# Work and energy

• Work and energy are both measured in Joules ($J$).
• 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.
• $\text{work} = (\text{force component in direction of displacement})(\text{displacement})$
• 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: $\text{KE} = \frac{1}{2} mv ^2$
• 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: $W_\text{net} = K - K_0$
• The net-work done on a system is equal to its change in kinetic energy.
• Gravitational Potential Energy ($\text{GPE}$, or $\text{PE}\text{g}$, or $\text{U}\text{g}$. $\text{U}$ is a generic variable for different kinds of potential energy): $\text{U}_{g} = m g h$
• 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.