the displacement is different It is relative (depends on) the coordinate system = = +4 = 6 Notice that the change in position is negative The velocity is also negative Phys 114: Linear Motion 1-Mod 1 11 Phys 114: Linear Motion 1-Mod 1 1

3 Example: Displacement-3 If an object is initially at x=+4, moves to x=-1 stops for awhile, goes to x=-4, and then turns and ends the motion at x=- The change in position (displacement) depends only on the start and end positions Final position Initial position This is the same displacement as the previous slide, yet the total distance travelled is different Distance travelled was 10 meters total (Note: Distance is a scalar) x= +4 m x= + m x=0 x=- m x=-4 m = = +4 = 6 Notice that the change in position is negative The velocity is also negative Time Interval A time interval is a change in time A scalar so no direction Always positive Phys 114: Linear Motion 1-Mod 1 13 Module 1 14 in the SI System Introduction: Fundamental Quantities () Length (m) Mass (kg) Time (s) Electrical current (A) Temperature (K) Amount (mol) Luminous Intensity (cd) Derived Quantities: Definitions based on combinations of fundamental quantities Velocity (m/s) Density (kg/m 3 ) Module 1 15 Module 1 16 in the SI System Quantity Name Symbol Derived Unit Other Useful Forms Fundamental Displacement X m Time t s Mass m kg Velocity (Speed) v m/s Acceleration a m/s Unit Analysis Use to check equations you are using Notice that the equation below is not valid The unit analysis shows that the units on the right do not reduce to the units on the left m v = 4 x F Velocity Force m s Mass = m s = m = s s kg m m kg s kg s m kg m Displacement Module 1 17 Module

4 Unit Conversion Convert 467 lb/in to N/ Use the pattern: Conversion factor for lb and N Under Forces in the conversion factor table 467 lb/in (conversion factor) (conversion factor) = (new value) N/ = "# "# Conversion factor for in and Under length in the conversion factor table Introduction: Measurement "# = $ "# Module 1 19 Module 1 0 Significant Figures Measurement Devices Count all non-zero digits Count zeros between non-zero digits Count zeros after the decimal if also after a non-zero digit Don t count zeros used only for column placement Try these: a b 1030 c 301 d 310 e 30 f 0000 g Analog: You must read from a scale Digital: You have a display screen with the value given Module 1 1 Module 1 How Many Digits to Write Uncertainty Analog: Write digits until the one you must interpolate Digital: Write what is shown on the screen Write: 164 Write: 94 Only one reading is possible or reasonable Single measure digital: Values are rounded by the device before we see them You must specify the range of values that might have been rounded to the number shown Single measure analog: Values are read and the last digit is an interpolation between marks You must make a judgement call about how others might reasonably read they same value Multiple measure (both digital and analog): In this case, it is possible to take several measurements Using the many values, the uncertainty must be calculated Module 1 3 Module 1 4 4

5 Uncertainty: Single measure digital Uncertainty: Single measure analog Consider all the values that would round to the number on the display Write: value +/- uncertainty range Draw the pdf (probability density function) and label its center and both sides Upper side is value + range Lower side is value - range Write: (164 +/- 005) lb Single measure analog Consider all the values that would likely be read by a very careful person making the reading in the same situation as you In the example I debated in my mind between 94 and 95 and decided 94 was better The indecision helps me think of the uncertainty as 01 instead of something larger like 0 Write: value +/- uncertainty range Draw the pdf (probability distribution function) and label its center and both sides Upper side is value + range Lower side is value - range Write: (94 +/- 01) 1635 lb 164 lb 1645 lb Module Module 1 6 Uncertainty: Single Measure Analog Consider all the values that would likely be read by a very careful person making the reading in the same situation as you In the example the marks are close together and the line farther from the scale The reading is larger than 17 and less than 18 I chose 175 as the best reading I can make and selected the range as 005 Notice how this is NOT the same as a single DIGITAL reading Notice the last digit read is in the same column as the uncertainty Another possible reading would have been 175 +/- 00 Write: (175 +/- 005) Module Uncertainty: Multiple Reading Decide how many digits to measure At least 10 are needed Draw Histogram or number line to check for outliers Look at spread & keep >90% You may need to make more measurements to test for multiple outliers If you think you have 3, you need to make more measurements to a total of at least 30 Calculate Average Calculate Range by taking the largest difference from the average Module 1 8 Uncertainty: Multiple Reading Identify Uncertainty Calculate uncertainty by choosing largest distance from average Look at Historgram and identify width of box to include >90% Box center is at average Min Avg Max Avg-Min Max-Avg Choose Largest Uncertainty: Multiple Reading /- 03 N= (9%) 7 6 N= / Notice that the green uncertainty is better The yellow one is very wide due to the outliers Two outliers are allowed because the students went back to take more measurements to make the total greater than 0 Module 1 9 Module

6 Measurement: Summary Type of measurement Single Reading Digital Single Reading Analog Multiple Reading (both digital and analog) Diagram Number of digits reported Example Rectangle Copy the display 456 +/ sec Notice that the uncertainty is one digit past the reading Triangle Number-line scatter plot to check for outliers To the first digit interpolated All digits used in calculations Final report is consistent with uncertainty after rounding 456 +/- 00 sec Notice that the uncertainty is the same digit as the last digit in the reading / sec Notice that the uncertainty is rounded to significant figures and the reading is rounded to the same decimal place Module