# Coefficient of drag of a ping pong ball

1. Jul 25, 2013

### Dayton

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

This problem is from a homework assignment. The professor says that the the ping-pong ball will go up if the cd = 0 and will go down if the cd is much larger than one. Is this logic correct? I keep thinking about how if an aerodynamic car is pushed by wind, the car with the larger cd will go be pushed harder.

2. Relevant equations

3. The attempt at a solution

2. Jul 25, 2013

### sonnyfab

Your logic is sound and the answer that you wrote down is backwards from correct. You might have copies it wrong, or your professor might have written it down incorrectly from his notes.

Here's how to see that if C$_{d}$ = 0, the ball drops.

The ball accelerates in the direction of the net force.

There is a downward force from gravity. The upward force is the "drag" because drag is the force from air on an object.

Rearranging your equation, F$_{d}$ = ρv$^{2}$AC$_{d}$/2.

The net force is F$_{d}$ - mg, upward.

If C$_{d}$ is 0, then F$_{d}$ is also 0, and the ball has acceleration of -mg. Gravity is the only force acting on the ball.

Clearly, when C$_{d}$ is very large, then F$_{d}$ is also very large and the ball is pushes upwards to infinity (and beyond.)

Hope this helps.

Dr Peter Vaughan
BASIS Peoria Physics

3. Jul 26, 2013

### Dayton

Thanks

Ok, I thought that that reasoning was correct.

My professor replied with this when I emailed to ask if my car analogy was correct:

I just want to be sure if my logic was correct before I ask him about it again.

4. Jul 26, 2013

### sonnyfab

He seems to be referring to "drag" as a force that is additional to the blow dryer force and pointing downward. That is not my (nor your) interpretation. My advice: draw two free body diagrams: one with gravity down and "drag from vacuum cleaner" going up, and another with "force from vacuum cleaner" upwards and BOTH gravity and drag down. Ask him which one is correct. Than you'll know both what the problem is asking, and how to solve it.

Dr Peter Vaughan
BASIS Peoria Physics