Scalars-and-Vdsdsdsdsdectorsasdasasasasas.pptx

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1. Vector and Scalar Quantities Scalar quantities have size (“magnitude”) only but no direction. Scalar or Vector? Scalar Vector Mass Distance Speed Velocity Energy Power Time Force Acceleration Displacement Vector quantities have both size and direction. How is Distance different from Displacement?

2. Distance vs Displacement Distance is a Scalar quantity that refers to how much ground an object has covered during its motion Displacement is a Vector quantity that refers to how far out of place an object is; it is the objects overall change in position Confused?

3. Distance vs Displacement Peach goes for a walk round a park, first walking north for 80m, then turns around and walks 80m south. What final distance has she travelled? What is her final displacement?

4. Peach goes for a walk round a park, first walking north for 80m, then turns around and walks 80m south. 80m 80m Distance = 80m + 80m Distance = 160m Distance Distance is a Scalar quantity So we just need to add the values! Her final distance travelled is 160m

5. 80m 80m Displacement = +80m - 80m Displacement = 0m Displacement N E S W SW NW NE SE +y -y +x -x Displacement is a Vector quantity So we need to use direction too Her final displacement is 0m She is back where she started! Peach goes for a walk round a park, first walking north for 80m, then turns around and walks 80m south.

6. Distance vs Displacement Peach goes for another walk round a park, first walking north for 80m, then turns around and only walks 50m south (because she’s tired). What final distance has she travelled? What is her final displacement?

7. Peach goes for another walk round a park, first walking north for 80m, then turns around and only walks 50m south (because she’s tired). 80m 50m Distance = 80m + 50m Distance = 130m Distance Distance is a Scalar quantity So we just need to add the values! Her final distance travelled is 130m

8. 80m 50m Displacement = +80m - 50m Displacement = 30m Displacement N E S W SW NW NE SE +y -y +x -x Displacement is a Vector quantity So we need to use direction too Her final displacement is 30m Peach goes for another walk round a park, first walking north for 80m, then turns around and only walks 50m south (because she’s tired). (30m in a North Direction) 30m North

9. Distance vs Displacement Peach goes for yet another walk. First she walks north for 40m, then turns right and walks east for 30m. What final distance has she travelled? What is her final displacement?

10. Peach goes for yet another walk. First she walks north for 40m, then turns right and walks east for 30m. 40m 30m Distance = 40m + 30m Distance = 70m Distance Distance is a Scalar quantity So we just need to add the values! Her final distance travelled is 70m

11. 40m 30m Displacement 2 = 40 2 + 30 2 Displacement 2 = 2500 Displacement N E S W SW NW NE SE +y -y +x -x How can we find the Displacement? Her final displacement is 50m Peach goes for yet another walk. First she walks north for 40m, then turns right and walks east for 30m. But in what direction? 50m Displacement = 50m a 2 + b 2 = c 2 We need to use Pythagoras!

12. 40m 30m Displacement N E S W SW NW NE SE +y -y +x -x How can we find the Angle? Peach goes for yet another walk. First she walks north for 40m, then turns right and walks east for 30m. 50m We need to use S.O.H.C.A.H.T.O.A θ sin( θ ) = opposite hypotenuse θ = 37° sin -1 (0. 6) cos( θ ) = adjacent hypotenuse tan( θ ) = opposite adjacent Let’s use = 30 50 = 0.6 θ = 37° Her displacement is 50m at an angle of 37°

13. A trickier example A man walks round a park, first walking north for 80m, then turning right and walks for 50m. He turns right again, and after 10m takes a left turn and continues for 70m.

14. 80m 50m 10m 70m A man walks round a park, first walking north for 80m, then turning right and walks for 50m. He turns right again, and after 10m takes a left turn and continues for 70m.

15. A man walks round a park, first walking north for 80m, then turning right and walks for 50m. He turns right again, and after 10m takes a left turn and continues for 70m. 50m 10m 70m Distance = 210m 80m Displacement + 50m + 10m + 70m 80 m = 120m Horizontal = 50 m + 70m Split into horizontal and vertical Vertical = 80m - 10m = 70m 120m 70m a 2 + b 2 = c 2 = Displacement 2 = 120 2 + 70 2 Displacement 2 = 19,300 Displacement = 139m 139m

16. A man walks round a park, first walking north for 80m, then turning right and walks for 50m. He turns right again, and after 10m takes a left turn and continues for 70m. 50m 10m 70m 80m 139m 120m 70m Now to find the angle θ sin( θ ) = opposite hypotenuse 70 139 0.5036 θ = 30° 30° sin -1 (0.5036) His final displacement is 139m at an angle of 60° (from North) 60° But what about from North?

17. Some for you to try A car drives 35km North and then 60km East. What distance does it travel? What is its final displacement?

18. A car drives 35km North and then 60km East. What distance does it travel? What is its final displacement? 60km Distance = 95km 60km 69km 35km 35km Displacement = 69km Angle = 30 ° 30 ° Angle = 60 ° 60 °

19. Some for you to try Peach goes for a run. First she runs 60m North then 60m East then 40m South and finally 30m East.

20. Peach goes for a run. First she runs 60m North then 60m East then 40m South and finally 30m East. 60m 40m 30m Distance = 190m 30m 36m 60m 20m Displacement = 36m Angle = 34 ° 34 ° Angle = 56 ° 56 °

21. Some for you to try A man goes for a walk. He walks 40m North, 20m East, another 30m North, another 40m East. He then heads South for 50m

22. A man goes for a walk. He walks 40m North, 20m East, another 30m North, another 40m East. He then heads South for 50m 20m 50m Distance = 190m 60m 63m 40m 20m Displacement = 63m Angle = 18 ° 18 ° Angle = 72 ° 72 ° 30m 40m

23. Some for you to try A hippo walks 120m East and then runs 60m South. He then walks 20m West

24. A hippo walks 120m East and then runs 60m South. He then walks 20m West 120m 60m 20m Distance = 200m 100m 117m 60m Displacement = 117m Angle = 59 ° 59 °