pmt notes

• Vector


  Quantity with both magnitude and direction
• Scalar


  Quantity with only magnitude
• Examples of scalars

  • Speed
  • Distance
  • Time
  • Energy
  • Mass
• Examples of vectors

  • Velocity
  • Displacement
  • Acceleration
  • Force
  • Momentum
• Scalars cannot be negative, but vectors can be, as a certain direction is positive
• Displacement is 0 at the height of a cliff, above the cliff the ball has positive displacement, and below the clifftop the ball has negative displacement
• Speed


  Velocity when given a direction
• A car travelling round a roundabout at constant speed has a constantly changing velocity, so it is accelerating
• Vectors

  Can be represented by arrows, with their size/length representing the vector magnitude
• Types of forces

  • Non-contact (electrostatic, gravitational attraction)
  • Contact (normal contact force, friction)
• Gravitational field

  All matter has a gravitational field, and attracts all other matter. The larger the mass, the stronger the field, the greater the attraction
• Weight

  The force exerted on a mass by the gravitational field, in Newtons. Weight = mass x gravitational field strength
• On Earth, the gravitational field strength, g, is 9.8
• The acceleration in free fall is due to gravity, and is the same as g, i.e. 10 m/s^2
• The weight of an object is considered to act at the object's centre of mass
• Resultant force

  A single force representing the sum of all the forces acting on an object
• Skydiver example

  1. Initially, only weight acts

  2. As he falls, air resistance increases, so resultant force decreases

  3. Eventually air resistance equals weight, so resultant force is 0 and he reaches terminal velocity
• Free body diagram


  Shows the forces (and their directions) acting on an object
• Resolving forces


  A force F at angle θ to the ground can be resolved parallel and perpendicular to the ground using Pythagoras' Theorem
• Work

  Work Done = Force x Distance
• One joule of work is done when a force of one newton causes a displacement of one metre
• Work done against frictional forces causes a rise in temperature of the object
• Deformation


  Changing the shape of an object
• Elastic deformation


  The object returns to its original shape when the load has been removed
• Plastic deformation


  The object does not return to its original shape when the load has been removed
• Hooke's Law


  The extension of an elastic object is directly proportional to the force applied, provided the limit of proportionality is not exceeded
• Force-extension graph

  • Linear line in elastic region following Hooke's Law, gradient is spring constant k
  • Non-linear line in plastic region not following Hooke's Law
• Work done on a spring


  Work Done = 1/2 kx^2, where k is the spring constant and x is the extension
• Moment of a force


  Moment = Force x Perpendicular distance from pivot to line of force
• Equilibrium is when the sum of anticlockwise moments equals the sum of clockwise moments
• Gears

  • Can change speed, force or direction by rotation
  • If connected to a smaller gear, the second gear will turn faster but with less force, in opposite direction
  • If connected to a larger gear, the second gear will turn slower but with more force, in opposite direction
• Pressure


  Pressure = Force / Area
• Pressure in a fluid


  Pressure in a liquid varies with depth and density, leading to an upwards buoyancy force
• The atmosphere gets less dense with increasing altitude
• The weight of the air causes the atmospheric pressure
• Upthrust

  A partially (or totally) submerged object experiences a greater pressure on the bottom surface than on the top surface, creating a resultant force upwards
• Earth's Atmosphere

  • A thin layer (relative to size of the earth) of air around the Earth
  • The atmosphere gets less dense with increasing altitude
• The atmosphere is a thin layer (relative to the size of the Earth) of air round the Earth. The atmosphere gets less dense with increasing altitude.
• Idealised Assumptions, for a simple model of the atmosphere


  • Isothermal, so it is all at the same temperature
  • Transparent to solar radiation
  • Opaque to terrestrial radiation
• Distance

  How far an object moves, does not involve direction, a scalar quantity