Mathematics: Mechanics 2 (Notes 2 of 2)

Kinetic energy is \(\frac{1}{2}\)\(mv^2\) where \(m\) = mass and \(v\) = velocityGravitational potential energy is \(mgh\) where \(m\) = mass, \(g\) = gravitational acceleration and \(h\) = height above 0 PE level.The total mechanical energy is constant providing that no external forces, such as friction, act on the system. This means initial KE + initial PE = final KE + final PE.The work done by (or against) a force = Force x Distance moved PARALLEL to force. If the force has been applied at an angle to the distance travelled then work out the correct component of the force to use in the equation. If an external force (a force pulling something or a frictional force) acts on the body then conservation of mechanical energy can't be used, but the energy should still be considered, as the initial energy + energy added to the system (ie. work done by external forces) = final energy, for example:Work done by a force = Increase in KE + Increase in PE + Work done against resistancePower is the rate at which work is done = \(\frac{Work done}{Time taken}\)For a moving vehicle with a forward driving force, the power of the engine equation can be rewritten as Power = Tractive force x VelocityThis can be combined with Newtons \(2^{nd}\) law if the tractive force is constant. 

Energy, Work and Power