Mechanics M18 - M23

• Work done = force x displacement moved in the direction of the force

  work done = area under force vs displacement graph
• Principle of conservation of energy


  Energy cannot be created or destroyed
• Gravitational energy


  Is the work done to raise an object through a height
• Kinetic energy


  Is the energy of an object due to its motion
• Work is …


  Is the energy transferred

  work done = Fscosθ
• GPE equation


  g = mgΔh
• KE equation 


  KE = 1/2 m v^2
• Power is …


  Is the rate of doing work(transferring energy)
• Power equation (2)


  P = W/Δt
• Work done per second equation


  WD = force x distance moved per second

  P = Fv
• examples of energy transfers


  -air resistance

  -friction of wheels against an incline surface - heat
• Newton’s first law 


  An object will remaat rest or in uniform motion unless acted on by a resultant force
• Newton’s second law


  The rate of change of momentum of an object is proportional to the resultant force applied to it
• F = ma

  F = (Δ(mv))/Δt = (mv - mu)/t

  F = ma is only for objects with constant mass
• Momentum equation

  P = mv
• what is impulse

  Impulse is the change of momentum

  FΔt = Δ(mv)
• Momentum is …

  Momentum is defined as the product of an objects mass and velocity

  -it is a vector in the same direction as velocity

  -unit Ns/kgms^-1
• What is the gradient of a momentum vs time graph

  Force
• What is the area under a momentum vs time graph

  Impulse
• Vehicle safety measures are designed to increase contact time to decrease the impact force for the same change in momentum
• Newton’s third law


  Is when two objects interact they exert an equal and opposite forces in each other
• Air bag = N2

  Crumple zone = N2

  Seat belts = N2 and N1 - we need to decelerate with the car, otherwise we’d remain constant velocity and hit windscreen

  all = F = Δmv/Δt
• What is the area under a force vs time graph

  Momentum
• Due to a change in velocity of the object when coming hit a surface, and the change in velocity after the surface was hit. The Δp equals the two changes in velocity or = 2mv

  Δp = 2mv - change direction - hit a wall and rebound
• Newton’s third law characteristics: (5)


  -equal magnitude

  -opposite direction

  -same type (e.g. both gravitational)

  -same line of action

  -act on different objects
• The total linear momentum of a system remains consatnt in COLLISIONS/EXPLOSIONS provided no external forces are applied
• Conservation of energy equation

  M1U1 + M2U2 = M1V1 +M2V2
• About a rebound collision

  -it is elastic

  -momentum is conserved

  -kinetic energy is conserved
• About a coalescence collision

  -inelastic

  -momentum conserved

  -kinetic energy is not conserved (before>after)
• About an explosion collision


  -inelastic

  -momentum is conserved

  -kinetic energy is not conserve (before<after)
• collisons:

  -momentum is conserved in all collisions

  -kinetic energy is conserved in elastic collisions

  -in interactions in which kinetic energy is not conserved - the energy has come from chemical energy/the energy (has gone) is used to deform materials
• The rate of change of momentum for a fluid undergoing an acceleration is given by:

  F = pAv^2

  p - momentum

  A - area

  v^2 - velocity squared