A rigid display stand weighs 100 N. When tilted about its right-hand base edge, the vertical line through its centre of gravity is first 9 cm inside that edge, and after further tilting 7 cm outside it. (a) Calculate the magnitude of the weight's moment about the edge in each position. (b) Explain which position is stable against toppling when released. (c) Describe how to find the centre of gravity of a thin irregular card experimentally.

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Accepted Answer

9 N m restoring; 7 N m toppling; use intersecting plumb lines from different suspension points. A moment uses the perpendicular distance from the pivot to the force's line of action. In the first position the magnitude is 100 × 0.09 = 9 N m after converting centimetres to metres. The centre-of-gravity line is inside the support edge, so weight tends to rotate the stand back towards its base. The restoring moment makes this position stable against toppling on release, assuming the base does not slip. In the second position the magnitude is 100 × 0.07 = 7 N m. The line is outside the base, reversing the moment's sense so the stand topples farther outward. Suspend the card freely from one point and mark the vertical line indicated by a plumb line. Repeat from another point; their intersection locates the centre of gravity. A third suspension checks the construction, and the card must swing without frictional restraint.

A tilted display stand 7

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