Vectors and Scalars Scalars have magnitude only e

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Vectors and Scalars • Scalars have magnitude only e. g. mass, speed, distance •

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…….

Adding Vectors • Vectors are represented by arrows : • 10 N to left

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

North Adding Vectors • Add the vectors : 6 N north plus 8 N

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 ø 10 N on a bearing of 0530

Velocity and Displacement • Displacement ( vector ) : Distance as the crow flies

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

North Velocity and Displacement • A student walks 3 km north then 3 km

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

Acceleration • Rate of change of velocity : Vector

Acceleration • Rate of change of velocity : Vector

Graphs • Slope of velocity time graph is acceleration • Area under velocity time

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

Equations of Motion

Equations of Motion

Projectile Motion • Horizontal and vertical motion • Ignore spin and friction : horizontal

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

Projectile Motion • Consider vertical motion a v Ball falling vertically. Accelerates at -

Projectile Motion • Consider vertical motion a v Ball falling vertically. Accelerates at - 9. 8 ms-2 t t

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

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

Projectile Motion • Combine both motions : Horizontal velocity remains constant BUT the vertical

Projectile Motion • Combine both motions : Horizontal velocity remains constant BUT the vertical velocity increases at a rate of 9. 8 m s-2

Forces • Force is a push or a pull • Forces change the speed,

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

Newton’s Second Law of Motion • Fun = m. A Man in lift !

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

Newton’s Second Law of Motion • Fun = m. A Man in lift !

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

Newton’s Second Law of Motion • Vehicles accelerate to right at 2 m s-2

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

Conservation of Energy • Ep to Ek Work done against friction

Conservation of Energy • Ep to Ek Work done against friction

Momentum • • Product of mass and velocity Vector units kg ms-1 or N

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

Momentum • Momentum is conserved provided NO external forces act • Elastic collision Ek

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

Impulse This is called the impulse of the force and it equals the change

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

Impulse • In collisions the bigger the collision time the smaller the force acting

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

Density • Mass per unit volume • 1 g per cm 3 1 kg

Density • Mass per unit volume • 1 g per cm 3 1 kg per m 3

Density • Densities of solids and liquids are approx 1000 times greater than gases.

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 ) but a gas would only contain 1 particle per cube hence density of solid is c. a. 1000 times that of gas

Pressure = Force Area (1 N/m 2 = 1 Pascal )

Pressure = Force Area (1 N/m 2 = 1 Pascal )

Pressure in Liquids Pressure in liquids acts in all directions

Pressure in Liquids Pressure in liquids acts in all directions

Greater the depth the greater the weight of liquid Greater the density of liquid

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

Buoyancy F upthrust F gravity • Pressure on bottom of sub > pressure on

Buoyancy F upthrust F gravity • 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

Kinetic Theory of Gases • Matter is made of small particles • Particles are

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

Kinetic Theory of Gases • Gas exerts a pressure because the particles hit wall

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 )

Kinetic Theory of Gases • As Temp increases the Ek of particles increases, they

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

Absolute Zero • At 0 Kelvin , particles of a gas would have NO

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 = - 2730 C 0 0 C = 273 K • A temp difference of 1 K equals a temp difference of 1 0 C

Gas Laws

Gas Laws

Pressure Volume • At constant Temperature

Pressure Volume • At constant Temperature

Pressure Temperature • At Constant Volume

Pressure Temperature • At Constant Volume

Volume Temperature • At Constant Pressure

Volume Temperature • At Constant Pressure