Tuesday, April 5, 2011

The Physics Of Flopping

My son, who weighs around 59 kg (~130 lb), flops onto his bed from a distance of about 0.5 meters above it. From standing to sitting he has accelerated to approximately 4.9 m/s by the time he hits the mattress, assuming it takes him about 0.5 seconds to go from standing to sitting. At the moment when he hits the mattress the force he's applying to it and the frame is about 289.1 kg*m/s. He's had this bed for about 5 years now, or about 1,931 days.

So if we average out flopping down about once per day for that time period, and average out his weight from then until now (say, about 40 kg as the average), then we have:

1,931 days * 40 kg * 0.5 s * 9.8  m/s2  =  378,476 kg*m/s of force over that time period!

That's the equivalent of a 909 kg (1 ton) car traveling at 1,499 km/h (~931 miles/hour), just amortized over five years.

Is it any wonder that he broke the bed's frame this evening?