What is the drag coefficient of the cue ball

[Paulbird20]

Homework Statement

hile playing pool on a cruise ship, you accidentally hit the cue ball over the railing and it falls into the ocean below. If the cue ball (a sphere of diameter = 57.15 mm, m = 160 g) reaches a terminal velocity of 1.55 m/s in the water (), what is the drag coefficient of the cue ball in water?

Homework Equations

Cd= Fd/ 1/2 pv^2A
Cd= coef of drag
Fd= drag force
p = mass density of the fluid
V= speed
A = area of the sphere

The Attempt at a Solution

Ok from the above equation i am able to determine all of the items except Drag force

I got the area from pi * d^2 for the sphere (pi*55.15^2= 10260.82)
adn the rest you can fill in

I am stuck trying to figure out the drag force

 

[mgb_phys]

At terminal velocity the gravity force downwards is equal to the drag force upward.

 

[Paulbird20]

even when in water?

 

[Paulbird20]

so M * G ---) 1.568 = drag force?

 

[Paulbird20]

air is less dense than water is why i ask

 

[Paulbird20]

also converting the Area to m 10.26m is that correct?

 

[Paulbird20]

if my numbers are correct i arrange the problem

1.56 / (1/2 * 1000*1.55^2 * 10.26)

doing the math Coefficient of drag = 1.26e-4?

 

[Paulbird20]

i feel like I am making a mistake in converting the reference area since the object is falling

 

[mgb_phys]

It's the cross sectional area, so pi r^2 is correct, it would be safest to work in metres