Why do we travel to the moon?
2 answers:
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Answer:
Afterward the magnitude of the acceleration of the stone is four times as great
Explanation:
A stone tied to a string and whirled at a constant speed in a horizontal circle will have a centripetal acceleration given by
Where is the centripetal acceleration
is the speed
and is the radius of the circle
Here, the radius of the circle is the length of the string.
Now, from the question
The speed is then doubled without changing the length of the string,
Let the new speed be , that is
and without changing the length of the string means radius is constant.
To determine the magnitude of the acceleration of the stone afterwards,
Let the new acceleration be .
Then we can write that
From
Recall that
∴
Now, we will put the value of into
Then,
The new magnitude of the acceleration of the stone is four times the initial acceleration.
Hence,
Afterward the magnitude of the acceleration of the stone is four times as great