# What is the drag coefficient of the cue ball

1. Jul 21, 2009

### Paulbird20

1. The problem statement, all variables and given/known data

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?

2. Relevant 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

3. 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

2. Jul 21, 2009

### mgb_phys

Re: Drag

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

3. Jul 21, 2009

### Paulbird20

Re: Drag

even when in water?

4. Jul 21, 2009

### Paulbird20

Re: Drag

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

5. Jul 21, 2009

### Paulbird20

Re: Drag

air is less dense than water is why i ask

6. Jul 21, 2009

### Paulbird20

Re: Drag

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

7. Jul 21, 2009

### Paulbird20

Re: Drag

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?

8. Jul 21, 2009

### Paulbird20

Re: Drag

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

9. Jul 21, 2009

### mgb_phys

Re: Drag

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