Create assignment, 00224, Homework 1, Jan 10 at 4:03 pm
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Gravity on a New Planet
13:05, trigonometry, numeric,
>
1 min, nor
mal.
001
Having landed on a newly discovered planet,
an astronaut sets up a simple pendulum of
length 0
.
7 m and finds that it makes 120 com
plete oscillations in 446 s. The amplitude of
the oscillations is very small compared to the
pendulum’s length.
What is the gravitational acceleration on
the surface of this planet?
Correct answer: 2
.
00056 m
/
s
2
.
Explanation:
Basic Concept
A simple pendulum oscil
lating with small amplitude has period
T
= 2
π
s
‘
g
where
‘
is the pendulum’s length and
g
is the
gravitational acceleration at the pendulum’s
location.
The pendulum in question made
n
= 120 complete oscillations in time
t
=
446 s, which implies the period of
T
=
t
n
.
Thus
t
n
= 2
π
s
‘
g
t
2
n π
=
s
‘
g
t
2
4
n
2
π
2
=
‘
g
g
=
4
n
2
π
2
‘
t
2
Thus the planet’s surface gravity is
g
=
4
n
2
π
2
‘
t
2
= 2
.
00056 m
/
s
2
.
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 Spring '10
 Avram
 Physics, Gravity, Work, 1 m, 2 g, 0.7 m, 0.5 cm, 2.4 m/s

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