Because the Earth rotates about its axis, a point on the equator experiences a c

Question

Because the Earth rotates about its axis, a point on the equator experiences a centripetal acceleration of 0.033 7 m/s2, whereas a point at the poles experiences no centripetal acceleration. Assume the Earth is a uniform sphere and take g = 9.800 m/s2. (a) If a person at the equator has a mass of 75.6 kg, calculate the gravitational force (true weight) on the person. (b) Calculate the normal force (apparent weight) on the person. (c) Which force is greater? the normal force the gravitational force

Explanation / Answer

a) Gravitational Force = m*ac = 75.6*0.0337 = 2.55 N

b)   Let : ac = 0.0337 m/s^2    and m = 75.6 kg

Since the centripetal acceleration of a person is inward (toward the Earth’s axis),

Fc = m*ac = m*g Wa ==========>   Wa = m(g - ac) = 75.6(9.8 - 0.0337) = 738.33 N = Normal Force

c) From a) and b) its clear that normal force is greater than gravitational force.

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