Does weight change when someone goes down a well?

Question

Help. I need to know if weight changes when one goes down a hole in the ground like a well. Thanks.

Answer 1

Yes, but probably not by very much. The overall gravitational force will decrease as you approach the center of the earth. But if you are just decending 10 metres or so this will not be a big change.

Answer 2

Yes, your weight decreases as you descend down the well. As far as gravitation is concerned, all the mass of the earth at a radius less than you are can be considered to be concentrated in a point at the centre of the earth, and the rest of the mass has no effect on your weight (because there is no gravitational field contributed by the hollow shell). Your weight at radius r is then given by GMm/r^2 where M is that part of the mass of the earth within the radius r, and m is your mass. As M is proportional to r^3, then your weight is proportional to r^3/r^2, ie proportional to r. That is, your weight varies linearly with your distance from the centre of the earth. So, if you are half way down the hole, you will have half your weight at the top of the hole.

I am assuming for the purposes of the question that the earth is of uniform density, which of course it is not!

Answer 3

Your weight gradually decreases as you go down a well. This is because more of the earth is above you - pulling you up. As mentioned at the centre of the earth you would weigh nothing.

The equation f=GMM/R^2 applies to point masses and the last time I looked the earth was a bit bigger than a point!

Answer 4

If Earth had uniform density, than the weight would decrese.

But since Earth core is made of denser material (like iron),
than crust (like rock), the weight usually first increases
slightly, then start to decrease. When you reach the center
of the Earth, the weight goes down to zero.

Answer 5

if you are talking about your everyday fresh water well, the change in gravity is so minuscule that without an ultra-sensitive detector, you would never notice. this well would have to go well into the mantle before a noticable weight change would occur...

Answer 6

Yes, as one approaches the center of Earth's gravity, one's weight will increase. From the universal gravitation equation:

F=Gm1m2/r^2

The ratio of the two weights of two identical masses at different radii can be given by F2/F1 = r1^2/r2^2.

So if one takes the radius of the Earth as 6400 miles, if one descended one mile their weight would increase by about 0.03%. Not very significant.

However, if one were able to go down about 1000 miles, the increase would approach 50%.

Answer 7

Well Well, a sensible question at last... only if they guzzle quite a lot of water

Answer 8

F=ma
wt=m*g ___________ incase of unif. velocity
wt=m(g-a)__________ incase of ununif. velocity
so if some one goes down a hole his wt will be constant if he moves down with constant velocity but if he/her moves down with acceleration his/her wt will change