Question

An early major objection to the idea that Earth is spinning on its axis was that Earth would turn so fast at the equator that people would be thrown off into space. What centripetal force is needed for a person of mass 69.6 kilograms at the equator? The radius of Earth is about 6400 kilometers. Include units in your answer. Answer must be in 3 significant digits.

Answer 1

2.35 N

Explanation:

The centripetal force can be calculated using the following formula:

`Fc_{}=(m\cdot v^2)/(r)`

We need to calculate the speed in order to find the centripetal force since we know the mass ( 69.6 kilograms) and the radius (6400000 meters). The speed is given by the distance traveled (perimeter of the earth) divided into the time spent in one revolution (the period), that is, one day (86400 seconds).

`\begin{gathered} v=(2\cdot3.14\cdot6400000)/(86400) \\ v=465.19\text{ m/s} \end{gathered}`

Replacing:

`\begin{gathered} F_C=(69.6\cdot465.19^2)/(6400000) \\ F_C=2.35\text{ N} \end{gathered}`

The centripetal force is 2.35 N