Assume that the earth is perfectly round

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In summary, the force of gravity at the equator is .03 m/s^2 less than at the poles due to the rotation of the earth. In this case, the value for g should be 9.80 m/s^2 at the equator, based on the given equations and values. However, due to rounding errors, the percentage error is greater than the adjustment made by factoring in centrifugal force.
  • #1
bullroar_86
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r = 6400 km

how much less does a 100kg person weigh at the equator than at the poles because of the rotation of the earth?


Ok I have figured out that g(equator) is .03 m/s^2 less than it is at the poles due to the rotation on the earth.

so
F(pole) = (100kg)(g)

and

F(equator) = 100kg(g - .03m/s^2)



My question is what should be the value for g in this case?
If i make g = 9.8, then it will be 9.77 at the equator

or should it be g = 9.83 ... making it 9.80 at the equator.

not a big difference, but I'm just wondering which one is correct.
 
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  • #2
bullroar_86 said:
r = 6400 km

how much less does a 100kg person weigh at the equator than at the poles because of the rotation of the earth?


Ok I have figured out that g(equator) is .03 m/s^2 less than it is at the poles due to the rotation on the earth.

so
F(pole) = (100kg)(g)

and

F(equator) = 100kg(g - .03m/s^2)



My question is what should be the value for g in this case?
If i make g = 9.8, then it will be 9.77 at the equator

or should it be g = 9.83 ... making it 9.80 at the equator.

not a big difference, but I'm just wondering which one is correct.
It should be less. Your centrifugal force is counteracting the force of gravity leaving a net force less than the force of gravity alone. (A good clue is that the problem asked how much less does a person weigh.)

Of course, the problem with this problem is that all of your numbers are rounded to 2 significant digits and you're adjusting the third significant digit. The equatorial radius is actually 6378.137 km and the force of gravity at the equator is actually 9.798 m/s^2. The percentage error due to rounding off is greater than the percentage of the adjustment due to centrifugal force.

Of course, the choice of numbers used probably isn't up to you, so you have to go with what you've been given.
 
  • #3
bullroar_86 said:
r = 6400 km

how much less does a 100kg person weigh at the equator than at the poles because of the rotation of the earth?


Ok I have figured out that g(equator) is .03 m/s^2 less than it is at the poles due to the rotation on the earth.

so
F(pole) = (100kg)(g)

and

F(equator) = 100kg(g - .03m/s^2)



My question is what should be the value for g in this case?
If i make g = 9.8, then it will be 9.77 at the equator

or should it be g = 9.83 ... making it 9.80 at the equator.

not a big difference, but I'm just wondering which one is correct.

Take the difference between your two forces before substituting in a value for g. Simplify the result. Then think about your final question again.
 

1. What evidence supports the theory that the earth is perfectly round?

The most compelling evidence comes from observations of the earth's shape from space. Satellites and spacecraft have captured images of the earth's curvature, and even amateur photos taken from high-altitude balloons show a distinct curvature. Additionally, measurements taken by ships and airplanes traveling around the earth have consistently shown that the earth is round.

2. Why do some people believe the earth is flat?

The belief that the earth is flat is largely based on conspiracy theories and misinformation. Some people may also have a mistrust of scientific institutions and reject evidence that goes against their beliefs. It is important to note that there is no scientific evidence to support a flat earth, and the overwhelming consensus among scientists is that the earth is round.

3. How do we know that the earth is not a perfect sphere?

While the earth is approximately round, it is not a perfect sphere. This is because the rotation of the earth causes a slight bulge at the equator and a flattening at the poles. This is known as the earth's oblate spheroid shape. Scientists have been able to measure this deviation from a perfect sphere through various methods, such as satellite observations and gravity measurements.

4. Are there any other planets in our solar system that are perfectly round?

Yes, there are several other planets in our solar system that are approximately round. The gas giants Jupiter, Saturn, Uranus, and Neptune are all oblate spheroids like the earth. However, smaller rocky planets like Mercury and Mars have more irregular shapes due to their smaller size and lack of a significant atmosphere.

5. How does the earth's shape affect our daily lives?

The earth's round shape has a significant impact on our daily lives. For example, it is responsible for the changing of seasons, the earth's magnetic field, and the ocean tides. It also allows us to accurately navigate using tools such as GPS, and it plays a crucial role in our understanding of the universe and our place in it.

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