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Unformatted text preview: Phys374, Spring 2006, Prof. Ted Jacobson Falling sphere with air drag force We considered the drag force and argued that to a good approximation it might depend just on the radius of the sphere R , the density of the air , and the speed of the sphere through the air v . Only one combination of these three quantities has the dimensions of force: F drag R 2 v 2 . (1) We cant infer the dimensionless coefficient. Lets define b as the product of this unknown coefficient times R 2 , so F drag = bv 2 . (2) Note that the dimensions of b are M/L . If the sphere has mass m and falls in a gravitational field with grav- itational acceleration g , then Newtons law (taking the down direction as positive) says m dv dt = mg- bv 2 . (3) If the sphere begins at rest it will initially accelerate with acceleration g . As it speeds up the drag force increases until it balances the gravity force. This will happen asymptotically, i.e. in an infinite amount of time. Lets work out the details....
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- Fall '10