Energy & Work

Is the ability to do work, measured in $Joules \space (J)$
- Work, then, is measured in joules too. It is the change in energy of an object, so basically $\Delta E$
- This is $F_s$
Energy is a conserved quantity. Then, Energy can neither be created nor destroyed, though it can be transferred or transformed.
- Transfer = type of energy is unchanged
- Transform = one type of energy becomes another type
We're only really interested in two types of energy;
- Mechanical energy i.e kinetic and gravitational potential,
  - Kinetic: $E_x=\frac{1}{2}mv^2$. This is a scalar
  - Gravitational Potential: $E_p=mgh$. This is
  - Applied Force: $F_{s}=Nm$
- For objects in motion (inc. stationary), it is assumed that their total mechanical energy (TME) = $E_{x}+E_{p}$ will be constant for that object.

A bird realises it is a flightless bird and plummets to the ground. What is its final velocity as it hits the ground? It has a mass of $15.4kg$ and falls from a height of $1.58m$. It was "flying" at a speed of $3.44m\space s^{-1}$
To solve,
Construct a vector diagram
- We know energy is conserved, so both things need to add up in both states.
- There is no initial kinetic energy and no gravitational potential energy in the end
- So, the gravitational potential energy at the start is equal to the kinetic energy at the end.
- $mgh=\frac{1}{2}mv^2$ $\therefore v=\sqrt{2gh}=5.56m \space s^{-1}$.
- Now we have the horizontal and vertical vector components, so we can determine the resultant, which is the final velocity.