Early skeptics of the idea of a rotating Earth said that the fast spin of Earth would throw people at the equator into space. The radius of Earth is about 6400 km. Show why this objection is wrong by determining the following information.
(a) Calculate the speed of a 98-kg person at the equator.
m/s

(b) Calculate the force needed to accelerate the person in the circle.
N

(c) Calculate the weight of the person.
N

(d) Calculate the normal force of Earth on the person, that is, the person's apparent weight.
N

a)

b)

c)

d)

Explanation:

For this case we have the following data:

represent the radius of the Earth

The gravity for this case is assumed

m =98 kg represent the mass of the person

represent the angular velocity for the Earth

Part a

Since we need to find the speed of the person at the equator we can use the following formula:

Part b

We can use the formula for the centripetal force for the person at the equator to allow the rotation like this:

And if we replace we got:

Part c

The weight of the person is just defined as:

And if we replace we got:

Part d

The normal force of Earth on the person represent the apparent weight and is given by:

And since we have the weight and the centripetal forc we can replace like this:

unbalanced force

explanation: