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If the earth has a radius of 6.4 x 10^6 and it spins once per day, what is the centripetal force on a 100 kg man who is on the equator? This would make him weigh (less/more) by ____N

User Ben Gates
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1 Answer

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Answer:

The spinning of the Earth would make him to weigh less.

Step-by-step explanation:

Given data,

The radius of the Earth, R = 6.4 x 10⁶ m

The rotational period, T = 86400 s

The mass of the man, m = 100 kg

The centripetal force at equator,

f = m v²/R

Since,

T = 2π/ω & v = Rω

v²/R = 4π²R/T²

Substituting in the equation for centripetal force,

f = 4π²mR/T²

Substituting the values,

f = 4π² x 100 x 6.4 x 10⁶ / 86400²

= 3.39 N

The centripetal force is directed along the radius towards the center, the centrifugal force acts opposite to it.

The gravitational force acting the man towards the center,

F = mg

= 100 x 9.8

= 980 N

The net force acting on the person,

F' = F - f

= 980 N - 3.39 N

= 976.61 N

Hence, this would make him to weigh less.

User Yonnaled
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