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: $f_{s}\leq \mu _{s}|\mathbf {N} |$
   • 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

$a_{r}={\frac {v^{2}}{R}}$

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

Work, Kinetic, and Potential Energy

Work

${\begin{aligned}W&=\int _{r_{1}}^{r_{2}}Fdr\\&=F\cdot \Delta r&{\mbox{if F is constant}}\\&=\Delta K=K_{f}-K_{i}\end{aligned}}$

Kinetic Energy

$K={\frac {1}{2}}mv^{2}$

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

$K_{i}+U_{i}+W_{nc}=K_{f}+U_{f}$