thought we’d try it here for you. The feather happens to be, appropriately, a falcon feather for our
Falcon. And I’ll drop the two of them here and, hopefully, they’ll hit the ground at the same time.
167:22:43 Scott
: How about that!
167:22:45 Allen
: How about that! (Applause in Houston)
167:22:46 Scott
: Which proves that Mr. Galileo was correct in his findings.
Newton’s Law.
Using this footage, we can also attempt to confirm another famous bit of
physics: Newton’s law of universal gravitation. Newton’s laws predict that any object dropped
near the surface of the Moon should fall
1
2
G
M
R
2
t
2
meters
after
t
seconds, where
G
is a universal constant,
M
is the moon’s mass in kilograms, and
R
is
the moon’s radius in meters. So if we know
G
,
M
, and
R
, then Newton’s laws let us predict how
far an object will fall over any amount of time.
To verify the accuracy of this law, we will calculate the difference between the predicted dis-
tance the hammer drops and the actual distance. (If they are different, it might be because New-
ton’s laws are wrong, or because our measurements are imprecise, or because there are other
factors affecting the hammer for which we haven’t accounted.)
Someone studied the video and estimated that the hammer was dropped 113 cm from the
surface. Counting frames in the video, the hammer falls for 1.2 seconds (36 frames).
Question 3.3.1.
Complete the code in the next cell to fill in the
data
from the experiment.
In [32]:
# t, the duration of the fall in the experiment, in seconds.
# Fill this in.
time
= 1.2
# The estimated distance the hammer actually fell, in meters.
# Fill this in.
estimated_distance_m
= 1.13
In [33]:
_
=
ok
.
grade(
'
q331
'
)
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Running tests
---------------------------------------------------------------------
Test summary
Passed: 5
Failed: 0
[ooooooooook] 100.0% passed
10

Question 3.3.2.
Now, complete the code in the next cell to compute the difference between the
predicted and estimated distances (in meters) that the hammer fell in this experiment.
This just means translating the formula above (
1
2
G
M
R
2
t
2
) into Python code. You’ll have to re-
place each variable in the math formula with the name we gave that number in Python code.
In [34]:
# First, we
'
ve written down the values of the 3 universal
# constants that show up in Newton
'
s formula.
# G, the universal constant measuring the strength of gravity.
gravity_constant
= 6.674 * 10**-11
# M, the moon
'
s mass, in kilograms.
moon_mass_kg
= 7.34767309 * 10**22
# R, the radius of the moon, in meters.
moon_radius_m
= 1.737 * 10**6
# The distance the hammer should have fallen over the
# duration of the fall, in meters, according to Newton
'
s
# law of gravity.
The text above describes the formula
# for this distance given by Newton
'
s law.
# **YOU FILL THIS PART IN.**
predicted_distance_m
=
(
1/2
)
*
gravity_constant
*
(moon_mass_kg
/
(moon_radius_m
**2
))
*
(
1.2**
# Here we
'
ve computed the difference between the predicted
# fall distance and the distance we actually measured.
# If you
'
ve filled in the above code, this should just work.

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