Mechanics

• Scalar quantity


  Quantity with magnitude only
• Vector quantity


  Quantity with both magnitude and direction
• Examples of scalar quantities

  • speed
  • distance
  • power
  • energy
  • time
• Examples of vector quantities

  • velocity
  • displacement
  • momentum
  • moments
• Moment


  The force times the perpendicular distance from the pivot to the line of action of the force
• Moment


  • Measured in Newton-metre (Nm)
  • Sometimes called a torque
• Couple


  A pair of equal and opposite forces whose lines of action do not coincide
• Moment of a couple


  The force times the perpendicular distance between the lines of action of the forces
• Centre of mass


  The point through which the weight appears to act
• At the centre of mass, the moment due to the weight of the object is zero
• The centre of mass of a uniform regular solid is at its midpoint
• Equilibrium


  Resultant force = 0 and the resultant moment = 0
• Newton's First Law (N1L): An object will stay at rest or move with constant velocity unless acted on by a resultant force
• Newton's Second Law (N2L)

  F = ma
• Practical to investigate N2L

  1. Attach a string to a dynamics trolley and a weight

  2. Run the string over a pulley

  3. Attach a card to the trolley and make sure it passes through a light gate

  4. Use a datalogger and computer to work out the acceleration

  5. Draw a table of results

  6. Repeat for different weights

  7. Plot a graph of force (weight) against acceleration
• Terminal velocity

  The maximum speed reached by a falling object when the air resistance force equals the weight
• Independence of motion: Horizontal and vertical motion are independent of each other
• For an object fired on Earth (no air resistance): Horizontal velocity is constant, vertical velocity increases
• Elastic collision


  Kinetic energy is conserved
• Inelastic collision


  Kinetic energy is not conserved, some energy is transferred as heat or sound
• An explosion is always inelastic
• In an explosion, the momentum before the explosion will be zero, and the momentum after the explosion must also be zero
• Momentum


  A vector quantity, has magnitude and direction
• Newton's 2nd Law (N2L) revisited

  F = rate of change of momentum
• Speeding up during a race

  1. Small negative impulse

  2. Large positive impulse

  3. Total area positive

  4. Increase in momentum

  5. Accelerate
• Constant speed during a race

  1. No resultant impulse

  2. No change in momentum

  3. Constant speed, velocity
• Slowing down during a race

  1. Large negative impulse

  2. Small positive impulse

  3. Total area negative

  4. Decrease in momentum

  5. Decelerate
• Inelastic collision


  Kinetic energy is not conserved