# Key Equations of Work, Energy, Power & Simple Machines

Last updated on October 2nd, 2023 at 04:16 pm

Here we enlist important **key equations** or formulas from the **Work, Energy, Power & Simple Machines** chapter.

## Equations related to Work, Power and the Work-Energy Theorem

Let’s examine how doing work on an object changes the object’s energy. We will use cases related to a piece of rock to apply different equations from work & energy.

Equation for work[Work is the application of force, F, to move an object over a distance, d, in the direction that the force is applied.] | W=Fd |

Force to lift a rock off the ground[The force we exert to lift the rock is equal to its weight, w, which is equal to its mass, m, multiplied by the acceleration due to gravity, g.] | F=w=mg |

work equivalencies[The work we do on the rock equals the force we exert multiplied by the distance, d, that we lift the rock. The work we do on the rock also equals the rock’s gain in gravitational potential energy, PE._{e} | W=PE=mgd_{e} |

kinetic energy[Kinetic energy depends on the mass of an object and its velocity, v.When we drop the rock the force of gravity causes the rock to fall, giving the rock kinetic energy.] | KE=(1/2)mv^2 |

Work-Energy Theorem[When work done on an object increases only its kinetic energy, then the net Work equals the change in the value of the quantity (1/2)mv ^{2}. This is a statement of the work-energy theorem, which is expressed mathematically as the equation written in the next cell. | W=ΔKE = (1/2)mv_{2}^{2} – (1/2)mv_{1}^{2} |

power | P=Wt |

## Equation related to Mechanical Energy and Conservation of Energy

Mechanical energy can be either potential or kinetic. This equation shows how energy is transformed from one of these forms to the other. We will also see that, in a closed system, the sum of these forms of energy remains constant.

conservation of energy | KE_{1}+PE_{1}=KE_{2}+PE_{2} |

## Equations related to Simple Machines

Ideal Mechanical advantage (IMA) of different simple machines, input work, output work, and efficiency – Get equations of all these here.

ideal mechanical advantage (general) | IMA = F_{r}/F_{e} = d_{e}/d_{r} |

ideal mechanical advantage (lever) | IMA= L_{e}/L_{r} |

ideal mechanical advantage (wheel and axle) | IMA=R/r |

ideal mechanical advantage (inclined plane) | IMA=L/h |

ideal mechanical advantage (wedge) | IMA=L/t |

ideal mechanical advantage (pulley) | IMA=N |

ideal mechanical advantage (screw) | IMA=2πL/P |

input work | W_{i}= F_{i}d_{i} |

output work | W_{o}=F_{o}d_{o} |

efficiency output | % efficiency=(Wo/Wi)×100 |

Note: **Numerical problems**: Here is the link to one useful post in this portal where you will find a good collection of **solved numerical problems on energy conversion or transformation**.