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Exercise 10A: The Shell Theorem

A

B

C

D

E

F

G

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

other’s 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.