high jumper

Physics has given us a great many simple principles that make it easier to understand what’s going on in the world, some better-known than others. To wit: Every action has an equal and opposite reaction; what goes up must come down—both classics, for good reason. And the blingiest of the axioms, E=mc², is particularly useful for understanding why a fistful of plutonium can cause such a big bang. Less famous but far more important on a day-to-day basis if you’re an SUV designer, a high jumper or—as in the present case—a crane operator, is the principle that any object will behave as if all its weight is concentrated at its center of mass.

Finding an object’s center of mass is fairly simple. It’s the point at which half the mass is above the center and half below, half is on the right and half on the left, and half is in front and half in back. If you stand straight up with your arms at your sides, your center of mass is a little below your bellybutton (unless you’re J. Lo). But here’s the important part: If your center of mass is not above your feet, you’re going to fall over. The same principle works for a crane. If the center of mass of the total system—crane plus whatever it’s carrying—moves to one side of the crane’s base, the crane will tip.

As our crane lifts the bus out of the water, trouble is a-brewin’. The water itself is holding up the partially submerged bus. (Remember Archimedes? No? Here: Water pushes up on an object with a force equal to the weight of the water being displaced—this is the reason things feel lighter in water.) As the bus leaves the river, the crane takes on more of its weight until the center of mass shifts so far away from the crane’s arm that suddenly there’s a tip, a splash and the call for a bigger crane. —Michael Moyer

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