(49) Because the earth rotates about its axis, a point on theequator experience

Question

(49) Because the earth rotates about its axis, a point on theequator experience a centripetal acceleration of 0.0337 m/ s s ,whereas a point at the poles experience no centripetalacceleration. (a) Show that at the equator the gravitational forceon an object must exceed the normal force required to supportthe object. That is, show that the object's true weight exceeds itsapparent weight. (b) What is the apparent weight at the equator andat poles of a person having a mass of 75.0kg? Assume the earth is auniform sphere and take g = 9.800 m/ss .

Explanation / Answer

(a)      By applying Newton's secondlaw:                   - T + m g = m a                    or T = m g - m a Tension will be down ward at equator so to balance the object,true weight m g > > ma (apparent weight) (b)      Weight of person               T = mg    at ploes                   = 75 * 9.8   = 735 N down atploes At equator , apparent weight is :                  T1 = m g - m a                        = 75*9.8 - 75*0.0337                         =732 down at equator. Hope this helps u!

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