Work and energy - Ben Borgers

Work and energy are both measured in Joules ( $J$ $J$ ).
- This makes sense because work is a quantification of how much energy is transferred from one form to another.
  - If you’re doing work to something, you’re changing the number of Joules of energy that object has.
Work is the amount of energy transferred by a force when it moves an object through a displacement.
- Work refers to energy transfers - putting energy into something or removing it.
- Energy is the ability of an object to produce a change in itself or its environment.
  - For example, an item has the energy to crash into the wall, or a stretched rubber band has the stored energy to snap back.
- Mechanical energy is a specific type of energy due to position or motion.
- Work does not have a direction, but it does have a sign (which represents adding energy vs. removing energy).
  - Positive work occurs when force and displacement are in the same direction (example: throwing a ball). Negative work occurs when the force and displacement are in opposite directions (catching a ball).
  - There can be zero work, for example riding a skateboard. Force goes downwards while the displacement is horizontal. This makes sense, because the skateboard’s energy is not affected by the skateboard pulling down.
  - There is also zero work if the object is not moving (zero displacement).
- You do more work if:
  - You apply more force.
  - That force is applied over a greater displacement.
- $\text{work} = (\text{force component in direction of displacement})(\text{displacement})$ $work = (force component in direction of displacement) (displacement)$
  - The units make sense: $J = N * m$
  - This equation applies to mechanical energy, so:
    - Kinetic energy (energy due to motion)
    - Potential energy (stored energy, such as gravity or elastic)

Equations

Kinetic energy: $\text{KE} = \frac{1}{2} mv ^2$ $KE = \frac{1}{2} m v^{2}$
- if a ball is falling towards the ground, two things would give it more energy transfer to the ground: more mass (heavier ball) and more speed (the faster it goes).
Net-work: $W_\text{net} = K - K_0$ $W_{net} = K - K_{0}$
- The net-work done on a system is equal to its change in kinetic energy.
Gravitational Potential Energy ( $\text{GPE}$ $GPE$ , or $\text{PE}<em>\text{g}$ $PE < e m > g$ , or $\text{U}</em>\text{g}$ $U < / e m > g$ . $\text{U}$ $U$ is a generic variable for different kinds of potential energy): $\text{U}_{g} = m g h$ $U_{g} = m g h$
- Things that increase gravitational potential energy: mass, gravity, and height from which the object falls.
- Not dependent on the path taken, only the final position.