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I already posted this in the MCAT Discussions forum before I was aware of this subforum, so I will repost my question here and hope the mods merge the two threads.
The following is a passage from Nova's "The MCAT Physics Book," Chapter 5.
Consider an object sitting on a scale at the surface of the Earth.The scale reading is the magnitude of the normal force which the scale exerts on the object. To a first approximation, there is force balance, and the magnitude of the scale's force is the magnitude of the gravitational force:
F = GMm/(R^2) (1)
Where F is the gravitational force, G is Newton's constant, M is the mass of the Earth, and R is the radius of the Earth. The simple result is that the force of gravity, and the reading of the scale, is proportional to the mass:
F = mg (2)
Where g has the value GM/(R^2) = 9.8 m/(s^2). We have made several idealizations, however, and if we want to calculate the scale reading, we need to be more careful.
For example, we have ignored the rotation of the Earth. Consider a man standing on a scale at the equator. Because he is moving in a circle, there is a centripetal acceleration. The result is that the scale will not give a reading equal to the force of gravity (equation [1]).
We have also assumed that the Earth is a perfect sphere. Because it is rotating, the distance from the center of the Earth to the equator is greater than the distance from center to pole by about 0.1%.
A third effect we have ignored is that the Earth has local irregularities which make it necessary to measure g in the local laboratory, if we need an exact value of the effective acceleration due to gravity.
Now for the question...
If two identical men stood on scales at the south pole and at the equator of an Earth identical to this one but nonrotating, how would the reading of the polar scale compare to the equatorial one?
A. It would be less.
B. It would be the same.
C. It would be greater.
D. There is not enough information to answer this question.
My question is this: How can C be the correct option? According to the second-to-last paragraph, the only reason there is a difference between the distance from the center of the earth to the equator and from the center to the pole is because the earth is rotating. If one were to measure the force of gravity at the equator and poles of a nonrotating earth, their distances would be the same, and thus their gravitational force (and scale reading) would be the same. Wouldn't it?
The following is a passage from Nova's "The MCAT Physics Book," Chapter 5.
Consider an object sitting on a scale at the surface of the Earth.The scale reading is the magnitude of the normal force which the scale exerts on the object. To a first approximation, there is force balance, and the magnitude of the scale's force is the magnitude of the gravitational force:
F = GMm/(R^2) (1)
Where F is the gravitational force, G is Newton's constant, M is the mass of the Earth, and R is the radius of the Earth. The simple result is that the force of gravity, and the reading of the scale, is proportional to the mass:
F = mg (2)
Where g has the value GM/(R^2) = 9.8 m/(s^2). We have made several idealizations, however, and if we want to calculate the scale reading, we need to be more careful.
For example, we have ignored the rotation of the Earth. Consider a man standing on a scale at the equator. Because he is moving in a circle, there is a centripetal acceleration. The result is that the scale will not give a reading equal to the force of gravity (equation [1]).
We have also assumed that the Earth is a perfect sphere. Because it is rotating, the distance from the center of the Earth to the equator is greater than the distance from center to pole by about 0.1%.
A third effect we have ignored is that the Earth has local irregularities which make it necessary to measure g in the local laboratory, if we need an exact value of the effective acceleration due to gravity.
Now for the question...
If two identical men stood on scales at the south pole and at the equator of an Earth identical to this one but nonrotating, how would the reading of the polar scale compare to the equatorial one?
A. It would be less.
B. It would be the same.
C. It would be greater.
D. There is not enough information to answer this question.
My question is this: How can C be the correct option? According to the second-to-last paragraph, the only reason there is a difference between the distance from the center of the earth to the equator and from the center to the pole is because the earth is rotating. If one were to measure the force of gravity at the equator and poles of a nonrotating earth, their distances would be the same, and thus their gravitational force (and scale reading) would be the same. Wouldn't it?
