Transcript projectiles & review

PH 201
Dr. Cecilia Vogel
Lecture 25
REVIEW
universal gravitation
Force & PE
accel of grav
orbits
OUTLINE
universal gravitation
Kepler’s 3rd Law
Generalize projectiles
Escape velocity
Keppler’s Laws
Keppler’s 1st Law
planets travel in elliptical orbit,
with Sun at one focus
Keppler’s 2nd Law
planet sweeps out equal areas in equal times
Keppler’s Laws
Keppler’s 3rd Law=“Law of Periods”
T2 is proportional to a3,
perfect circle:
F=ma
closer planets go
2
GMm
v
m
2
r
r
GMm
4 r
m 2
2
r
T
2
GM 4
 2
3
r
T
2
GM 4 2
 2
3
a
T
How to Weigh the Sun
Observe planet
the period
and
or
Calculate the mass of the Sun
GM 4
 2
3
a
T
2
Geosynchronous Orbits
Artificial satellite
if it is to keep over same point,
T =
also M =
so
2
GM 4
 2
3
r
T
All circular geosynchronous orbits are at
r = 42000 km
h = 36,000 km
Projectiles
Projectile near planet’s surface
behave like constant
Projectiles going high
accel varies
often can use energy conservation
GMm 1 2
GMm 1 2
E
 mv1  
 mv2
r1
2
r2
2
Applies to projectiles going
or
or
so long as no
Projectile Example
Rocket projected upward from moon’s
surface at a speed of 100 m/s. How high
will it go, before it begins to fall back?
GMm 1 2
GMm 1 2
E
 mv1  
 mv2
r1
2
r2
2
Escape Velocity
escape velocity is speed
Initial
r = R, v = vE
Final
r = ∞, v = 0
Not in orbit, don’t use orbit eqn!!!!
Gm1m2 1 2
E
 mv  0
r
2
2GM
2
vE 
R
Black hole
Light cannot escape
if escape velocity =
2GM
c 
R
2
Summary
Kepler’s Laws
ellipse, foci, semi-major axis, periods
Projectiles still conserve energy,
but U is not mgh
Escape velocity – zero mechanical energy
PAL
Imaginary planet has a mass of 1024 kg, a
radius of 108 m.
1. Find the acceleration of gravity on the
planet’s surface.
2. What initial speed must a rocket have to
reach a height of 3X108 m?
3. Find the escape speed of this planet.
G=6.67X10-11 Nm2/kg2.