Problem 4.3 -- Create a force balance for the 'HOOP STRESS'
I won't say much about this problem, except that you often see a 'hoop stress' when dealing with a cylindrical member in which the internal pressue exceeds the external pressure by some amount, 'p':
To facillitate a FORCE BALANCE for a cylinder [or band] with net internal pressure, you can:
Model by cutting the cylindrical band down the middle
Find the net force from the PRESSURE on this ('cut') half.
By symmetry, this net force is clearly vertically 'upward' here.
The band can only provide a TENSION force.
Balance the tension with the net force due to pressure.
Problem 4.3 does not involve a pressure
force, but perhaps this treatment of a hoop stress resulting from
pressure forces can guide your thinking on balancing all the forces generated by the spinning of the metal band.
