phy 53 lecture dr. brown 2 november 2010
grade reassurance mean = 65
more gravity
\vec{F} = -\frac{G M m}{r^2} \hat{r}
issue = non-contact force ; Newton invents a "field" to explain this
\vec{g} = \frac{\vec{F}}{m} = \frac{-G M}{r^2}
really important -- would be better to say only fields exert forces than to talk about "contact" forces
gravitational fields satisfy the superposition principle
example -- find gravitational field at a point on the x-axis due to two masses which are at +a and -a onthe y-axis
there exist a number of ways to represent a vector solution -- pick one and use it -- ie. you must show both magnitude and direction [all components, magnitude and picture, magnitude and clear words, polar coordinates, ...]
what about continuous distributions of mass ... integrals ... not going to force this class to do these -- but you must believe some presented facts
1. spherical ball of mass -- field outside a spherically symmetric mas is the same as that of a point mass at the center
R_{earth} approx 4000 miles or approx 6400 km
G = 6.67 \times 10^{-11}
g approx 10
so you can find M_{earth}
2. inside a spherical shell, gravitational field = o
so... you can solve homework problem...#4 ; does this example
gravitational field inside earth at radius r
g_r = \frac{G m}{R^3} r ; linear in r
We would like to work with with scalars -- potential, work, energy
Define change in gravitational potential
\Delta U = - \frac{GMm}{r_1} + \frac{GMm}{r_0}
define U(\infty} = 0
U(\vec{r}) = - \frac{GMm}{r}
Now two dimentional motion in gravitational field
defines U_{effective}
and does hwk prob with U_{effective} graph -- identify circular, elliptical, parabolic, and hyperbolic curves
Escape velocity or escape energy E_{tot} >= 0
approx 11km/s