Coefficient of drag of a ping pong ball

[Dayton]

Homework Statement

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.

Homework Equations

The Attempt at a Solution

 

[sonnyfab]

Your logic is sound: the answer supplied is incorrect

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

 

[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:

Just think a little bit simpler, if you have two objects that
has strong friction between them then it will hard to move
one of the object. In this case, CD >> 1.

If you do not have friction (CD = 0), then it will be
very easy to move it. In this case, Fd = mg = Cd*0.5*v*v*Area
if CD = 0, area is not zero, then v must be super larger
because mg is not zero. The ping pong ball will fly to infinite!

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

 

[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