Calculating Gravity: Determine G from Acceleration

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The discussion focuses on calculating the gravitational constant G from the acceleration of two spheres with masses of 1.00 g and 100 kg, positioned 15.0 cm apart. The smaller sphere moves 0.534 mm towards the larger sphere in one minute, leading to an acceleration calculation of 0.3 m/s². The user also explores using Newton's second law to derive acceleration, resulting in a different value of 2.9 x 10^-7 m/s², highlighting a discrepancy in the methods used for calculation.

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Miike012
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Sorry.. I think I posted this post already but I can't find the original thread..

Problem:
Two spheres of masses m = 1.00 g and m' = 1.00 * 10^2
kg are isolated from all other bodies and are initially at
rest, with their centers a distance r = 15.0 cm apart. One
minute later, the smaller sphere has moved 0.534 mm
toward the larger sphere. Compute the acceleration and
the value of G.

Solution:
Acceleration: x = xi + Vxi(t) + (a)(t^2)/2

0.149m = a(1s)^2/2
a = (0.149m)(2) = 0.3 m/s/s

Is this correct for acceleration?

Could I have also used Newtons second law some how to solve for acceleration?
such as...
F = (m1)(m2)(G)/.149^2 = 2.98*10^-11
F = F1... 2.98*10^-11 = (m1)(a)
a = 2.98*10^-11/m1 = 2.9*10^-7

But obviously these answers are not the same...
 

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