Your friend starts out by hanging is fuzzy dice from a spring. On the surface of the Earth, he finds the length of the spring to be 8.5 cm. With his car drifting in space (as in diagram B, above) he finds the length of the spring to be 3.6 cm (this is called the equilibrium length of the spring). What would be the length of the spring in a situation similar to diagram C above, if the car were accelerating upward at a rate of 9.8 m/s²? 8.5 cm Submit 2) If the spring is supporting the dice on the surface of a planet, the amount that the spring stretches (the difference between its length and its equilibrium length, 3.6 cm) is directly proportional to the strength of gravity on that planet. If it is pulling the fuzzy dice in space with zero gravity, the difference between its length the equilibrium length is directly proportional to the acceleration of the rocket ship. What would be the length of the spring in a situation similar to diagram C above if the car were accelerating upward at a rate of 12.6 m/s??
Your friend starts out by hanging is fuzzy dice from a spring. On the surface of the Earth, he finds the length of the spring to be 8.5 cm. With his car drifting in space (as in diagram B, above) he finds the length of the spring to be 3.6 cm (this is called the equilibrium length of the spring). What would be the length of the spring in a situation similar to diagram C above, if the car were accelerating upward at a rate of 9.8 m/s²? 8.5 cm Submit 2) If the spring is supporting the dice on the surface of a planet, the amount that the spring stretches (the difference between its length and its equilibrium length, 3.6 cm) is directly proportional to the strength of gravity on that planet. If it is pulling the fuzzy dice in space with zero gravity, the difference between its length the equilibrium length is directly proportional to the acceleration of the rocket ship. What would be the length of the spring in a situation similar to diagram C above if the car were accelerating upward at a rate of 12.6 m/s??
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Question
Q3 p
![c In space, accelerating
upward at 9.8 m/s
A Standing on Earth
B Drifting in space
SCALE
SCALE
SCALE
There is a lot to read here. It will be worth it to you to read all of it!
The diagrams above show an astronaut in a sealed room (with air). The astronaut is
weighing a pink vase under three conditions. In diagram A, the room is on the surface
of the Earth. In diagram B, the room is floating in space (far from planets, stars, and
other gravitational bodies) so that there is effectively zero gravity. In diagram C, the
room is also far from gravitational bodies but the room is accelerating upward at 9.8
m/s?.
In diagram B, the scale would read that the weight of the vase is zero. In
both diagrams A and C, the scale would read the weight of the vase on the surface of
the Earth. In situations A and C, the astronaut would feel exactly the same (with a
force equal to the weight of the astronaut between her feet and the floor). The
central idea of Einstein's General Theory of Relativity is that there is no experiment
the astronaut could do to determine whether she was in situation A or situation C. The
two situations are identical. A tremendous amount of evidence corroborating Einstein's
idea has been compiled in the last century.
In diagram A, the scale measures the gravitational mass of the vase. On the surface
of the Earth, the weight of an object is its gravitational mass multiplied by 9.8
m/s. In diagram C, the scale is measuring the inertial mass of the vase. The scale
would read zero if the vase had no inertia, but since it does have inertia the scale
reads the inertial mass of the vase multiplied by its acceleration which is 9.8 m/s in
diagram C. Another way of stating the central idea of General Relativity is
that gravitational and inertial mass are exactly the same. We know of no
fundamental reason why this has to be true, but it seems to be true.
The questions that follow explore the effect of inertial mass on the fuzzy dice that
your friend has hanging from the rearview mirror of his car. [Note: Air Force pilots in
WWII began hanging real dice from the windows of their fighter planes for good luck.
That idea evolved into fuzzy dice in automobiles after the war.]
Rearview mirror
String
Fuzzy dice
To answer the questions below, it may be useful to think of your friend's car driving on
a level road on the surface of the Earth, or maybe in space accelerating upwards at 9.8
m/s2
(or some other rate of acceleration, depending on the question).
of](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0990909b-34c0-4684-9ad1-52cde8ec56e1%2F0a583ae5-13b3-4f22-8e69-797a33456888%2F3wpga8b_processed.png&w=3840&q=75)
Transcribed Image Text:c In space, accelerating
upward at 9.8 m/s
A Standing on Earth
B Drifting in space
SCALE
SCALE
SCALE
There is a lot to read here. It will be worth it to you to read all of it!
The diagrams above show an astronaut in a sealed room (with air). The astronaut is
weighing a pink vase under three conditions. In diagram A, the room is on the surface
of the Earth. In diagram B, the room is floating in space (far from planets, stars, and
other gravitational bodies) so that there is effectively zero gravity. In diagram C, the
room is also far from gravitational bodies but the room is accelerating upward at 9.8
m/s?.
In diagram B, the scale would read that the weight of the vase is zero. In
both diagrams A and C, the scale would read the weight of the vase on the surface of
the Earth. In situations A and C, the astronaut would feel exactly the same (with a
force equal to the weight of the astronaut between her feet and the floor). The
central idea of Einstein's General Theory of Relativity is that there is no experiment
the astronaut could do to determine whether she was in situation A or situation C. The
two situations are identical. A tremendous amount of evidence corroborating Einstein's
idea has been compiled in the last century.
In diagram A, the scale measures the gravitational mass of the vase. On the surface
of the Earth, the weight of an object is its gravitational mass multiplied by 9.8
m/s. In diagram C, the scale is measuring the inertial mass of the vase. The scale
would read zero if the vase had no inertia, but since it does have inertia the scale
reads the inertial mass of the vase multiplied by its acceleration which is 9.8 m/s in
diagram C. Another way of stating the central idea of General Relativity is
that gravitational and inertial mass are exactly the same. We know of no
fundamental reason why this has to be true, but it seems to be true.
The questions that follow explore the effect of inertial mass on the fuzzy dice that
your friend has hanging from the rearview mirror of his car. [Note: Air Force pilots in
WWII began hanging real dice from the windows of their fighter planes for good luck.
That idea evolved into fuzzy dice in automobiles after the war.]
Rearview mirror
String
Fuzzy dice
To answer the questions below, it may be useful to think of your friend's car driving on
a level road on the surface of the Earth, or maybe in space accelerating upwards at 9.8
m/s2
(or some other rate of acceleration, depending on the question).
of
Transcribed Image Text:1)
Rearview mirror
Spring
Fuzzy dice
Your friend starts out by hanging is fuzzy dice from a spring. On the surface of the
Earth, he finds the length of the spring to be 8.5 cm. With his car drifting in space (as
in diagram B, above) he finds the length of the spring to be 3.6 cm (this is called the
equilibrium length of the spring).
What would be the length of the spring in a situation similar to diagram C above, if the
car were accelerating upward at a rate of 9.8 m/s??
8.5
cm
Submit
2) If the spring is supporting the dice on the surface of a planet, the amount that the
spring stretches (the difference between its length and its equilibrium length, 3.6
cm) is directly proportional to the strength of gravity on that planet. If it is pulling
the fuzzy dice in space with zero gravity, the difference between its length the
equilibrium length is directly proportional to the acceleration of the rocket ship.
What would be the length of the spring in a situation similar to diagram C above if the
car were accelerating upward at a rate of 12.6 m/s?
9.9
cm
Submit
Your submiss 9.9 /
Computed value: 9.9
Submitted: Monday, January 31 at 11:28 PM
Feedback: Right answer !
3) What would be the length of the spring in a situation similar to diagram C above if
the car were accelerating upward at a rate of 6.8 m/s?
cm
Submit
Expert Solution
Part 1
Given information:
The length of the spring when it is in free space (L0) = 3.6 cm
The length of teh spring when it is on earth (L) = 8.5 cm
Now, when the car is accelerating in space with an acceleration of 9.8 m/s2 the spring would be of the same length as it would be on earth.
That is the length of the spring as in the situation C is "8.5 cm"
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