U physicist James Kakalios explains how the redistribution of energy helped people survive the collapse of the I-35W bridge.
Why so many survived
Physics is one reason the I-35W bridge collapse casualty count wasn't higher
By Deane Morrison
September 7, 2007
When the I-35W bridge fell on August 1, several cars rode the bridge down and came to rest on pieces of pavement in the middle of the Mississippi River. The people who emerged from their cars could count themselves lucky; they had just survived a 60-foot drop. Besides sheer luck, one reason they made it was the way the laws of physics worked in their favor, says University physics professor James Kakalios. "According to the [video] tapes, the bridge took four seconds to fall," Kakalios says. Normally, a 60-foot drop would take close to two seconds. The extra time came from the crumbling of the bridge supports. Or, as Kakalios explains it, from the redistribution of energy. Consider a bridge the size of I-35W falling freely. At rest, it would have a great deal of potential energy; as it fell, it would convert the potential energy to kinetic energy--the energy of motion. The farther it fell, the faster it would go, the more energy it would have, the greater the force needed to slow it down or stop it, and the greater the impact it would have when it finally stopped. When the I-35W bridge fell, the steel girders under the middle part resisted the fall. As they crumbled, they absorbed energy from the falling concrete bridge deck, slowing it down. The energy of the falling bridge also went into pushing a large volume of air out of the way. The energy to set the air in motion came from the kinetic energy of the plummeting structure, and overcoming this air resistance may not have been a trivial matter.
"According to the [video] tapes, the bridge took four seconds to fall," Kakalios says."In autos, 25 to 60 percent of the energy of gasoline is used to fight air resistance," says Kakalios. "Without air resistance, fuel economy would be much higher."
A note on kinetic
Because an object's kinetic energy rises in proportion to the square of its speed, doubling the speed gives the object four times as much kinetic energy. Conversely, cutting the speed by half cuts the kinetic energy down to a quarter of what it would have been. If the falling bridge was indeed slowed from 40 to 20 mph, it's easy to see how the reduction in energy available for doing damage may well have saved lives.