 # 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,

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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 or - 10 N 20 N to the right or + 20 N Resultant is +20 + - 10 = +10 N

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 North ø 10 N on a bearing of 053 0

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

Velocity and Displacement A student walks 3 km north then 3 km west. North Distance travelled = 3 + 3 + 6 km. Displacement is resultant of vector addition = 315 0 from north to finishing point

Acceleration Rate of change of velocity : Vector

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

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 v t Ball falling vertically. Accelerates at - 9.8 ms -2 a t

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

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, 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 F un = m. A Man in lift ! Weight F g Reaction force of floor on man F r F g > F r therefore unbalanced force, F un acts downwards

Newton’s Second Law of Motion F un = m. A Man in lift ! Weight F g Reaction force of floor on man F r F r > F g therefore unbalanced force, F un acts upwards

Newton’s Second Law of Motion Vehicles accelerate to right at 2 m s -2 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 1000 kg 5000 kg

Conservation of Energy E p to E k Work done against friction

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 E k is conserved Inelastic collision E k is ‘lost’ Explosion E k is ‘gained’

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 and the less damaged caused. Crumple zones on cars increase the collision time. Force time Area under graph = change in momentum

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. 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

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

Pressure in Liquids Pressure in liquids acts in all directions

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 gravity F upthrust 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 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 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 E k 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 kinetic energy and would be stationary. This is the lowest temperature in the universe. 0 K = - 273 0 C 0 0 C = 273 K A temp difference of 1 K equals a temp difference of 1 0 C

Gas Laws

Pressure Volume At constant Temperature

Pressure Temperature At Constant Volume

Volume Temperature At Constant Pressure

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