## universal gravity

1. The problem statement, all variables and given/known data
A sensitive gravimeter is carried to the top of Chicago's Sears Tower, where its reading for the acceleration of gravity is 0.00136 m/s^2 lower than at street level.

Find the height of the building.

2. Relevant equations

F = GMm/(r^2)

and maybe

K + U = K_o + U_o

3. The attempt at a solution

don't know where to start!
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 consider other units for m/s^2
 Well I think I could use (g - 0.00136) = g_t. I dont know how I could use this though.

## universal gravity

wait could I do this :

(9.8 - 0.00136) = GMm/r^2 ?
 Recognitions: Homework Help Yes, so you can then write ... g*r12 = G*M= (g - .00136)*r22

 Quote by LowlyPion Yes, so you can then write ... g*r12 = G*M= (g - .00136)*r22

what happened to small m

(9.8 - 0.00136)(r^2) = GM (m?)
 Recognitions: Homework Help m*g*r12 = G*M*m= m*(g - .00136)*r22 If that makes you happier. It isn't a factor. F = m*g = GM*m/r2 g = GM/r2
 so, let G_t = (9.8-0.00136); then, G_t*r^2 = GM M = G_t*r^2 / G and r is the radius of the earth and G is the universal gravity constant. m ~ 9.3579 * 10 ^ 17 But what does this mean? This is the mass of th building and....
 Recognitions: Homework Help In case you didn't notice you don't need G and you don't need M and you don't need m. You just need re and g. Building height will be Δr = r2 - r1 where r1 = re
 why is that?
 so (9.8-0.00136) r^2 = GM and GM is just dropped? why?

Recognitions:
Homework Help
 Quote by tnutty so (9.8-0.00136) r^2 = GM and GM is just dropped? why?
The answer is because you can.

g*r12 = (g - .00136)*r22

You just need re and g.

Building height will be Δr = r2 - r1

where r1 = re
 OK, i guess. so (9.8-0.00136) ( 6.37 * 10^6)^2 = R1; R1 - R2 = height of tower R1 ~ 3.976 * 10^14 R2 = (6.37 * 10^6) right I got 6.37 * 10^6 as the radius of the earth from my book.
 Recognitions: Homework Help No. Try being more careful. (6378)2 km = 40678884 now multiply by 9.81/(9.81 - .00136) = ... then take the square root. Then subtract one from the other. Keep as much precision as you can. Your answer will be less than a km. Multiply by 1000 for meters.
 (6378)^2 = 40678884 ans * 9.81 / (9.81-0.00136) = 40684524.26 sqrt(ans) = 6378.44 ??
 confused even more. Dont know where 6378 came from and why sqrt ( ans * 9.81/(9.81-0.00136) ) ... ...

Recognitions:
Homework Help
 Quote by tnutty confused even more. Dont know where 6378 came from and why sqrt ( ans * 9.81/(9.81-0.00136) ) ... ...
I used radius of earth as 6378 km. And g you recognize as 9.81
 sqrt(ans) = 6378.44
Right.

Now 6378.44 - 6378 = .44 km = 440 m = height of building.

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