Vectors and Scalars

1. Vectors and Scalars • Scalars have magnitude only e.g. mass, speed, distance • Vectors have magnitude and direction e.g. force of 10 N to the left.. Velocity, displacement, weight ,acceleration…….

2. Adding Vectors • Vectors are represented by arrows : • 10 N to left or - 10 N • 20 N to the right or + 20 N • Resultant is +20 + - 10 = +10 N

3. North Adding Vectors • Add the vectors : 6 N north plus 8 N to the East. • Draw a Vector diagram , add the vectors Head to Tail. Use Pythagoreus or scale diagram to calculate resultant. Use trig or measure angle ø 10 N on a bearing of 0530 ø

4. Velocity and Displacement • Displacement ( vector ) : Distance as the crow flies from start to finish plus the direction

5. North Velocity and Displacement • A student walks 3 km north then 3 km west. Distance travelled = 3 + 3 + 6 km. Displacement is resultant of vector addition = 3150 from north to finishing point

6. Acceleration • Rate of change of velocity : Vector

7. Graphs • Slope of velocity time graph is acceleration • Area under velocity time graph is displacement • Slope of displacement time equals velocity • Velocity / acceleration / displacement downwards normally negative

8. Equations of Motion

9. Projectile Motion • Horizontal and vertical motion • Ignore spin and friction : horizontal velocity remains constant • Vertical velocity subject to gravitational force

10. Projectile Motion • Consider vertical motion a v Ball falling vertically. Accelerates at - 9.8 ms-2 t t

11. Projectile Motion • Consider horizontal motion v Ball travels at constant horizontal velocity t

12. Projectile Motion • Combine both motions : Horizontal velocity remains constant BUT the vertical velocity increases at a rate of 9.8 m s-2

13. Forces • Force is a push or a pull • Forces change the speed, shape or direction of an object • Unbalanced forces cause vehicle to accelerate ( velocity changes ) • I N causes a vehicle of mass 1 kg to accelerate at 1 m s-2

14. Newton’s Second Law of Motion • Fun = m . A Reaction force of floor on man Fr Fg > Fr therefore unbalanced force, Fun acts downwards Man in lift ! Weight Fg

15. Newton’s Second Law of Motion • Fun = m . A Reaction force of floor on man Fr Fr > Fgtherefore unbalanced force, Fun acts upwards Man in lift ! Weight Fg

16. Newton’s Second Law of Motion • Vehicles accelerate to right at 2 m s-2 1000 kg 5000 kg Force transmitted through towbar accelerates car at 2 m s-2 = m. a = 1000 x 2 = 2 000 N Total force applied accelerates tractor and car at 2 m s-2 = m. a = 6000 x 2 = 12 000 N

17. Conservation of Energy • Ep to Ek Work done against friction

18. Momentum • Product of mass and velocity • Vector • units kg ms-1 or N s • p = m.v

19. Momentum • Momentum is conserved provided NO external forces act • Elastic collision Ek is conserved • Inelastic collision Ek is ‘lost’ • Explosion Ek is ‘gained’

20. Impulse This is called the impulse of the force and it equals the change in momentum

21. Impulse • In collisions the bigger the collision time the smaller the force acting and the less damaged caused. Crumple zones on cars increase the collision time. Force Area under graph = change in momentum time

22. Density • Mass per unit volume • 1 g per cm3 1 kg per m3

23. Density • Densities of solids and liquids are approx 1000 times greater than gases. • Particle spacing in a gas is approx 10 times greater than in a solid • If a solid is made up of millions of cubes then each cube would contain 1000 particles ( 10 x 10 x 10 ) but a gas would only contain 1 particle per cube hence density of solid is c.a. 1000 times that of gas

24. Pressure Pressure = Force Area (1 N/m2 = 1 Pascal )

25. Pressure in Liquids Pressure in liquids acts in all directions

26. Greater the depth the greater the weight of liquid Greater the density of liquid the greater the weight acting at the same height Greater g greater the weight P = ρ.g.h

27. Pressure on bottom of sub > pressure on top • Pressure = force acting per unit area • Hence force acting on bottom surface > force acting on top • Unbalanced force acts upwards : called Upthrust or Buoyancy Force Buoyancy F upthrust F gravity

28. Kinetic Theory of Gases • Matter is made of small particles • Particles are different sizes for different elements • Particles cannot be compressed • Particles are always moving • At same temp ALL particles have the same kinetic energy • ALL collisions are ELASTIC

29. Kinetic Theory of Gases • Gas exerts a pressure because the particles hit wall of container ( pressure = force per unit area ) • Pressure depends on • number of collisions per second • force acting per collision ( actually change in momentum )

30. Kinetic Theory of Gases • As Temp increases the Ek of particles increases, they hit the wall with a bigger force and more frequently hence pressure increases • As volume decreases the number of collisions per second increases and the average force acting increases : pressure increases

31. Absolute Zero • At 0 Kelvin , particles of a gas would have NO kinetic energy and would be stationary. This is the lowest temperature in the universe. • 0 K = - 2730C 0 0C = 273 K • A temp difference of 1 K equals a temp difference of 1 0C

32. Gas Laws

33. Pressure Volume • At constant Temperature

34. Pressure Temperature • At Constant Volume

35. Volume Temperature • At Constant Pressure