A modeling approach to the 8.01 final exam equation sheet.
Page Contents |
|---|
Interactions
General Definitions
Work
Unknown macro: {latex}
\begin
Unknown macro: {large}
[ W = \int_
Unknown macro: {r_0}
^
Unknown macro: {r_f}
\vec
Unknown macro: {F}
\cdot d\vec
Unknown macro: {r}
]\end
Potential Energy
Unknown macro: {latex}
\begin
Unknown macro: {large}
[\Delta U = -W_
Unknown macro: {rm conservative}
= -\int_
Unknown macro: {A}
^
Unknown macro: {B}
\vec
Unknown macro: {F}
_
Unknown macro: {c}
\cdot d\vec
Unknown macro: {r}
]\end
Power
Unknown macro: {latex}
\begin
Unknown macro: {large}
[P = \vec
Unknown macro: {F}
\cdot\vec
Unknown macro: {v}
]\end
Impulse
Unknown macro: {latex}
\begin
Unknown macro: {large}
[ I = \int_
Unknown macro: {t=0}
^
Unknown macro: {t=t_f}
\vec
Unknown macro: {F}
(t)\:dt ]\end
Torque
Unknown macro: {latex}
\begin
Unknown macro: {large}
[\vec
Unknown macro: {tau}
_
Unknown macro: {S}
= \vec
Unknown macro: {r}
_
Unknown macro: {PS}
\times\vec
Unknown macro: {F}
_
Unknown macro: {P}
\qquad \qquad |\vec
_
Unknown macro: {S}
| = |\vec
Unknown macro: {r}
_
Unknown macro: {PS}
||\vec
Unknown macro: {F}
_
Unknown macro: {P}
| \sin\theta = r_
Unknown macro: {perp}
F = r F_
]\end
Specific Interactions
Gravity – Universal
Unknown macro: {latex}
\begin
Unknown macro: {large}
[ \vec
Unknown macro: {F}
_
Unknown macro: {12}
= - G\frac{m_
Unknown macro: {1}
m_{2}}{r_
^{2}}\hat
Unknown macro: {r}
_
Unknown macro: {12}
\qquad\qquad U_
(r) = - G\frac{m_
Unknown macro: {1}
m_{2}}{r_{12}}]\end
Gravity – Near Earth
Unknown macro: {latex}
\begin
Unknown macro: {large}
[ F = mg \mbox
Unknown macro: { (directed straight downward)}
\qquad \qquad U
= mgy ]\end
Contact Force
Unknown macro: {latex}
\begin
Unknown macro: {large}
[ \vec
Unknown macro: {F}
_
Unknown macro: {contact}
= \vec
Unknown macro: {N}
+ \vec
Unknown macro: {f}
]\end
Friction – Static
Unknown macro: {latex}
\begin
Unknown macro: {large}
[ 0 \le f_
Unknown macro: {s}
\le f_
Unknown macro: {s,max}
= \mu_
N \mbox
Unknown macro: { (directed opposite net force neglecting friction)}
]\end
Friction – Kinetic
Unknown macro: {latex}
\begin
Unknown macro: {large}
[ f_
Unknown macro: {k}
= \mu_
N \mbox
Unknown macro: { (opposes motion with respect to the surface)}
]\end
Springs
Unknown macro: {latex}
\begin
Unknown macro: {large}
[ F = k|\Delta x| \mbox
Unknown macro: { (restoring)}
\qquad \qquad U
= \frac
Unknown macro: {1}
Unknown macro: {2}
k x^
]\end