Exercise 10A: The Shell Theorem
This exercise is an approximate numerical test of the shell theorem. There are seven masses A-G,
each being one kilogram. Masses A-E, each one meter from the center, form a shape like two Egyp-
tian pyramids joined at their bases; this is a rough approximation to a six-kilogram spherical shell of
mass. Mass G is five meters from the center of the main group. The class will divide into six groups
and split up the work required in order to calculate the vector sum of the six gravitational forces
exerted on mass G. Depending on the size of the class, more than one group may be assigned to deal
with the contribution of the same mass to the total force, and the redundant groups can check each
otherís results.
1. Discuss as a class what can be done to simplify the task of calculating the vector sum, and how to
organize things so that each group can work in parallel with the others.
2. Each group should write its results on the board in units of piconewtons, retaining six significant
figures of precision.
3. The class will determine the vector sum and compare with the result that would be obtained with the
shell theorem.
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