Physics 105A
Analytical Mechanics
Cavendish Experiment
Momentum
Rocket Motion
1-D Collisions
28 June 2016
Manuel Calderón de la Barca Sánchez
The Cavendish Experiment
Devised in 1783 by John Michell
Died in 1793. Apparatus ended in Cavendish’s hands.
Reported measurements in 1798.
 Wooden rod, 1.8m.
 Lead sphere (51 mm diameter) at each end of rod (0.73 kg each).
 Hang rod from a wire.
 Place two larger lead spheres (300 mm, 158kg) near the smaller
spheres.
 Separation between them: ~230mm
 Wire twists: torque from wire balances torque from gravity.
 Result: Density of earth is 5.448 ± 0.033 times that of water

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Cavendish Experiment
Top view
q
Wire (out of page)
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Cavendish and his apparatus
 Experiments to determine the density of the Earth.
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A very careful
experimeter!
-7
Forces involved in torsion: ~ 1.47 x 10 N.
Compare to weight 0.73 kg mass: ~ 7.1 N
Weight of small ball is ~48,700,000 times
the gravitational force between the balls!
 Have to prevent air currents and temperature
changes messing up the experiment!
 Motion of the rod ~ 4.1 mm
 Had to measure this deflection to better than
1/100th of an inch.
 Accuracy was not improved for 97 years!
 His result for earth’s density, converted to G, is
within 1% of currently accepted value.

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Rocket Motion
mdv = -u dm
=
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Two Stage Rocket
 Allows to reach higher speeds
 Allows to keep fuel/payload not
too big.
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1-D Collisions
m
v
M
 Elastic collisions:
Conserve momentum
Conserve energy
 Can treat motion in lab frame or CM frame (or whatever
frame is most convenient).
 Example above: Before collision, mass m moves at v,
mass M is stationary. Find final velocities after collision.
28 June 2016
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m
v
M
 What is the total momentum in lab frame?
 What is the speed of the CM?
 What are the speeds of the masses in the CM frame?
Check: relative speed in CM frame should still be v.
Check: total momentum in CM frame should be 0.
– Ratio of speeds?
 What happens to total momentum after collision.
What does this mean for the total energy? For the speeds?
28 June 2016
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m
v
M
 Final lab velocities:
m-M
vm = v
m+ M
2m
vM = v
m+ M
 Interesting limits:
m=M
M>>m
M<<m
28 June 2016
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