Transcript 1.4 mm

Lecture series from Conceptual Physics, 8th Ed.
The Falling Apple
p166
Newton new that inertia kept the moon moving
around the Earth.
So, there must be a force that pulled it into an
elliptical orbit.
The same force that pulled the apple to the ground must
extend to the moon.
The Falling Moon p167
Falls 1.4mm
during one sec.
Falls 4.9m
the first sec.
Gmemm (6.67x10-11)(5.98x1024)(7.36x1022)
F=
=
2
d
(3.84x108)2
F = 1.99x1020N
F
And then, a = m =
1.99x1020N
7.36x1022kg
a = 0.0027 m/s2
And, finally…d = ½ at2
d = ½ (0.0027)(1)2 = 0.0014 m
d = 1.4 mm in the
1st second.
The apple falls 4.9 m in the 1st second.
d = ½ g t2 = (0.5)(9.8)(1)2 = 4.9 m
Circular Orbits
p168
Without tangential velocity, the
Earth would fall into the sun.
Fig 9.5- No work is
done on bowling
ball because force is
perpendicular to
motion of ball.
We can see the
curvature but the
force is still
perpendicular.
At 8 km/s the bb
doesn’t need the
track.
Elliptical Orbits
p170
Fig 9-8 Satellite is moving
faster than 8 km/s.
a) Goes outside circle and
slows down.
b) Falls back to Earth
gaining speed.
c) Does it over again.
8 km/s
Initial thrust
gets rocket off
the ground.
The trajectory of a
cannon ball is part of
an ellipse that would
occur if the Earth
didn’t get in the way.
Sideways thrust gets it
to orbital speed.
Both up and sideways are
done together.
Energy Conservation and Satellite Motion
p172
For a circular orbit the energy is constant.
Satellite is slow at apogee. Has small KE.
Satellite is faster at perigee.
Has large KE.
Conservation of energy:
KE + PE = k.
In an ellipse the force is not always
perpendicular to the motion.
Here a component of the force is
speeding up the satellite.
Recall: work = delta KE.
This component of the force is
doing work on the satellite.
The other component doesn’t do
work. It changes the direction of
the satellite.
vesc =
Escape Speed
p176
vesc =
2GM
d
2(6.67x10-11)(5.98x1024)
6.37x106
vesc = 11,200 m/s
d won’t fall back.
However, you could escape at any
speed, 2 m/s, if you kept the motor
turned on all the way.
The end