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 103-kg person at the equator.

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

c.) Calculate the weight of the person.

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

To answer these questions, we'll need to use some basic physics principles and formulas. Let's go through each part step by step:

a.) Calculate the speed of a 103-kg person at the equator.
The speed of a person at the equator can be calculated using the formula for tangential speed:

Speed = radius x angular speed

The radius of the Earth is given as 6400 km, which we need to convert to meters (1 km = 1000 meters). The angular speed can be calculated using the fact that the Earth completes one full rotation in 24 hours.

Radius = 6400 km = 6400 x 1000 meters = 6,400,000 meters
Time taken for one full rotation = 24 hours = 24 x 60 x 60 seconds = 86,400 seconds

Angular speed = (2π rad) ÷ (time taken for one full rotation)
= 2π rad ÷ 86,400 seconds

Now we can calculate the speed of the person:

Speed = 6,400,000 meters x (2π rad ÷ 86,400 seconds)

Calculate this expression to find the speed of the person.

b.) Calculate the force needed to accelerate the person in the circle.
The force needed to accelerate the person in the circular path is provided by the centripetal force. The centripetal force can be calculated using the formula:

Centripetal force = mass x (tangential speed)^2 ÷ radius

We have the mass of the person (103 kg) and the speed calculated in part (a). Use this information to calculate the centripetal force.

c.) Calculate the weight of the person.
The weight of a person can be calculated using the formula:

Weight = mass x g

Where g is the acceleration due to gravity, approximately 9.8 m/s^2. Use the given mass of the person (103 kg) and the value of g to calculate the weight.

d.) Calculate the normal force of Earth on the person, that is, the person's apparent weight.
The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, it is the force exerted by the Earth on the person. According to Newton's third law of motion, the normal force is equal in magnitude and opposite in direction to the weight of the person.

The normal force can be calculated using the formula:

Normal force = Weight

So, the normal force is equal to the weight of the person calculated in part (c).

Calculate all the necessary values to get the answers to parts (a), (b), (c), and (d).