IGCSE Physics 0625: Centre of Gravity, Base Width and Toppling

A furniture designer is comparing two possible designs for a free-standing wooden bookcase. Both designs have the same total mass and the same overall height. Design 1 has a narrow rectangular base, with most of its mass in the upper shelves. Design 2 has a wider rectangular base, with heavy storage drawers built into the very bottom of the unit.

(a) State two features of an object's design, other than its total mass, that affect how easily it topples over. [2]

(b) Explain, in terms of the position of the centre of gravity and the width of the base, why Design 2 is less likely to topple over than Design 1. [3]

(c) The bookcase is gradually tilted to one side, for example because it is standing on a slightly uneven floor. Describe, in terms of the centre of gravity and the base of the bookcase, the condition at which it would just begin to topple over rather than settle back down. [2]

Part (a): Design features affecting toppling

Two features (other than total mass) that affect how easily an object topples over are:

the width of its base, and
the height of its centre of gravity above the base.

Part (b): Why Design 2 is more stable

Because Design 2 has heavy drawers built into the very bottom of the unit, its overall centre of gravity is lower than Design 1’s, whose mass is concentrated in the upper shelves. Design 2 also has a wider base than Design 1.

Both of these differences matter for the same reason: an object topples over once the vertical line through its centre of gravity moves outside its base. A wider base means the centre of gravity has further to move sideways before it reaches the edge of the base, and a lower centre of gravity means the object must tilt through a larger angle before that vertical line reaches the edge of the base at all. So Design 2, with a lower centre of gravity and a wider base, can be tilted much further than Design 1 before it topples over.

Part (c): The condition for toppling

As the bookcase is tilted, it will return to its upright resting position as long as the vertical line through its centre of gravity still passes through its base. The weight then produces a moment that turns it back upright.

The bookcase will just begin to topple over at the moment the vertical line through its centre of gravity moves to just outside the base of the bookcase. Beyond this point, the weight produces a moment that continues to turn the bookcase over, rather than restoring it to the upright position.

Final answers

(a) Base width and height of the centre of gravity above the base
(b) Design 2 has a lower centre of gravity and a wider base, so it must tilt through a larger angle before toppling, making it more stable than Design 1
(c) Toppling begins once the vertical line through the centre of gravity moves outside the base of the bookcase