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A cone is glued to a hemisphere. When you place it on a table in what position does it come to rest?

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More Bridge Building


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Stage: 5 Challenge Level: Challenge Level:1

Andre from Tudor Vianu National College, Bucharest, Romania produced a good solution to this question. Can you build on these ideas to answer the extension parts of the question?

The net force on the horizontal axis must be zero at each pin joint, so the projections of the forces on X and Y on the horizontal axis must have opposite directions. So, even if we do not know their magnitude we can still determine whether they are in compression or in tension.

If X is under tension then we must have:

The forces must be symmetrical in respect to a vertical axis which passes through the central weight. Starting from the left toward the centre, I obtained the following type of forces throughout the framework:

For the second part, a similar analysis shows that the structure must be as follows:

There would be a net downward force at P, so the equilibrium would not be stable.