Forces and Motion

• Vector


  Quantity with both magnitude and direction
• Scalar


  Quantity with only magnitude
• Scalars cannot be negative, but vectors can be, as a certain direction is positive
• Examples of scalars and vectors

  • Speed (scalar)
  • Velocity (vector)
  • Distance (scalar)
  • Displacement (vector)
  • Time (scalar)
  • Acceleration (vector)
  • Force (vector)
  • Mass (scalar)
  • Momentum (vector)
  • Energy (scalar)
• Displacement is 0 at the height of a cliff, above the cliff the ball has positive displacement, and below the cliff top the ball has negative displacement
• In long answer questions, you may be able to decide where the "0" point of a vector may lie, for example you could set zero to be bottom of cliff, so the ball will never have negative displacement
• Speed is only velocity when given a direction


  Thrown 10m/s is its speed but thrown 10m/s at 30° above the horizontal is the velocity
• A car travelling round a roundabout at constant speed

  While its speed is constant, its direction is constantly changing – so its velocity is constantly changing therefore it is accelerating
• Vectors can be represented by arrows

  The 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
• Weight


  The force exerted on a mass by the gravitational field, in Newtons
• Weight is measured by a force meter (also known as calibrated spring-balance)
• On Earth, g = 9.8
• 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, the skydiver has no air resistance and the only force acting on him is weight

  2. As he falls, he accelerates, increasing his speed

  3. As air resistance increases, the resultant force from weight decreases

  4. So acceleration decreases, so he is not speeding up as quickly

  5. Eventually they are equal and balance, so there is no resultant force
• Free Body Diagrams show the forces (and their directions) acting on an object
• Resolving forces


  1. A force F at angle θ to the ground can be resolved parallel and perpendicular to the ground

  2. Using Pythagoras' Rule, the two components are calculated
• Work done


  When energy is transferred from the object doing the work to another form
• 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
• Types of deformation


  • Elastic (object returns to original shape)
  • Plastic (object does not return to original shape)
• 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 k
  • Non-linear line in plastic region not following Hooke's Law

  
• Moment of a force


  Force x perpendicular distance from pivot
• Equilibrium is when: sum of anticlockwise moments = 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
• The second gear will always turn in the opposite direction to the first gear
• Pressure


  Force per unit area
• Pressure produces a net force at right angles to any surface
• Buoyancy force


  The upwards force that counteracts the weight of a floating object, equal to the weight of the fluid displaced
• The atmosphere gets less dense with increasing altitude
• The weight of the air is the force which 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