## Sunday, October 28, 2012

### Physics of Dunking a Basketball

By Kathryn Taylor

Basketball players exert a huge amount of force when they are jumping and cutting during games. Dunking is one of the skills that requires the greatest amount of force to jump as high as possible and virtually drop the ball downwards through the hoop. In his day Michael Jordan was one of the greatest dunkers and was known as Air Jordan.

To make the situation a little simpler I am going to look at dunking a ball from just standing under the rim. This takes away the horizontal component of the situation which would have little effect anyway as there is negligible acceleration in that direction. Michael Jordan is 6’6” (1.98m) and in his playing days weighed 216lb (98kg) and would be dunking a ball of 624g. I found that he was thought to have a reach of 8’10” (2.7m) (http://thekitchensinkhole.blogspot.com/2007/02/
sinkhole-vertical-leaps.html). This means that the change in height for Michael Jordan dunking on a regulation rim (10’) would be just 1’2” (0.35m). This means that the minimum work done by his jump would be equal to ΔPE= mgΔh = (98+0.624kg)*(9.8m/sˆ2)*(0.35m) = 338.3J. This work was done over the distance that his knees bend which can be estimated to around 3’ (0.9144m). Using this the minimum applied force by Jordan into the ground to dunk the ball is equal to Work/distance = (338.3J/0.9144m)=370N.

The Guinness World Record dunk of 12ft was set by Michael “Wild Thing” Wilson who is part of the Harlem Globetrotters. For Jordan to complete this dunk his work would be mg
Δh = (98.624kg)*(9.8m/s^2)*(0.96m) = 927.9J. This relates to an applied force = (927.9J/0.9144m)=1014.7N. This is a huge increase in force required for a dunk only 2 feet higher than regulation.

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