peripatein
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Hello,
I am supposed to find an expression for the general stress wrt height within a truncated cone of lower and upper radii a and b (a>b), pulled down from its vertical axis by a force of the same magnitude as that pulling it up. The diagram implies that the height between the upper and lower base is h (see attached diagram).
Attempt at solution:
I did (a-b)/h = (a-r)/h' (since the slope is similar even at height h' from lower base of radius a),
From which I could find r and hence the difference in the stress: F(1/A_a - 1/A_r) where A_x denotes the surface area of radius x.
I am really not sure this is how it should be done. My initial inclination was to use integrals.
Should it indeed be done the way it is presented above? Please advise.
I am supposed to find an expression for the general stress wrt height within a truncated cone of lower and upper radii a and b (a>b), pulled down from its vertical axis by a force of the same magnitude as that pulling it up. The diagram implies that the height between the upper and lower base is h (see attached diagram).
Attempt at solution:
I did (a-b)/h = (a-r)/h' (since the slope is similar even at height h' from lower base of radius a),
From which I could find r and hence the difference in the stress: F(1/A_a - 1/A_r) where A_x denotes the surface area of radius x.
I am really not sure this is how it should be done. My initial inclination was to use integrals.
Should it indeed be done the way it is presented above? Please advise.
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