Unit 1 ~ Learning Guide Name:

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Christiana Parsons
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1 Unit 1 ~ Learning Guide Name: Instructions: Using a pencil, complete the ollowing notes as you work through the related lessons. Show ALL work as is explained in the lessons. You are required to have this package completed BEFORE you write your unit test. Do your best and ask questions i you don t understand anything! Scientiic Notation: 1. Why was scientiic notation invented?. Do an Internet or book search and ind something in your universe that is represented by a REALLY small number. a) What is it that is being described? b) Show the value in scientiic notation: c) Show the value in regular notation: 3. Do an Internet or book search and ind something in your universe that is represented by a REALLY large number. a) What is it that is being described? b) Show the value in scientiic notation: c) Show the value in regular notation: 4. Convert the ollowing to scientiic notation in standard orm. a) b) c) d) e) Page 1 o 15

2 5. Round the ollowing to the number o igures shown and convert to scientiic notation in standard orm. a) round to sig igs b) round to sig igs c) round to 1 sig igs 6. Indicate the number o signiicant igures in the number given (ans. a) b) c).0013 d) e) ) g) x 10 3 h) 9 x Ensure you can use your calculator to easily acquire the given results (use EE or EXP button i available. a. (5.98 x 10 4 kg ) (7.35 x 10 kg) = b. (5.98 x 10 4 kg ) / (7.35 x 10 kg) = Signiicant Figures: 1. What is the main purpose or learning about signiicant igures in science and/or technology courses?. Students sometimes get conused between the terms "scientiic notation" and "signiicant igures." Figure out a way that will ensure you don't get conused between the two. Describe your method below. (HINT: deine notation, deine signiicant). Page o 15

3. Suppose that three people were told to determine the length o a piece o wood and were given a tape measure whose smallest markings were at 0.1 centimeter intervals.

3 3. Suppose that three people were told to determine the length o a piece o wood and were given a tape measure whose smallest markings were at 0.1 centimeter intervals. They report the ollowing values: Person Value measured or length cm cm cm Who is documenting this measurement correctly? The correct question is "who recognizes the questionable digit and documented accordingly?" Justiy your answer. 4. What is your best score on the Sig Fig Bomb Game (include level and score). Page 3 o 15

4 5. Evaluate the ollowing and use the correct number o signiicant igures in your answer (Show all work) a..35 cm x 4.6 cm b) 4/3 ( )(4.7 in) 3 c) d) 1.5m 3. m 3.4m km 4.5hr e) 301cm cm + 9.0cm 6. Summarize the dierence between the rules or signiicant igures when adding/subtracting and when multiplying/dividing? Page 4 o 15

5 Equation Solving: 1. Solve or x in the ollowing equations (show all work): a. = 5 + x ans. -3 b. 19 = x + 7 ans. 6 c. 3 5x = 14 ans. -. d. x 5 ans. 10. Rearrange the equation, solving or the variable shown (clearly show all steps). kqq 1 a. Solve or Q 1 where F r b. Solve or "t" where d = ½at Page 5 o 15

6 vo v c. Solve or v o where d t d. Solve or "a" where v = v i + ad e. Solve or d where v d t d t i i. Solve or m where E p mgh g. Solve or m where E 1 k mv Page 6 o 15

7 h. Solve or t i where v d t d t i i i. Solve or v o where 1 d v t o at j. Solve or v i where v = v i + ad vo v k. Solve or v where d t l. Solve or v where E 1 k mv Page 7 o 15

How high does the ladder reach? How ar is the base o the ladder rom the wall? h = b = b) In the igure below, the 4.

8 Trigonometry: 1. Solve the ollowing triangles using SOHCAHTOA and Pythagoras. Show all work. a) In the igure below, the 4.0 meter ladder is making a 60. degree angle with the ground. How high does the ladder reach? How ar is the base o the ladder rom the wall? h = b = b) In the igure below, the 4.0 meter is reaches only 1.5 meters up the wall. How ar is the base o the ladder rom the wall? What is the angle the ladder makes with the ground? b = = Page 8 o 15

9 c) Solve or x, y, and A. x = y = A = d) Solve or R and ɵ. R = = e) Solve or R and ɵ. BC = Total Height = Page 9 o 15

10 Units o Measure: 1. Unit conversions (show all work lay out in brackets, same as lesson examples) a..67 hours into seconds b. 80. km/hr to m/s c. 34 km into meters d. 1.0 day into seconds e. 1 hours into seconds km/hr into m/s g. 40 km/hr into m/s h. 1 m/s into km/hr i. 00 g into kg j. 10 kg into grams Page 10 o 15

11 . We can only add and subtract numbers in Physics i they have the same units. For example I can add 5.0m to 1m to get 17m but I cannot add 5.0m to 10m/s. You cannot add a velocity (10m/s) to a distance (5m) and get anything meaningul. Use dimensional analysis to ensure that the kinematic equations shown below adhere to this rule. (Note: it does not matter at this stage i you understand the physics behind the equations). The units or each variable are given. The irst one is done or you. Variable Units d m v i m/s v m/s a m/s t s a. v = v i + at v = v i + at Step 1: replace each variable with units only [m/s] = [m/s] + [m/s ][s] Step : cancel and simpliy where possible [m/s] = [m/s] + [m/s ][s] Step 3: compare resulting terms (same?) [m/s] = [m/s] + [m/s] Conclusion: Since each term has the units o m/s, the equation is likely valid. b. v = dt c. d = vt conclusion: valid / invalid (circle one) conclusion: valid / invalid (circle one) d. d = v i t + ½at (remember that the ½ doesn t have a unit so isn t considered) conclusion: valid / invalid (circle one) Page 11 o 15

12 Graphing Data: 1. Describe how you can recognise a positive vs. a negative vs a zero slope on a graph. Sketch and explain.. What does a y-intercept on a graph represent? 3. Describe each letter in the equation y=mx+b. 4. What type o graph does y=mx+b represent? How do you recognize a graph that can be represented by it? 5. How do you determine the units o a y-intercept rom a graph? Provide an example. 6. How do you determine the units o slope rom a graph? Provide an example. Page 1 o 15

13 7. Find the slope and y-intercept o the ollowing lines, then answer with the resulting equation o the line in y=mx + b ormat. Show work or slope calculation. a) b) c) Page 13 o 15

14 8. Suppose that the water level o a river is 34 meters and that it is receding at a rate o 0.50 meters per day. Write an equation or the water level, L, ater d days. In how many days will the water level be 6 meters? (include units or everything) 9. A plumber charges $5 or a service call plus $50 per hour o service. Write an equation in slope-intercept orm or the cost, C, ater h hours o service. (include units or everything) 10. A runner gets a 30.0 meter head-start then runs 5.0 km/hr. Write an equation (in base SI units) which will represent the runners distance rom the start line at any second. (include units) 11. A car begins at a speed o 0. m/s then increases its speed by.0 m/s each second. Write an equation that represents the speed o the car as a unction o time. (include units) Page 14 o 15

15 Answers: Scientiic Notation: 4) x10 4,.35x10-4, -.3x10 6, -1.50x10-5, 7.50x10-3 5) 6.3x10 5, 3.5x10-3, 3x10 6),6,3,5,5,3,4,1 7) 4.40 x 10 47, 81.4 Signiicant Figures: 1) communication (expand) 3) Person3 5) 11cm, 430in 3, -1.m, 160km/hr, 3144cm Equation Solving: 1) -3, 6, -., 10 (all work shown) Fr d ) a) Q1 b) t c) v kq a E p Ek ) m g) m h) T i gh v k) v d vot l) v t E m k o d v t v vi d) a e) d vt vti di t d vt di d i) v v 0 1 d at j) t Trigonometry: 1) a) h=3.5 m, b=.0 m b) b=3.7 m, = c) x=8.0, y=11, A=45 d) R=8.0, Ɵ=3 e) 6.7m, 8.m Units o Measure: 1)a)9600s B) m/s C) m d) s e) 4.3x j) g ) 7.7 m/s g) 11 m/s h) 43 km/h i) 0. kg Graphing Data: 7) a) y=x+(m=1, b=) b) y=3x+1(m=3, b=1) c) y=-x+1, or y=-3/4x+1 8) L=-0.5d+34, 16 days 9) C=50h+5 10) d=1.4t+30 11) v=.0t+0 Page 15 o 15

Measurement and Uncertainty

Measurement and Uncertainty Name: Date: Block: There is uncertainty in every measurement due to of accuracy and precision. Accuracy: how close the instrument measures to an accepted. Precision: how closely