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Introduction to Motion

Introduction to Motion. SPH3U – Unit #1 Kinematics. Overall Expectations. By the end of this unit, students will… Analyze technologies that apply to concepts related to kinematics, and assess the technologies’ social and environmental impact;

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Introduction to Motion

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  1. Introduction to Motion SPH3U – Unit #1 Kinematics

  2. Overall Expectations By the end of this unit, students will… • Analyze technologies that apply to concepts related to kinematics, and assess the technologies’ social and environmental impact; • Investigate, in qualitative and quantitative terms, uniform and non-uniform linear motion, and solve related problems; • Demonstrate an understanding of uniform and non-uniform linear motion, in one and two dimensions.

  3. Big Ideas Concepts that students should retain after this course are: • Motion involves a change in the position of an object over time. • Motion can be described using mathematical relationships. • Many technologies that apply concepts related to kinematics have societal and environmental implications.

  4. Motion Learning Goals After this topic I will be able to… • Define motion, • define and state the difference between distance, position, and displacement, and • measure time accurately, and • state the difference between and give examples of scalars and vectors, and • define and state the difference between uniform and non-uniform motion.

  5. Motion Everything in our universe is in a state of motion. Our planet moves around our sun along with other objects and planets in our solar system. Our solar system moves around our galaxy the Milky Way located within a universe of countless other galaxies which are all moving. People, air, animals, and countless other objects that make up our planet all move about the Earth’s surface. The elementary particles that make up all matter in the universe, too, are in constant motion. Scientists call the study of motion kinematics. Kinematics: the study of motion.

  6. Motion Motion: is the the movement of an object from one place to another, as measured by an observer. Two objects are considered in motion with respect to (wrt) each other if the straight-line segment between them changes in: • Length • Direction • Or both

  7. Motion A thought experiment between motion and the observer. Bob is on his way to the gate to catch his flight at Toronto airport. Bob is currently standing on the motorized walkway as it moves along. How would you describe Bob’s motion wrt: • Someone sitting on a bench. • Someone standing beside Bob. (a) Bob is moving at the same speed as the walkway (b) Bob is not moving. In (b) Bob is not moving wrt to the observer since there was no change in direction, length, or both.

  8. Distance, Position, and Displacement There are three ways we measure the length of which an object has travelled: Distance (d): is the total length of the path travelled by an object in motion. It is a scalar quantity. Position ( ): is the distance and direction of an object from a reference point. It is a vector quantity. Displacement ( ): is the change in a position of an object. Note that the Greek letter Δ represents, “change in”. It is a vector quantity. Note: The S.I. units for all three is the metre (m).

  9. Distance, Position, and Displacement Displacement Total Displacement Where is the displacement where is the total displacement is the final position is displacement #1 is the initial position is displacement #2 Note: For convenience, the arrows in the formulas above are often dropped.

  10. Distance Vs. Displacement The diagram below shows the difference between distance and displacement. Distance is dependent on the path taken, regardless of the direction which is why it is a scalar quantity. Displacement on the other hand, is concerned with how far you are from the starting point and which direction it is in.

  11. Examples • Danielle goes for a walk to the store to located 500 m north from her house. What is her (i) distance and (ii) displacement for the trip from home? (i) 500 m (ii) 500 m [N]

  12. Examples • On her return home, Danielle stops at a friends house which is located 250 m [S] of the store. What is her (i) total distance and (ii) displacement for the trip from home? (i) d = 500 m + 250 m = 750 m (ii) ΔdT = Δd1 + Δd2 = 500 m [N] + 250 m [S] = 500 m [N] – 250 m [N] = 250 m [N]

  13. Examples • Danielle has finally made it home. What is her (i) total distance and (ii) displacement for the trip from home? (i) d = 500 m + 500 m = 1000 m (ii) ΔdT = Δd1 + Δd2 = 500 m [N] + 500 m [S] = 500 m [N] – 500 m [N] = 0 m

  14. Examples • The next day, Danielle has decided to get a coffee on the way to school which is 200 m [E] of her house. It takes another 50 m [S] to get to the school. What is her (i) distance travelled and (ii) displacement for her trip from home to school? (i) d = 200 m + 50 m = 250 m (ii) First we need to set-up our vectors “tip” to “tail” to show the route she travelled: (Scale is 1 cm: 10 m) What we have is a right angle triangle: We will solve the scalar portion first: Since c2 = a2 + b2 ΔdT2 = Δd12 + Δd22 = √{(200 m)2 + (50 m)2} = 210 m Now the direction of the new vector: tanΘ= opp/adj Θ= tan-1 (50 m/200 m) = 14° her displacement from home to school is 210 m [E14°S]

  15. Activity Now that you’ve gotten some terms under your belt, let’s get test those old math skills. Instructions: • With your table partner or a small group of no more than 3, complete Part A of the activity, “Position and Time” • Ensure that you take your time completing the graph as you will need it later!

  16. Motion You will need your graph from the activity you just completed as a reference. From the activity just completed you should have noticed that the graph produced a line that is linear. This represents uniform motion. Uniform Motion: is the movement of an object at a constant speed in a constant direction. This means the distance travelled will be the same for equal intervals of time! However, most motion we see in our daily lives is not like this. Non-Uniform Motion: is movement that involves changes in speed, direction, or both.

  17. Example • Are the motions described below uniform or non-uniform? Explain. • A rubber stopper is thrown in the air and hits the floor. • A car is travelling at a steady rate of 85 km/h due west. • A motorcycle rider applies the brakes to come to a stop. • A race car travels around a circular track at a constant speed. a) non-uniform – speed is changing b) uniform – speed and direction are constant c) non-uniform – speed is changing d) non-uniform – direction is changing

  18. Homework • Read pg. 8-11 • Practice Problems: pg. 13 #1-4

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