17. Five cylinders are placed between two smooth walls. The weights of the five cylinders are independently and normally distributed with w_i ~ N(µ_i, σ_i), i=1,2,…5, where w_i=20 lb (i=1,2…5), and σ₁=0.1, σ₂=0.2, σ₃=0.3, σ₄=0.4 and σ₅=0.5, respectively. Determine the normal reactions at points A and B.

Solution

All cylinders:

Since five cylinders follow their own normal distributions independently, we can obtain

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Bottom coin:

Then, we can have

Also, we have

Finally, we can obtain

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