The setup shown by the diagram below was used to calculate the force experienced by a small mass m situated at a distance r from the geometric center of a spherical shell with mass M, radius R, and a wall thickness of t. M C de R 0 Rde A Rsine B r l dF l Ф p m If the mass is situated outside the spherical shell, the force can be calculated by integration from = (r-R) to l (r+ R), as shown here: l=r+R R - JdF - T Compar (14²=² de = 1+ dl l=r-R What would the limits of integration be if the mass were situated inside the spherical shell? Include a labeled diagram to represent this situation.

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1. The setup shown by the diagram below was used to calculate the force experienced by a small mass m
situated at a distance r from the geometric center of a spherical shell with mass M, radius R, and a wall
thickness of t.
M
=
с
dᎾ
R
0
Rde
A
B
Rsine
r
l
r
Ф
p
dF
l
If the mass is situated outside the spherical shell, the force can be calculated by integration from l = (r - R)
(r+ R), as shown here:
to l
l=r+R
R
-
5 d² - T Gompert (1+²^²=R²) 21
SdF =
Jae
l=r-R
m
What would the limits of integration be if the mass were situated inside the spherical shell? Include a
labeled diagram to represent this situation.
Transcribed Image Text:1. The setup shown by the diagram below was used to calculate the force experienced by a small mass m situated at a distance r from the geometric center of a spherical shell with mass M, radius R, and a wall thickness of t. M = с dᎾ R 0 Rde A B Rsine r l r Ф p dF l If the mass is situated outside the spherical shell, the force can be calculated by integration from l = (r - R) (r+ R), as shown here: to l l=r+R R - 5 d² - T Gompert (1+²^²=R²) 21 SdF = Jae l=r-R m What would the limits of integration be if the mass were situated inside the spherical shell? Include a labeled diagram to represent this situation.
2. Using the limits of integration from Q1 (above), show that the gravitation force within a spherical shell with
mass M, radius R, and a wall thickness of t is zero. Explicitly show each step. (Hint: there should be at least
eight steps.)
Transcribed Image Text:2. Using the limits of integration from Q1 (above), show that the gravitation force within a spherical shell with mass M, radius R, and a wall thickness of t is zero. Explicitly show each step. (Hint: there should be at least eight steps.)
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