PHYS 218 Exam 2

Newton's Laws

1. Inertia Law (object in motion stays in motion)
2. $\sum \mathbf{𝐅}=m\mathbf{𝐚}$
3. Action/Reaction

Force/Reaction Pairs

1. Normal
2. Friction
   • static: $f_s\le {\mu }_s|\mathbf{𝐍}|$
   • dynamic/kinetic: $f_k={\mu }_k|\mathbf{𝐍}|$
3. Weight: $mg$
4. Spring: $F_s=-k(x-l_0)$
5. Magnetic/Electric

Free-body Diagrams

(with proper angles)

Equilibrium

Defined as:

• sum of forces is 0
• velocity is constant
• acceleration is 0

be sure to include all points of interest

Circular Motion

$a_r=\frac{v^2}{R}$

$a_{\varphi }=\frac{d|\mathbf{𝐯}|}{dt}$

Work, Kinetic, and Potential Energy

Work

$\begin{array}{rl}W& =\underset{r_1}{\overset{r_2}{\int }}Fdr\\ & =F\cdot \mathrm{\Delta }r& \text{if F is constant}\\ & =\mathrm{\Delta }K=K_f-K_i\end{array}$

Kinetic Energy

$K=\frac{1}{2}m{v}^2$

Potential Energy

• Gravitational: $U=mgh$

Energy Diagrams

Points of equilibrium

slope (force) is 0

Stable

forces want to return object to that point (concave up)

Unstable

any slight deviation will cause forces to pull object (concave down)

Possible range of movement

Given a total energy ($U+K$) at $y=U$, then range of movement will be anything where $K>0$

Conservation of Energy

$K_i+U_i+W_{nc}=K_f+U_f$