This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 ρ , and the speed of the sphere through the air v . Only one combination of these three quantities has the dimensions of force: F drag ∝ ρR 2 v 2 . (1) We can’t infer the dimensionless coefficient. Let’s define b as the product of this unknown coefficient times ρR 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 Newton’s 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. Let’s work out the details....
View
Full
Document
This note was uploaded on 12/29/2011 for the course PHYSICS 374 taught by Professor Jacobson during the Fall '10 term at Maryland.
 Fall '10
 Jacobson
 Force

Click to edit the document details