Homework-3
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School
Course
ASTR 12600
Subject
Physics
Date
Oct 27, 2024
Pages
4
Uploaded by MinisterScienceRaccoon39
ASTR 12600 - Homework 3 (note: always show your work) 1)
Measurements of the displacement y
of a spring by different masses M
are given in the Table below. A linear relationship is expected since the mass and spring will reach equilibrium when M
g = ky
, where g=9.81 m/s
2
. Make a plot of y
versus M
(including the uncertainties on the data points) on a graph paper. Use the maximum and minimum slope method to determine the best slope and its uncertainty. Derive the spring constant k and its uncertainty. Include in your submission the graph paper with the data points and the maximum and minimum slope lines. (15 points) y
±
࠵?
y
(cm)
M
(kg) 1.75±0.25
1 2.50±0.25
2 3.75±0.25 3 4.75±0.25 4 2)
Alessandro performed ten measurements of a reference weight reported below. (150.16, 149.94, 149.95, 149.89, 150.09, 149.77, 150.17, 149.92, 150.03, 149.98) g Calculate their average W
avg
, standard deviation ࠵?,
and uncertainty on the mean ࠵?
avg
. Francesca performed one hundred measurements of the same weight with a different scale obtaining the following mean value and uncertainty on the mean: W
F
= 149.74 ± 0.01 g
Are the two measurements compatible? (15 points) 3)
The gravitational force between two objects of mass m
1
and m
2
separated by a distance r
is: Using dimensional analysis determine the dimensions and units of the gravitational constant G (10 points)
4)
Galileo's contributions to science include the invention of the telescope. He was the first to observe Jupiter's moons and from their movement realized that they were not stars, but satellites orbiting around the planet. In the graphs at the end of the homework observations over nine consecutive days of the position of four of Jupiter's moons are reported, with distance scale in millions of km. Question 1: From these observations, determine (approximately) the period of revolution of each moon and its radius. Explain your procedure. Question 2: Use your results for Ganemede and the 3
rd
Kepler's law to determine the mass of Jupiter (15 points) 5)
In a 1971 live broadcast on television, astronaut David Scott conducted Galileo's famous experiment on the moon surface during the last Apollo 15 moonwalk. He dropped a hammer and a feather which landed ground at the same time. The objects were left free at a height of 1.6 m, and it took 1.4 s for them to reach ground. a) What is the acceleration of gravity on the moon? b) Why do the hammer and the feather reach ground at the same time? c) What is the acceleration of gravity on the surface of Jupiter? Use the value obtained in your answer to a) and the data in the Table below to answer this question. (15 points)
Mass (10
24
kg) Radius (km) Moon 0.073 1737 Jupiter 1898 71492
6)
In the Sci-Fi TV-show the "Expanse", Belters (human colonists born in the asteroid belt) are used to lower gravity than Earth. A Belter spaceship (figure below) employs a centrifuge wheel turning with a period of 45 s to provide astronauts with the required artificial gravity, 0.3 g. (20 points) a)
The sleeping quarters for the astronauts are located at the center of the wheel (point C in figure). What is the value of the artificial gravity in that location? Explain your answer. b)
A tunnel T
connects the wheel compartment to the sleeping quarters. An astronaut in point B
at the center of the tunnel leaves her hold on the tunnel stairs' handrail. Will she fall to the sleeping quarters C
or be pushed to point A on the wheel? Explain your answer. c)
What is the radius of the wheel? (Hint: the centripetal acceleration must be equal to the artificial gravity) (15 points) 7)
Briefly describe the differences between Aristoteles, Newton and Einstein views as you learned from reading Chapt. 4 of the textbook, Loss of Independence
. (15 points)
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