Which do you think would stronger the gravitational interaction between an apple and earth or the gravitational interaction betw
een an apple and the moon?
2 answers:
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1) The forces are equal (Newton's third law of motion)
2) The force between the spheres will quadruple
3) The force of gravity exerted by the notebook on you is negligible
Explanation:
1)
In this part of the problem, we want to compare the gravitational force exerted by the larger mass sphere on the smaller mass sphere to the force exerted by the smaller mass sphere to the larger mass sphere.
We can do this by using Newton's third law of motion, which states that:
<em>"When an object A exerts a force (called </em><em>action</em><em>) on an object B, then object B exerts an equal and opposite force (called </em><em>reaction</em><em>) on object A"</em>
In this problem, we can identify the larger mass sphere as object A and the smaller mass sphere as object B. This law tells us that the two forces are equal in magnitude and opposite in direction: therefore, the gravitational force exerted by the larger mass sphere on the smaller mass sphere is equal to the force exerted by the smaller mass sphere to the larger mass sphere.
2)
The magnitude of the gravitational force between the two spheres is given by
where
G is the gravitational constant
are the masses of the two spheres
r is the separation between the two spheres
In this problem, we are asked to find what happens when the distance between the spheres is halved, therefore when the new distance is
Substituting into the equation, we find
So, the force between the two spheres will quadruple.
3)
We can give an estimate for the gravitational force exerted by your notebook on you.
As we said, the magnitude of the gravitational force is
Where:
is the gravitational constant
Let's estimate the following:
is your mass
is the mass of the notebook
, assuming the notebook is at 1 metre from you
Substituting,
We see that this force has an extremely small value: therefore, it is almost negligible in daily life, where other much stronger forces act on you.
Learn more about gravity:
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