Step-by-step explanation:
The centripetal force acting on a 75 kg person standing at the equator of the earth due to the earth's rotation on its axis can be calculated using the following formula:
F = m x a
where F is the force, m is the mass of the person, and a is the centripetal acceleration.
The centripetal acceleration can be calculated using the formula:
a = v^2 / r
where v is the tangential velocity and r is the distance from the axis of rotation (in this case, the radius of the earth at the equator).
At the equator of the earth, the radius is approximately 6,378 km, and the earth completes one rotation in approximately 24 hours. Therefore, the tangential velocity can be calculated as:
v = 2 x pi x r / T
= 2 x pi x 6,378,000 m / 86,400 s
= 465.1 m/s
Using this value for v, the centripetal acceleration can be calculated as:
a = v^2 / r
= (465.1 m/s)^2 / 6,378,000 m
= 0.0339 m/s^2
Finally, the centripetal force can be calculated as:
F = m x a
= 75 kg x 0.0339 m/s^2
= 2.54 N
If the person moves to the north or south pole, they will be closer to the axis of rotation, so the radius will be smaller. At the poles, the radius is approximately 6,357 km. Using this value for r, the tangential velocity can be calculated as:
v = 2 x pi x r / T
= 2 x pi x 6,357,000 m / 86,400 s
= 368.3 m/s
Using this value for v, the centripetal acceleration can be calculated as:
a = v^2 / r
= (368.3 m/s)^2 / 6,357,000 m
= 0.0341 m/s^2
The centripetal force can then be calculated as:
F = m x a
= 75 kg x 0.0341 m/s^2
= 2.56 N
As we can see, the difference in the centripetal force between the equator and the poles is relatively small, due to the small difference in radius.