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Grade 10 Science Motion Unit Significant Digits The correct way to record measurements is: Record all those digits that are certain plus one and no more These “certain digits plus one” are called significant digits ALL DIGITS INCLUDED IN A STATED VALUE (EXCEPT LEADING ZEROES) ARE SIGNIFCANT DIGITS Measurements Examples Table 1 Certainty of Measurements Measurement Certainty (#of Significant Digits) 307.0 cm 4 61 m/s 2 0.03 m 1 0.5060 km 4 3.00 x 10 8 m/s 3 2340.00 0.1240 2005 Decimal Absent Decimal Present 0.003450 A Red Arrow pops the 0’s 2500 like balloons until it sticks in a digit between 1 and 9. Then you count the rest of the digits that are left. Counted and Exact Values When you count the number of something (example – students in the class), this is an exact value and has an infinite number of significant digits. When you use a defined value such as 100 cm/m or 60 s/min, you also have an infinite number of significant digits. Note the calculation rules on BLM 9.2B Converting Units When you want to change 100cm/m units we use a conversion factor (or equality) 1000m/km Some Equalities 60 s/min 60 min/h Assignment : Significant Digits BLM 9.2a, 9.2b Complete the Significant Digits Worksheet See answer key Questions 1-6, 9 pg 349 in your text Relating Speed to Distance and Time Average Speed Vav is: The total distance divided by the total time for a trip Vav = d t See BLM 9.5a for examples Instantaneous speed – the speed an object is travelling at a particular instant. Ie. Radar trap Constant Speed (uniform motion) – if the instantaneous speed remains the same for a period of time. Ie. Cruise control on your car A car travels 45 km at a speed of 90 km/h. How long did the trip take? What do you know in the Question d= 45 km Vav = 90 km/h t=? Decide on a formula t= d Vav d Vav t Substitute the knowns into the formula and solve t = 45 km 90 km/h t = 0.5 h •Write a concluding statement: It takes 0.5 h for the car to travel 45 km at a speed of 90 km/h Problem Solving Summary List the variables you know Decide on a formula Substitute what you know into the formula Solve and write a concluding statement Speed- Click Me Assignment : Relating Speed to Distance and time BLM 9.5 a,b, d Answer Key Questions 1,2,3,6,7,8 pg 358 Answer Key Distance – Time Graphs Independent variable - X axis is always time Dependent Variable - Y axis is always distance Speed is determined from the slope of the best fit strait line of a distance – time graph SmartBoard Slope of a Line In the following diagram: See BLM 9.7a A = constant speed B = not moving C = accelerating Distance-Time Graphs Assignment : Distance – Time Graphs Lab 9.5 Graphing Distances During Acceleration Questions 3,4,5,6 pg 365 Answer Key Activity 9.9 Simulation : Average Speed on an Air Table BLM 9.9a Worksheet – Determining Speed from a d/t Graph Q 1-6 Answer Key Lab9.6 Balloon Cars Lab Lab 9.10 Determining an Average Speed Review Questions 1,3,4,7,9,11 pg 376 Answer Key Test Chapter 9 Chapter 11 Displacement and Velocity Introduction to Vectors Reference Point – origin or starting point of a journey. Ie. “YOU ARE HERE” on a mall map Position – separation and direction from a reference point. ie. “150 m [N] of “YOU ARE HERE” Vector Quantity – includes a direction such as position. A vector quantity has both size and direction ie. 150m [N] Scalar quantity – includes size but no direction. ie. 150 m Symbol Example Quantity Symbol Scalar Quantity Distance 292 km d Time 3.0 h t Vector quantity 2 km [E] (from Position d Subway) Displacement d 292 km [S] Displacement – a change in position. See BLM 11.1a Symbol Format – used when communicating a vector. See BLM 11.1b Drawing Vectors – state the direction (N,E,S,W) Draw the line to the stated scale or write the size of the vector next to the line The direction of the line represents the direction of the vector and the length of the line represents the size of the vector Assignment : Introduction to Vectors Questions 1,5,6,7,8 pg 417 Walk the Graph Activity pg 418 & BLM 11.2 Adding Vectors on a Straight Line Vector Diagrams – Join each vector by connecting the “head” end of one vector to the “tail end of the vector. next vector. Find the resultant vector by drawing an arrow from the tail of the first vector to the head of the last vector Resultant displacement - dR is a single displacement that has the same effect as all of the individual displacements combined. Adding vectors can be done by one of the following methods usingscale diagrams adding vectors algebraically combined method See BLM 11.3 11.3 Adding Vectors Along a Straight Line Two vectors can be added together to determine the result (or resultant displacement). Use the “head to tail” rule Join each vector by connecting the “head” and of a vector to the “tail” end of the next vector d1 d2 dR Resultant vector Scale Diagram Method Leah takes her dog, Zak, for a walk. They walk 250 m [W] and then back 215 m [E] before stopping to talk to a neighbor. Draw a vector diagram to find their resultant displacement at this point. Scale Diagram Method 1)State the direction (e.g. with a compass symbol) N 2)List the givens and indicate the variable being solved d1 = 250m [W], d2 = 215m [E], dR = ? 3)State the scale to be used 1 cm = 50 m 4)Draw one of the initial vectors to scale 5)Join the second and additional vectors head to tail and to scale 6)Draw and label the resultant vector dR 7)Measure the resultant vector and convert the length using your scale 0.70 cm x 50m / 1 cm = 35m [W] 8)Write a statement including both size and direction of the resultant vector The resultant displacement for Leah and Zak Is 35 m [W]. Adding Vectors Algebraically This time Leah’s brother, Aubrey, takes Zak for a walk They leave home and walk 250 m [W] and then back 175 m [E] before stopping to talk to a friend. What is the resultant displacement at this position. Adding Vectors Algebraically When you add vectors, assign + or – direction to the value of the quantity. (+) will be the initial direction (-) will be the reverse direction 1.Indicate which direction is + or – 250 m [W] will be positive 2.List the givens and indicate which variable is being solved d1 = 250 m [W], d2 = 175 m [E], dR = ? 3.Write the equation for adding vectors dR = d1 + d2 4.Substitute numbers (with correct signs) into the equation and solve dR = (+ 250 m) + (-175 m) dR = + 75 m or 75 m[W] 5.Write a statement with your answer ( include size and direction) The resultant displacement for Aubrey and Zak is 75 m [W] Combined Method Zak decides to take himself for a walk. He heads 30 m [W] stops, then goes a farther 50 m [W] before returning 60 m[E]. What is Zak’s resultant displacement? Combined Method 1)State which direction is positive and which is negative West is positive, East is negative 2)Sketch a labeled vector diagram – not to scale but using relative sizes 50m 30m 60m dR 3)Write the equation for adding the vectors dR = d1 +d2 +d3 4)Substitute numbers( with correct signs) into the equation and solve dR = (+ 30 m) + (+50m) + (-60m) dR = + 20m or 20m [W] 5)Write a statement with your answer (including size and direction) The resultant displacement for Zack is 20 m [W] Assignment : Adding Vectors in a Straight Line Questions 1-3,5-7 pg 423 Answer Key Activity “Bug Race” Adding Vectors at an Angle If we know the path an object takes we can draw an accurate to scale vector diagram of the journey. We can then determine the following; compare the final position to the reference point determine the resultant displacement Certain rules must be followed add vectors at an angle. See BLM 11.5a Adding Vectors at an Angle Scale 1 cm = 5 Km d R = 5cm dR = 5 cm x 5 Km/1cm d 1 = 3 cm dR = 25 Km [NW] N d 2 = 4 cm Assignment : Adding Vectors at an Angle BLM 11.5b Activity “Hide a Penny Treasure Hunt” Velocity Velocity – v a vector quantity that includes a direction and a speed ie. 100 km/h [E] Constant Velocity – means that both the size (speed) and direction stay the same Average Velocity – v av is the overall change of position from the start to finish. It is calculated by dividing the resultant displacement (which is the change of position) by the total time V av = dR t See BLM 11.7a,b Assignment : Velocity BLM 11.7c Questions 3,5,7, pg 436 Activity Tracking and Position pg 438 & BLM 11.9 Review Questions 4,8,9,10 pg 442 Test Chapter 11 Chapter 12 Displacement, Velocity, and Acceleration Position – Time Graphs Position and displacement are vectors and include direction. It is possible to represent vector motion on a graph. Very much like a distance – time graph. Can you see the differences? Can you see the differences? The slope of a position-time graph is equal to the velocity of the motion The slope of the tangent at a point on a position- time graph yields the instantaneous velocity. Instantaneous velocity is the change of position over an extremely short period of time. Instantaneous velocity is like instantaneous speed plus a direction Assignment : Position-Time Graphs Activity : Describing Position-Time Graphs “Walk the Dog” Activity : The Helicopter Challenge Exercise : BLM 12.1 a,b,c Velocity Time Graphs A velocity – time graph can show travel in opposite directions over a period of time. The slope of the line on a velocity –time graph indicates the acceleration of an object Acceleration – a is calculated by dividing the change in velocity by the time. Because there is a direction associated with the velocity, the acceleration is also a vector quantity. Constant acceleration is uniformly changing velocity. Formula a = v t Average Velocity of an object in motion can be determined from the ratio of total distance divided by total elapsed time. V av = dR t See BLM 12.2 a,b Assignment : Velocity – Time Graphs BLM 12.2 c Acceleration and Displacement Acceleration is the change of velocity over time Questions 5,7,8 pg 465 Test Chapter 12