- Energy is conserved; can’t be created / destroyed
- Kinetic Energy describes motion => mv^2
- Energy on earth originates from the sun
- Energy on earth is stored thermally and chemically
- Chemical energy is released by metabolism
- Energy is stored as potential energy in objects

### Conservation of Energy

Energy cannot be created or destroyed, but can be transformed other energies of another form.

- Dissipation of “heat” – Energy could be lost by transforming into heat

### Work

Work done is the dot product (scalar) of the force and the displacement times cos θ of the angle.

- W = F Δd cos θ = unit J (Joules)
- Work is only considered when the force applied is not perpendicular to the displacement
- In a uniform circular motion, the work done is always 0

#### Kinetic Energy

Work = Σ Force ( ΔDisplacement) = (mass)(acceleration)(Displacement)

$W=m(a\Delta d)=m\frac{1}{2}(v_{2f}-v_{2i})=\frac{1}{2}mv_{2f}-\frac{1}{2}mv_{2i}\Rightarrow \Delta K=K_{f}-K_{i} giving: K=\frac{1}{2}mv_{2}$

Constant Force $\Rightarrow$ $W=(F\cos \Theta )\Delta d$

Variable Force $W\approx F(\cos\Theta )\Delta d_{1}+F(\cos\Theta )\Delta d....$

#### Hooke’s Law

$W=\frac{1}{2}kX_{2}\Rightarrow with F_{x}(X)\Rightarrow (\frac{1}{2}kx)(x)$

#### Gravitational Potential Energy

$W_{gravity}=(F\cos\Theta )\Delta d$ for $W_{gravity}=mg(h_{i}-h_{f})$ with $|g|=9.8m/s_{2}$

- Take into consideration with only the parallel force to displacement Take $U_{grav}=mgh\Rightarrow W_{grav} =-\Delta U_{grav}$

For an object to fall, $\Delta U_{grav}$ < 0 for that the final Energy < initial Energy

#### Elastic Potential Energy

$W_{elastic}=\frac{1}{2}k x_{12}\frac{1}{2}kx_{f2}$

Similar to the gravitational potential energy, this energy is stored depending on distance, x.

#### Conservative vs Non‐conservative Forces

- A force is conservative when the
*work*it does on a moving object is independent of the path between the object’s initial and final positions. - A force is conservative when it does no work on an object moving around a closed path, starting and finishing at the same point.

### Gravitational, Elastic Spring and Electric Force are Conservative

$Work_{done}=Work_{Conservative}+Work_{Non-conservative}$

- $Work_{Non-conservative}=\Delta K+\Delta U=(K_{f}-K_{i})+(U_{f}-U_{i})$
- $W_{Nc}=(K_{f}+U_{f})-(K_{i}+U_{i})$
- $E=K+U$
- $W_{Nc}=E_{f}-E_{i}$
- $W_{Nc}=0$ $0=E_{f}-E_{i}$ $E_{f}=E_{i}$

### Power

**Power -** the rate of change of energy over time.

- P = Work / Time =
*$ΔW/Δt$*= Change in energy / time - Given Joule/ s = watt (W)
- Average Power = Force ( Average Velocity)
- Instantaneous Power = Power = Force (Velocity)

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