Asked by ajay
calculate the gravitational potential energy of a system of 8 masses of 10 kg each placed at the corner of qube of each edge equal to 0.25meter.
Answers
Answered by
drwls
The gravitational will be negative, because gravity helps pull them together.
For each pair of masses separated by R, the G.P.E. is -GM^2/R
(G.P.E. = gravitational potential energy)
For each of the eight masses, add up the GPE due to the presence of the other seven. Three will be at distance R = a, three will be at disance R = a*sqrt2, and one will be at distance R = a*sqrt3
a is the side length of the cube
Since all eight masses have the same relationship to the other seven, multiply the previous step by 8.
Divide by 2 to correct for double counting of pairs.
Result: G.P.E. = -4 (GM^2/R)*(3 + 3/sqrt2 + 1/sqrt3)
Check my thinking
For each pair of masses separated by R, the G.P.E. is -GM^2/R
(G.P.E. = gravitational potential energy)
For each of the eight masses, add up the GPE due to the presence of the other seven. Three will be at distance R = a, three will be at disance R = a*sqrt2, and one will be at distance R = a*sqrt3
a is the side length of the cube
Since all eight masses have the same relationship to the other seven, multiply the previous step by 8.
Divide by 2 to correct for double counting of pairs.
Result: G.P.E. = -4 (GM^2/R)*(3 + 3/sqrt2 + 1/sqrt3)
Check my thinking
Answered by
JITENDRA
-4.067*10^-7