Agenda Warm Up Correct HW Trigonometry Review Trigonometry Practice

1. AP PhysicsMonday 13.08.19Standards: NAObjective: SWBAT will be able to use pythagorean theorem, sines and cosines, and other trigonometric identities in order to solve problems. Warm Up Convert 0.004 mg -> Mg Agenda • Warm Up • Correct HW • Trigonometry Review • Trigonometry Practice • Homework • Finish: Thursday Aug.15th, • 5. a-f • 6. a-f • 7. a-h • -Think about how you could use Trigonometry to find the height of a lamppost for tomorrows lab. • Optional Reading on Conversions: p.10-13

2. AP PhysicsTuesday 13.08.20Standards: NAObjective: SWBAT use given tools and trigonometry to find the height of a lamp post Warm Up 5cos45sin45=? Agenda • Warm Up • Review Homework • Height of Flagpole Lab Homework % Difference & Error Practice

3. AP PhysicsWednesday 13.08.21Standards: NAObjective: SWBAT complete a rubric based lab write up Warm Up If the class measured the height of the D building and found it was 15.7 meters, what would be the percent difference of Mr.A’s measurement of 14.9 m. Agenda • Warm Up • Correct Homework • Percent Difference • How to Write a Lab Write UpBased on a Rubric • ** Time dependent: Percent Error & Difference Practice Homework Finish Lab Calculations, tables, and graphs.

4. AP PhysicsThursday 13.08.22Standards: NAObjective: SWBAT add and subtract vectors Agenda • Warm Up • Correct Homework • Notes: Adding and Subtracting Vectors Warm Up Compare what you would write about in the analysis section of a lab write up with the conclusion. Homework 8. a-e 9. a-f

5. AP PhysicsFriday 13.08.23Standards: NAObjective: SWBAT to break vectors into components and use vector notation. Warm Up What linear graph could you make out of the equation: K=1/2mv2 if v is your independent variable and k is your dependent variable. Agenda • Warm Up • Quiz • Work on Lab Report Homework Complete final draft of lab report.

6. Chart of Metric System Prefixes Base unit symbols: K, m, L, A, g, s Wherever you see an underscore ( ___) insert the Symbol of the base units you will use in your problem. Example, one type of unit is meters. The symbol for meters is m. Everywhere you see an underscore, insert an m

7. Measure the Height of a Lamppost • Using given materials you will be tasked to find the height of one of the lampposts. • Materials – A laser; a protractor; a meterstick; pen or pencil • Spend 3 minutes deliberating with your table groups on how this may be possible. • Go outside with the materials and find the height of the lamppost • Return to the classroom and debrief

8. Percent Difference Use percent difference to compare measurements to the groups average. You do this when you don’t know what the value that you measured should be. to compare with. % difference=|measured value – average value | x100 average value Since we don’t have a theoretical value of a lamp post, our best estimate of the actual height is our class average. In percent difference calculations we are comparing what we measured against the class average.

9. Percent Error/Percent Uncertainty Use percent error or % uncertainty to compare your measurement to a known value or a scientifically verified value. Whenever you already know what answer you should be getting and the purpose of your experiment is to verify the answer, you would use this equation to find error. % difference=|measured value – actual value| x100 measured value

10. Percent Difference & Error Practice • Measured mass: 5.6 kg, Average Mass: 22.5 kg • Measured length: 2.6m, Average Length 3.1m • Measured Force 20.21 N, Actual Force: 20.24 N • Measured current 12.1 A, Actual current: 11.7 A • Find the percent difference of each of the classmates measurements.

11. Lab Write Up Example • Question/Purpose • The purpose of this lab is to use our trigonometry skills to find a practical way to measure the height of the lamppost. • By finding the angle between the ground and the top of the lamppost at different distances, I will be able to find the height of the lamppost. • Materials/Procedures • 1 meterstick, 1 laser, 1 protractor, pencil, paper. • Step 1: Measure a 1 m distance from the flagpole • Step 2: Have one person shine the laser from the ground to the top of the flagpole. • Step 3: Have another person use the protractor to measure the angle the laser makes with the ground. • Step 4: Repeat at 2m, 3m, 4m, & 5m.

12. Lab Write up Continued Data Your Average Height: (Trial 1+Trial 2+Trial 3 + Trial 4 + Trial 5)/5= (15.4+15.3+14.8+16.1+15.8)/5=15.5m We’ll say that the class average for my theoretical experiment was 16.2m % difference = |Your Ave. Height – class average | x100 =______ class average % difference =|15.5m-16.2m|/16.2m x 100%= 4.3%

13. Data Continued Graphing: Things to consider • You choose your dependent and independent variables. • Once you graph the data, be sure to point out calculate the the slope made by the curve or the area under the curve, depending on the particular topic. • Be sure to scale correctly. If you are unsure, I can go over it. • Always label the x and y axes with the appropriate physics concept and its units that are being described by the graph. %difference based on slope: |15.4-16.2|/16.2x100%=5%

14. Analysis A proposed alternative technique to measuring the height of the lamppost was to use trigonometric relationships. Our model, the right triangle has an important known relationship: tanθ=y/x. By calling the height of the lamppost y and by choosing different lengths (independent variable) to shine a laser at the top of the lamppost we were able to find the angle (dependent variable) of the laser. This is θ in the right triangle model. I collected the data and received 5 different values for the height. Finding the average, I calculated 15.5m. Comparing it to the class average of 16.2 I had a 4.3% difference. For a potentially more accurate value of the height of the lamppost, I graphed the data. The relationship isn’t naturally linear so I graphed tanθvs 1/L. The slope should denote the height of the lamppost. The slope of the graph was 15.32 m which is comparable to 15.5m, but since it is the slope of a curve on a graph that shows a linear trend, I find it more reliable than a simple average. Data analysis: Things to Consider • What are your variables? • Which quantity did you change (the independent variable). • Which quantity changed as a result of changing the independent variable (the dependent variable) ? • How were the variables related? • What was their relationship based on your data and your graph? (The typical way to express relationships between variables is through an equation. You write it down, explain what each part means, and explain how you used your data to obtain the equation)

15. Conclusion My final results showed a lamppost with a height of 15.4m and below 5% difference between the rest of my class. We don’t have an actual value to compare to, but considering my data was within 5% of the class average suggests that our methodology has merit. If we all calculated very different heights that could have been a problem, possibly with our technique for measuring or even for our theoretical value. To really confirm that our hypothesis is correct and this method is valid for measuring height, we would need to either measure it with a traditionally accepted method, or contact the manufacturer with the height of the lamppost. Though our results remain slightly inconclusive, acquiring any of the above information is all we would need to have a more definitive result. The data we produced was generally good but we did have problems and the experimental setup could use refining. First of all the time of day was a problem. I could barely see the laser at the top of the pole so I actually didn’t have anything to stabilize the laser so it was wiggling up and down. This means my θ data could have been more accurate if it was both stable and on the ground. Also we used a meter stick to measure distances. A metric tape measure would have allowed us to measure more precisely, especially since we were measuring in the air and not on the ground. Another issue we had was that the ground was not level so that could have slightly thrown off our data. Finally, there has got to be a better way to measure an angle than with a protractor. That particular device is only good for general results. Future experiments can improve in these areas. • Concluding Remarks – Things to consider • Is your hypothesis, confirmed, falsified, or inconclusive. • Explain Why and use your data you collected to support this conclusion? • Sometimes inconclusive experiments seem like they should work “theoretically” but they don’t and there are sources of error that may be getting in the way. Describe possible sources of errors. • If you think the experiment is inconclusive, you should include your ideas for what type of experiment you could do, or what you could change about this experiment to obtain results that will confirm or falsify your hypothesis. • Confirmed experiments usually have less than 5% error. • Falsified experiments mean that you’ve done an experiment and your theory is wrong. The implications of this is that another theory is right. If your theory is wrong, give us a clue about what may be a substitute for the wrong theory. • Most of the time your experiment will be inconclusive.