Density, Pressure and Upthrust

Density

p=mv

Archimedes principle

upthrust=weight (volume) of liquid displaced

-When an object is immersed in a fluid, the fluid exerts an upwards force (upthrust) equal to the weight of the volume of fluid displaced by the object

stokes law

F=6πηrv

upthrust

The object pushes away some water in a process called displacement

• The water creates a pressure difference between the top and bottom of the object as a result of more weight lower down in a column of fluid

• This creates a resultant force upwards called upthrust, which has a magnitude equal to the weight of displaced water

Terminal Velocity

Terminal velocity is the constant maximum velocity an object reaches when falling through a fluid

- the resultant force acting on the object is zero.

-This occurs when the drag force equals the weight of the object.

terminal velocity equation

m=pv

(sphere as stokes law) — v=4/3πr³

upward force balanced by downwards as moving at constant velocity

weight=upthrust

mg=Fv + u

u=M(f) x g

u=(Pf x v) x g

so

mg=Fv + (Pf x v) x g

m=Do x Vo

PoVog=Fv + (Pf x v) x g

Fv = 6πηrv

PoVog=6πηrv + (Pf x v) x g

and

v=4/3πr³

so

4/3πr³Pog=6πηrv + 4/3πr³Pfg

-band is too near surface of honey so ball wont fall at terminal velocity

-and there is no actual method for checking the ball is falling at terminal velocity

v=s/t

v=4/3πr³

v=vg(ps-pl)/6πrη