Assume the Earth is a perfect sphere of radius 6,400 kilometers. Find the weight of a 75.0 kg

person at the North pole. Find the weight of this same person at the equator. (You don't need to use
Newton's Law of Gravitation but you do need to analyze the radial/centripetal force.)

Weight(pole) = mg,

Weight (equator) =mg - F(centripetal)=mg - mv²/R

To find the weight of a person at the North Pole and at the equator, we need to consider two forces acting on the person: gravitational force and centripetal force due to Earth's rotation.

At the North Pole:
Since the person is located at the North Pole, the centripetal force due to Earth's rotation is zero. Therefore, the only force acting on the person is the gravitational force.

The weight of a person is given by the equation:
Weight = mass × acceleration due to gravity

Acceleration due to gravity is approximately the same everywhere on Earth's surface and is denoted as "g." So, the weight of the person at the North Pole is:
Weight(NP) = mass × g

At the equator:
At the equator, the person is also experiencing the gravitational force, but there is an additional centripetal force acting outwards due to the person's rotation with the Earth.

The centripetal force acting on the person is provided by the equation:
Centripetal force = mass × (velocity^2 / radius of Earth)

The velocity of the person rotating with the Earth at the equator is given by:
Velocity = (2π × radius of Earth) / (time taken for one rotation)

Although we are not given the time taken for one rotation, we can calculate it using the knowledge that Earth completes one rotation in approximately 24 hours.

Step 1: Calculate the velocity at the equator:
Velocity = (2π × 6,400 km) / (24 hours)

Since we want the answer in meters per second, we first convert the radius of Earth from kilometers to meters:
Radius of Earth = 6,400 km × 1000 m/km = 6,400,000 m

Next, we convert 24 hours to seconds:
Time = 24 hours × 60 minutes/hour × 60 seconds/minute = 86,400 seconds

Now we can substitute the values into the velocity equation:
Velocity = (2π × 6,400,000 m) / 86,400 seconds

Step 2: Calculate the centripetal force at the equator:
Centripetal force = mass × (velocity^2 / radius of Earth)

Finally, we can calculate the weight of the person at the equator:
Weight(Eq) = mass × (g + (velocity^2 / radius of Earth))

Substitute your given values of mass and g into the equations to find the weight of the person at the North Pole and at the equator.