fallingsphere - Phys374, Spring 2006, Prof. Ted Jacobson...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the 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 , 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....
View Full Document

Page1 / 3

fallingsphere - Phys374, Spring 2006, Prof. Ted Jacobson...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online