P10 work, energy + power

• energy is measured in joules
• one joule is equal to the energy needed to raise a 1N weight by 1m
• work done is measured in joules
• the principle of conservation of energy states that:

  energy cannot be created or destroyed, merely transferred
• the principle of conservation of energy means that whenever energy is transferred, the total energy before the transfer must equal the total energy after the transfer
• work is done on an object when a force acting on it makes it move, causing energy to be transferred to the object
• the equation for work done is W = F s costheta

  W = work done in J

  F = force in N

  s = distance in m

  theta = angle between direction of motion and force
• if a force is at 90 degrees to the direction of motion, no work is done because costheta is equal to zero
• the area under a force-distance graph represents the work done
• kinetic energy is the energy of an object due to its motion
• kinetic energy is represented by $E_k$
• the faster an object moves, the more kinetic energy it has
• the equation for kinetic energy is Ek = 1/2(m v^2)

  Ek = kinetic energy in J

  m = mass in kg

  v = velocity in ms^-1
• potential energy is the energy of an object due to its position
• potential energy is represented by $E_p$
• the higher above the ground an object is, the more gravitational potential energy it has
• the equation for gravitational potential energy is Ep = mgh

  Ep = gravitational potential energy in J

  m = mass in kg

  g = gravitational field strength in ms^-2

  h = height in m
• power is defined as the rate of transfer of energy
• an equation for power involving energy is P = E/t

  P = power in W

  E = energy in J

  t = time in s
• an equation for power involving work done is P = W/t

  P = power in W

  W = work done in J

  t = time in s
• an equation for power involving speed is P = Fv

  P = power in W

  F = force in N

  v = speed in ms^-1
• when energy is transferred by a force doing work, the energy transferred is equal to the work done by the force, so the rate of transfer of energy is equal to the work done per second
• the area under a graph of force against displacement is equal to the work done
• efficiency is a measure of how well a system transfers energy
• to calculate efficiency, divide useful power output by total power input
• to calculate percentage efficiency, divide useful power output by total power input and multiply by 100