Forces

• 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
• Speed


  Velocity when given a direction

  
• A car travelling round a roundabout at constant speed

  Its velocity is constantly changing, therefore 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
• 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
• 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


  Work Done = Force × Distance

  
• Work done is 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
• Springs


  To stretch, bend or compress an object, more than one force has to be applied
• 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
• Moments and rotation


  • If a force is applied along a line passing through the pivot, the object does not rotate
  • If there is a distance between the pivot and the line of action of the force, the object rotates about the pivot, in the direction of the force applied
• Equilibrium


  Sum of anticlockwise moments = sum of clockwise moments
• 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