How much more does a 71kg man weigh at the north pole than at the equator? (in newtons)

Question

mrnood · Answer

you asked this question recently before - all the points made in the  last answers are still true and valid.

Unless you are given values for the variables to be used you are unlikely to get an answer that matches your online information.

6 - 7 N is the answer if you take into account the rotation effect, or 4-5 N if only taking the gravity effects

anonymous · Answer

So far I found 3.55, 3.692, and 4.615 are incorrect
So its likely im doing something wrong to get lower numbers?
How would you take in the rotation effect?
This question is frustrating...

anonymous · Answer

The question also says to assume the earth is a perfect sphere, Im not sure if I mentioned that or if it would be helpful

mrnood · Answer

but as I pointed out before - you are entering a value to 3 decimal places.

It is probable that the online has a value to 0,1 or 2 dp and oyu do not know which.

Any value oyu calculate will be based on figures for G an rpole, requator , each of which has some potential for error.

I think you understand the GMm/r^2 formula
that gives you the gravity effect due to difference in radius of earth.

Now consider the body at the equator - it is travelling in a circle and therefore is accelerating, so some of the gravity force is 'used up' in accelerating the body in the circle. (The body at the pole has a radius of 0 - therefore no force)

the value of that force is mrw^2  (where w is angular velocity)

This works out at pretty much 2N at the equator - but its precise value is subject to the same errors in value for radius.

NOte - some people would call this 'centrifugal force' but I resist this term because there is truly no 'outward force' - just a reduction of the inward gravity force

mrnood · Answer

AHHHHHH!
the perfect sphere means that you IGNORE the gravity force as the radius is 'constant'

SO

mrw^2 is your equation

PLEASE post ALL information when asking here - mostly info is not put in a questin unless it is required.

you need w (in rad/s  i.e. 2pi rad in 24hrs) and r (get it from google - otr the question

m = 71kg

the answer is very close to 2N

anonymous · Answer

wait what is w? we never went over that in class

mrnood · Answer

I said above w (actually normally written as omega) is earths angular velocity

You need to have it in rad/s

Earth rotates 2 pi rad in 24hours approx