1 - Forces and Motion (copy)

Speed

Speed

How fast you’re going with no regard to direction

Velocity

How fast you’re going, but also with the specified direction

Equation: Avg. speed, Distance, Time

v = s/t

Average speed = Distance moved/Time taken

[m/s] = [m]/[s]

Acceleration

How quickly velocity is changing

Equation: Acceleration, Change in velocity, Time

a = (v-u)/t

Acceleration = (Final velocity - initial velocity) / Time taken

[m/s²] = ([m/s]-[m/s]) / s

Equation: Final speed, Initial speed, Acceleration, Distance

v² = u² + 2as

(Final velocity)² = (Initial velocity)² + (2 x Acceleration x Distance)

[m/s]² = [m/s]² + 2 x [m/s²] x [m]

Distance-Time Graphs

• Gradient at any point = speed of object

• Flat section = stopped

• Steeper graph = faster speed

• Curve = acceleration

• Curve getting steeper = speeding up (increasing gradient)

• Levelling off curve = slowing down (decreasing gradient)

Velocity-Time graphs

• Gradient = acceleration

• Flat section = steady speed

• Steeper graph = greater acceleration/deceleration

• Uphill section = acceleration

• Downhill section = deceleration

• Area under any part of graph = distance travelled in that time interval

• Curve = changing acceleration

Investigating motion

• Set up apparatus as in diagram, holding car still just before light gate

• Mark a line on ramp to make sure car starts from same point each time

• Measure distance between each light gate - need this to find car’s average speed

• Let go of car just before light gate so it starts to roll down slope

• Light gates should be connected to computer
  When car passes through each light gate, a beam of light is broken and time is recorded by software

• Repeat experiment several times to get average time taken for car to reach each light gate

• Use these times and distances to find average speed of car on ramp and average speed of car on runway - divide distance between light gates by average time taken for car to travel between gates

Gravity

Gravity attracts all masses, but only noticeable when one of the masses is very big

This has three effects:

• On surface of planet, makes things accelerate towards ground

• Gives everything weight

• Keeps planets, moons, satellites in orbit

Weight vs Mass

• Mass is amount of ‘stuff’ in object - same value anywhere in universe

• Weight is caused by pull of gravity

• Object has same mass on Earth and Moon - but different weight

  1kg mass weighs less on Moon (1.6N) than Earth (10N) because force of gravity pulling on it is less

• Weight is force measured in newtons
  Mass is not a force

Equation: Weight, Mass, Gravity

W = mg

Weight = Mass x Gravitational field strength

[N] = [kg] / [N/kg]

Force

A push or pull

Vector quantity with size + direction

Gravity/Weight

When close to a planet this acts straight downwards

Reaction force

Acts perpendicular to surface and away from it (if surface is horizontal, reaction force acts straight upwards)

Electrostatic force

Between two charged objects

Direction depends on type of charge (like charges repel, opposites attract)

Thrust

e.g. push or pull due to engine/rocket speeding something up

Drag/air resistance/friction

Slows the object down

Lift

e.g. due to aeroplane wing

Tension

in a rope or cable

Drawing the forces acting on a body

• Many forces act on everything, but usually not noticed because they balance out

• Any object with weight feels reaction force back from the surface it’s on
  Otherwise it would just keep falling

• When an object moves in fluid (air, water etc.), it feels drag in opposite direction to motion

Friction

If an object has no force propelling it, it always slows down and stops due to friction (force that opposes motion)

To travel at steady speed, objects need driving force to counteract friction

Static friction

Friction between solid surfaces which are gripping

Can be reduced by putting lubricant (oil/grease) between surfaces

Sliding friction

Can be reduced by putting lubricant (oil/grease) between surfaces

Friction between solids often causes wear of two surfaces in contact

Drag

Keeping shape of object streamlined (sports car, boat hull) reduces drag in fluids
Lorries + caravans have ‘deflectors’ to make them more streamlines + reduce drag

Roof boxes on cars spoil their streamlined shape so slow them down
For a given thrust, higher drag = lower top speed of car

Opposite extreme is parachute (need as high drag as possible)

In fluid, friction always increases as speed increases

Newton’s First Law of Motion

As long as forces on object are balanced, it will stay still, or if already moving, it carries on at same velocity

Newton’s Second Law of Motion

If there is unbalanced force, object accelerates in that direction

Equation: Force, Mass, Acceleration

F = ma

Force = Mass x Acceleration

[N] = [kg] x [m/s²]

Newton’s Third Law of Motion

If object A exerts force on object B, then object B exerts an equal and opposite force on object A

e.g. swimming, push back against water with arms + legs, and water pushes you forwards with equal-sized force in opposite direction

Vector quantities

Have size and direction

e.g. force, velocity, acceleration, momentum

Scalar quantities

Only size, no direction

e.g. mass, temperature, time, length

Resultant force

When multiple forces act on object, you can find resultant force acting on object by adding/subtracting - need to know size of all different forces acting on object and their direction

Terminal velocity

Frictional forces increase with speed - but only up to a certain point

• When object first starts to fall, it has much more force accelerating it than resistance slowing it down

• As velocity increases, resistance builds up

• Resistance force gradually reduces acceleration until resistance force is equal to accelerating force
  At this point, object can’t accelerate any more, it has reached terminal velocity

Factors affect terminal velocity

• Accelerating force acting on all falling objects is gravity
  All objects would accelerate at the same rate without air resistance

• Air resistance causes things to fall at diff speeds, and terminal velocity of object is determined by its drag compared to its weight
  Drag depends on shape and area

Stopping distance

Distance covered in the time between driver first spotting a hazard and the car coming to complete stop

Stopping Distance = Thinking Distance + Braking Distance

Factors affecting thinking distance

• Speed - faster speed = further distance before stopping

• Reaction time - affected by tiredness, drugs, alcohol and old age

Factors affecting braking distance

• Speed - faster speed = further distance before stopping

• Mass of vehicle - larger mass = longer time to stop

• Quality of brakes - worn/faulty brakes increase braking distance

• Grip - depends on road surface, weather conditions (e.g. icy), tyres

Equation: Moment, Force, Perp distance from pivot

M = Fd

Moment = Force x perpendicular Distance from pivot

[Nm] = [N] x [m]

Centre of graivty

The point at which the weight of an object acts

A freely suspended object swings until centre of gravity is vertically below point of suspension

Finding centre of gravity

• Suspend shape and a plumb line from same point, and wait until they stop moving

• Draw line along plumb line

• Repeat but suspend shape from different pivot point

• Centre of gravity is where two lines cross

Principle of moments

If object is balanced:

Total Anticlockwise moments = Total Clockwise moments

Upwards forces with heavy object on light beam

• If a light rod (no weight) is being supported at both ends, upwards force provided by each support isn’t always the same

• If heavy object is placed on rod, support closest to object provides larger force

Equation: Pressure difference

p = h x ρ x g

Pressure difference = Height x Density x Gravitational field strength

[Pa] = [m] x [kg/m³]

Investigating how extension varies with applied force

• Set up apparatus as in diagram

• Measure length of spring using mm ruler when no load is applied
  Ensure ruler is vertical and measure spring at eye level (this is spring’s natural length)

• Add one mass at a time and allow spring to come to rest, then measure new length of spring
  Extension = change in length from original length

  Repeat process until you have enough measurements

• Once done, repeat experiment and calculate average value for length of spring for each applied weight

• Repat experiment using metal wire or rubber band instead of spring

Hooke’s Law

Extension of stretched wire is proportional to load/force

Metal spring (or other object) also obeys Hooke’s law if a pair of opposite forces are applied to each end

Force-extension graph

There’s a limit to force you can apply for Hooke’s law to stay true

First part of graph shows Hooke’s law being obeyed - straight-line relationship between force and extension

When force becomes great enough, graph starts to curve

If you increase force past elastic limit (marked E on graph), material is permanently stretched

When all force is removed, material will be longer than at the start

Elastic behaviour

Ability of material to recover to original shape after forces causing deformation have been removed

Equation: Momentum, Mass and Velocity

p = mv

Momentum = Mass x Velocity

[kg m/s] = [kg] x [m/s]

Conservation of momentum

Momentum Before = Momentum After

Equation: Force, Change in momentum, Time

F = (mv-mu) / t

Force = Change in momentum / Time

[N] = [kg m/s] / [s]

Example of Force from change in momentum

Safety features

• Larger force = faster change of momentum

• Similarly, if momentum changes very quickly (like in car crash), forces on body will be very large + more likely to cause injury

• So cars are designed to slow people down over longer time when they crash → smaller force → less severe injury

Crumple zones

Crumple on impact, increasing time taken for car to stop

Seat belts

Stretch slightly, increasing time taken for wearer to stop, reducing forces acting on chest

Air bags

Slow you down more gradually