P4 -- Explaining Motion

Revision Cards for P4 Module of OCR 21st Century Physics A Unit 2.

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• Created by: Alex
• Created on: 07-05-10 21:26

SPEED

• Speed = Distance/Time
• EXAMPLE: A cat skulks 20 metres in 40 seconds. Find: a) its speed, b) how long it will take to skulk 75m.
• a) speed = 20/40 = 0.5ms^-1
• b) time = 75m/0.5ms^-1 = 150s
• Pretty rare in real life for an object to stay at exactly the same speed for a long period of time.
• Usually want to find the average speed if the speed varies constantly for a long period of time.
• Speed cameras take an instantaneous speed of a car: Evenly spaced lines are printed on the road and the speed camera measures the time in which the car travels over the lines.
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SPEED AND VELOCITY

• On a distance time graph:
• Gradient = speed
• Flat sections = stationary
• Steep gradient = faster speed
• 'Downhill' = travelling in opposite direction
• Curves = Acceleration/deceleration
• Steepening curve = speeding up
• Levelling off curve = slowing down
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SPEED AND VELOCITY (Cont.)

• Gradient = Δy/Δx
• Always use standard units: m, kg, l etc.
• Distances can be positive or negative.
• 0 is always start point, +ve = one direction, --ve = other direction.
• Speed is the gradient of a distance/time graph.
• Speed = how fast something is going, it does not have a direction .
• Velociy describes the speed and direction of an object.
• Speed = scalar quantity (mass, temperature, time, length).
• Velocity = vector quantity (force, acceleration, momentum).
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VELOCITY

• Velocity can be positive or negative.
• Travel one direction at 20ms^-1, turn around and travel in the opposite direction at -20ms^-1.
• If two objects heading in opposite directions, one can be said to have positive veolcity while the other have a negative velocity.
• On a velocity/time graph:
• Gradient = acceleration
• Flat sections = steady speed
• Steeper sections = greater acceleration/deceleration
• 'Uphill' = acceleration
• 'Downhill' = deceleration.
• Area under any section (or all of) graph is equal to the distance travelled in that time interval.
• Curve = changing accelerations
• Tachographs plot speed/time when direction isn't important.
• Tachographs are found in lorries to tell managers how long a driver has gone without a break or if they have been speeding.
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FORCES AND FRICTION

• Forces occur when two objects interact
• When an object exerts a force on another subject, it interacts with an opposing force: an 'interaction pair'.
• If you push against a wall, the wall will push back just as hard.
• As soon as you stop pushingthe wall, so does the wall.
• If there was no opposing force, you and the wall would fall down.

• If you exert a force of 10N, the wall's results force will be 10N.
• NEWTON'S THIRD LAW!: If object A exerts a force on object B, then object B exerts anequal and opposite force on object A.

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FORCES AND FRICTION (Cont.)

• Moving object usually experience friction.
• When an object is moving relative to another, both objects experience a force in the direction that opposes the movement -- FRICTION!
• Friction between solid surfaces which are gripping (static).
• The Earth's tectonic plates trying to move but friction is so strong they stay put.
• Friction between solid surfaces which are sliding past each other.
• Eg. moving bits of a car.
• Reduce friction by using lubricant.
• Resistance or "drag" from fluids (liquids or gases).
• An object has to force its way past the molecules of the fluid.
• Big squarish objects carry more (air) resistance than a streamlines object.
• Friction only occurs if an object is moving through a fluid.
• Space has no fluids (as it's a vacuum) therefore there is no friction is space.
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FORCES AND MOTION

• Arrows show the size and direction of forces.
• Length of arrow shows the size of force; direction shows the direction of force.
• If opposite pairs (same direction AND size), the forces are balanced.
• If an object is resting on a surface its weight is pushing down (gravity), causing an equal reaction forcepushing up from the surface; the two forces are the same size so the arrows are the same size.
• If an object is moving with a steady speed the forces must be in balance. Just because something is moving doesn't mean there is an overall force acting on it -- unless it's changing speed or direction, the overall force is zero.
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FORCES AND MOTION (Cont.)

• The resultant force is the overall force acting on an object.
• This is the force when you take into account all individual forces and direction.
• Forces decides motion of the object (accelerate, decelerate or stay at a steady speed).
• 'Accelerate' means to change velocity. As velocity has speed AND direction accelerating doesn't always mean changing speed -- it could be changing direction, even if you stay at a steady speed.
• If there is a resultant force, its speed or direction (or both) changes.
• Unless there is an overall force on something it won't accelerate.
• Acceleration = unbalanced forces.
• If a larger force is exerted forward than backwards (DRAG!), it will not accelerate.
• If there is a bigger thrust arrow (forward) than the drag arrow (backward), there is a resultant force in the forward direction.
• The bigger the resultant force, the greater the acceleration.
• There are still forces in the other directions.
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MOMENTUM

• Momentum = mass x velocity (kg.ms^-1 = kg x ms^-1).
• Momentum is how hard it would be to stop an object moving.
• Heavy, fast objects would have a larger momentum than light, slow objects.
• Momentum is a vector quantity -- it has size and direction.
• A resultant force of zero means that a stationary object will stay still, if an object was moving it would stay at the same speed in the same direction.
• If the resultant force of an object changes, its momentum changes in the direction of the force.
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MOMENTUM (Cont.)

• Change of momentum (kg.ms^-1) = Resultant force (N) X Time for which the force acts (s).
• A resultant force causes a change of momentum.
• The change it causes depends on the size of the force and the time in which it acts for.
• EXAMPLE: A rock with mass 1kg is travelling through space at 15ms^-1. A comet hits the rock, giving it a resultant force of 2500N for 0.7 seconds. Calculate the rock's initial momentum, then calculate the change of momentum resulting from the impact of the comet.
• Momentum = mass X velocity. 1kg X 15ms^-1 = 15kg.ms^-1.
• Change of momentum = 2500N X 0.7s = 1750kg.ms^-1.
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MOMENTUM (Cont.)

• If somebody's momentum changes very quickly, the forces on the body will be very large and more likely to cause injury,
• Car safety reduces forces at change of momentum.
• You cannot affect the change of momentum in a collision. The average force of an object can be lowered by slowing the object down over a longer time period.
• Safety features increase collision time to reduce forces:
• CRUMPLE ZONES crumple to increase time for the car to stop,
• AIRBAGS slow the passenger down gradually.
• SEAT BELTS stretch (slightly) increasing time to stop and reducing forces on chest.
• HELMETS provide padding that increase the time for the head to stop if it hits something hard.
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WORK

• "Work Done" is "Energy Transferred".
• When a force moves an object, energy is transferred and work is done.
• Whether the energy is transferred "usefully" or is "wasted", you can still say that work is done.
• Change in energy (J) = Work done (J).
• Work Done (J) = Force (N) X Distance (m).
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KINETIC ENERGY

• Kinetic energy = energy of movement,
• Greater the mass and faster it is going, the bigger the kinetic energy.
• Kinetic Energy (J) = 1/2 X mass (kg) X velocity^2 ((ms^-1)^2).
• EXAMPLE: A car of mass 2450kg is travelling at 38ms^-1. Calculate the kinetic energy.
• KE = mv^-2/2 = 2450kg X 38(ms^-1)^2/2 = 1768900J.
• To increase kinetic energy, you have to increase its speed (you must apply a force).
• If you apply a force, you are doing work, If object A is causing object B's velocity to increase by exerting a force on it, then it is doing work and increasing object B's kinetic energy.
• If you do work on an object but it doesn't accelerate, you have not increased its kinetic energy.
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KINETIC ENERGY (Cont.)

• Increase in kinetic energy = work done.
• Energy is always conserved (it cannot be created or destroyed), it gets transferred from one form of energy to another.
• Some energy that gets transformed is wasted as heat due to friction and air resistance.
• 30J of work hitting a stationary object will be a bit less because of the heat created by air resistance.
• The increase in an object's kinetic energy is normally a bit less that the amount of work done on it.
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GRAVITATIONAL POTENTIAL ENERGY

• Gravitational potential energy is basically 'height energy'.
• Gravitational potential energy is the energy stored in an object when you raise it to a height against the force of gravity (a way of storing kinetic energy).
• The energy is only released when an object falls.
• Change in gravitational potential energy (J) = weight (N) X change in height (m).
• Falling objects convert gravitational potential energy into kinetic energy.
• The further an object falls, the faster it falls.
• Some gravitational potential energy is dissipated as heat due to air resistance.
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GRAVITATIONAL POTENTIAL ENERGY (Cont.)

• Kinetic energy gained = gravitational potential energy lost
• On a rollercoaster, if you ignore air resistance and friction, the kinetic energy that the carriages gain will be the same as the gravitational potential energy that is lost.
• EXAMPLE: The carriage on a rollercoaster has a weight of 5000N and the vertical height difference between point A and B is 20m. a) Ignoring friction and air resistance, how much kinetic energy is gained by the carriage moving from A to B. b) Assuming the rollercoaster was stationary at point A, calculate its speed at point B.
• a) Gain in kinetic energy = loss in gravitational potential energy. Weight X change in height = 5000N X 20m = 100000J.
• b) At B, it has 100000J of kinetic energy. As kinetic energy = 1/2 X mass (kg) X velocity^2 ((ms^-1)^2), 1/2 X mass (kg) X velocity^2 ((ms^-1)^2) = 100000J. velocity^2 = 100000 X 2/500kg = 400ms^-1. velocity = sqaure root of 400 = 20ms^-1.
• Rollercoasters constantly transfer energy from gravitational potential energy to kinetic energy and back again.
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