FORCES

• Vector


  Quantity with both magnitude and direction
• Scalar


  Quantity with only magnitude
• Examples of scalars


  • Speed
  • Distance
  • Time
  • Mass
  • Energy

  
• 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 cliff top 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, therefore it is accelerating
• Vectors


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


  • Non-contact - physically separated (electrostatic, gravitational attraction)
  • Contact - physically touching (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. 10m/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
• 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
• Types of deformation


  • Elastic (object returns to original shape)
  • Plastic or inelastically deformed(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 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
• Distance


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

  
• Displacement


  Includes both the distance an object moves, measured in a straight line from the start point to the finish point and the direction of that straight line, a vector quantity

  
• Speed


  Does not involve direction, a scalar quantity
• Velocity


  Speed in a given direction, a vector quantity

  
• The speed of a moving object is rarely constant

  
• Typical Speeds


  • Wind: 5 − 7𝑚𝑚𝑠𝑠−1
  • Sound: 330𝑚𝑚𝑠𝑠−1
  • Walking: ~ 1.5𝑚𝑚𝑠𝑠−1
  • Running: ~3𝑚𝑚𝑠𝑠−1
  • Cycling: ~6𝑚𝑚𝑠𝑠−1
  • Bus: 14km/h
  • Train: 125miles/h
  • Plane: 900km/h
• Distance measured in mm, cm, m and km and time measured in ms, s, mins and hours. Depending on lengths involved, use appropriate units

  
• Displacement-Time Graphs


  • Gradient is velocity
  • Sharper gradient means faster speed
  • Negative gradient is returning back to starting point
  • Horizontal line means stationary
  • 0 Distance means that it is back to starting point
  • Area under line = nothing
  • Curved Line means that the velocity is changing (acceleration)

  
• Velocity-Time Graphs


  • Gradient is acceleration
  • Sharper gradient means greater acceleration
  • Negative gradient is deceleration
  • Horizontal line means constant speed
  • 0 Velocity means that it is stationary
  • Area under line = distance travelled
  • Curved Line means that the acceleration is changing

  
• Newton's First Law


  An object has a constant velocity unless acted on by a resultant force. If a resultant force acts on the object, it will accelerate. If no resultant force acts on the object, and the object is stationary, it will remain stationary, and the object is moving, it will continue to move at the same velocity.
• Inertia


  The tendency for objects to continue in uniform velocity (or stay at rest)
• Newton's Third Law


  Whenever two objects interact, the forces they exert on each other are equal and opposite.
• Vehicle Stopping Distances


  After seeing a hazard, there is a thinking distance before you react, and then a braking distance as the car slows down and stops. The total stopping distance is the sum of these.

  
• Factors affecting Thinking Distance

  • Speed
  • Reaction time
  • Concentration
  • Tiredness
  • Distractions
  • Influence of drugs/alcohol