Forces Acting on Person Standing at Earth's Equator

In summary, the Earth is a rotating uniform sphere with a constant speed of v at its equator. A person standing on the equator would experience the following forces: gravity, normal force, friction at the point of contact with the Earth, and a centripetal force. Despite the constant speed, the person would still experience a net force towards the center of the Earth due to the changing direction of the velocity, resulting in acceleration. This is why a net force is necessary for an object to accelerate, even if its speed remains constant.
  • #1
forty
135
0
(a) Assume that the Earth is a uniform sphere with a radius r which rotates such that the speed of the ground at the equator is v which is constant.

(i) Draw a diagram showing the forces acting on a person standing on the equator.

There would be the following forces acting on the person:

Gravity (mg)
Normal (-mg)
Friction at the point of contact to the earth
Centripetal force (?)

(ii) Explain why a person in this situation must experience a net force even though their speed is constant.

Does this have to do with the centripetal force? So they need to have a net force towards the center of the earth??



Any help with these would be greatly appreciated.
 
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  • #2
Since you are talking about force diagrams, I assume you know about vectors. In (ii) the question says that [itex]|\vec v|[/itex] is constant, but is [itex]\vec v[/itex] constant as well?
 
  • #3
so the magnitude of v is constant but the direction is changing hence you are accelerating and if you are accelerating your are experiencing a net force?
 
  • #4
forty said:
so the magnitude of v is constant but the direction is changing hence you are accelerating and if you are accelerating your are experiencing a net force?
Absolutely. So redo your analysis of the forces acting on the person.
 

1. What is the Coriolis effect and how does it impact a person standing at the Earth's equator?

The Coriolis effect is a phenomenon caused by the Earth's rotation. It causes objects (including people) to appear to veer to the right in the Northern Hemisphere and to the left in the Southern Hemisphere. This is due to the different speeds at which different latitudes on Earth are rotating, with the equator rotating the fastest. However, the Coriolis effect is not strong enough to be noticeable on the scale of a person standing on the Earth's surface.

2. How does the Earth's rotation affect the weight of a person standing at the equator?

The Earth's rotation causes a centrifugal force at the equator that counteracts the force of gravity. This means that a person standing at the equator would weigh slightly less than they would at the poles. However, this difference is very small and would not be noticeable to a person.

3. Are there any other forces acting on a person standing at the Earth's equator?

Aside from the Coriolis effect and the centrifugal force caused by the Earth's rotation, the main force acting on a person at the equator is gravity. This is the force that keeps us on the surface of the Earth and is responsible for our weight. Other forces, such as air resistance and friction, may also be acting on a person, but they would be too small to have a noticeable effect.

4. How does the Earth's bulge at the equator affect the forces acting on a person standing there?

The Earth's equatorial bulge, caused by its rotation, does not have a significant effect on the forces acting on a person standing at the equator. This is because the gravitational force is still perpendicular to the surface of the Earth, regardless of its shape. The slight increase in distance from the center of the Earth at the equator may slightly decrease the force of gravity, but as mentioned before, this difference is very small.

5. Can a person feel the forces acting on them at the Earth's equator?

No, the forces acting on a person standing at the Earth's equator are too small to be felt by a person. The effects of the Coriolis effect, centrifugal force, and gravitational force are all too subtle to be noticeable at the scale of a human. However, these forces do have a significant impact on larger scale phenomena, such as ocean currents and weather patterns.

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