How Does Air Resistance Affect a Moving Tennis Ball?

[jd2]

Homework Statement

For a given tennis ball: Experimentally quantify the frictional effects of air resistance on a moving ball, including data needed to compute...
(1) the frictional force on the ball;
(2) how much of the ball's energy is lost to air resistance as it moves a certain distance;
(3) how the air resistance changes depending on the speed of the ball.

Homework Equations

The Attempt at a Solution

 

[LawrenceC]

All you have done is stated the problem. Unless you demonstrate that you have tried to solve the problem/experiment, we cannot help you.

 

[jd2]

We know that gravity acts on the ball, so through F = ma we can find the weight which would by W(for ball)= mg. We also know equation for frictional force = μkFN. For energy we can use equation such as conservation of energy which states that E(final) = E(initial). But looking at the problem, I don't think energy will be conserved since some of the energy will be lost to air.

Please give me some hints on where to start. How can I start the experiment if I don't have something to compare with. For I could do the experiment inside a place (vacuum) where there is no air resistance and compare my result where there is some but that is not possible?

I don't want any answers, just some advice to steer me in the right direction please.

Thanks

 

[jd2]

We know that gravity acts on the ball, so through F = ma we can find the weight which would by W(for ball)= mg. We also know equation for frictional force = μkFN. But what is then the normal force? Is there any? For energy we can use equation such as conservation of energy which states that E(final) = E(initial). But looking at the problem, I don't think energy will be consumed since some of the energy will be lost to air.

Please give me some hints on where to start. How can I start the experiment if I don't have something to compare with. For I could do the experiment inside a place (vacuum) where there is no air resistance and compare my result where there is some but that is not possible?

So I don't want any answers, just some advice to steer me to the right direction please.

Thanks

 

[LawrenceC]

Air resistance is quite a bit different than the friction on a block moving across a surface. Air resistance is computed by multiplying a drag coefficient by air density, crossectional area of the moving object and finally the velocity squared divided by 2.

Drag = rho*A*v^2/(2*g) if rho is in units of weight per unit volume. If it's mass per unit volume, forget the g. A=pi*d^2/4 for a sphere. Rho=P/RT from ideal gas law. V is the velocity.

You could look up the drag coefficient for a sphere on line. To an extent it is a function of velocity but I would not be concerned about that here as it is beyond the scope of the class you are taking.

You could use a vacuum to do a drop test. If you plan on rolling the ball, there will be some friction due to the rolling. Or you could do a drop test from a height and time how long the ball takes to get to the ground. Then you could calculate how long it should take by using applicable equations. This would provide the same data a drop in a vacuum would produce.

 

[LawrenceC]

The applicable equation I allude to is y = V0*t + .5*g*t^2, where V0 is initial velocity, y is distance fallen, and t is time. g is gravitational acceleration. There are some other equations along this line of analysis that I'm sure you are familiar with.

 

[jd2]

^Thanks a lot! We will be using a string to hang the ball and use a pendulum type set up to test the effects, so in that case there will be no friction due to rolling and so using Drag equation you advised will be the way to go?

Thanks, I will read the article on drag on wikipedia, see what I come up with.

 

[LawrenceC]

"But looking at the problem, I don't think energy will be conserved since some of the energy will be lost to air."

If the ball is dropped, it had an initial potential energy. In the case of zero drag, all the potential energy goes into kinetic energy of the ball. But when there there is friction, the potential energy is divided up between the kinetic energy of the ball and the work the ball does on the atmosphere which can be related to an average force times distance.

 

[jd2]

^ahhh yes! Thanks a lot, now it is making much more sense. So this is more a conceptual question..is the ball's total energy conserved as it moves from point A to point B in a pendulum type motion?
And will the ball's energy be conserved in a second case where as you explained you drop a ball from certain height and it hits the ground. In the introductory physics they say all the total potential energy is converted to kinetic right before the ball making contact with the ground (in an ideal case with no air resistance) but I would think some of the energy will be lost in the collision with ground right? Or is that energy further converted into other form?

 

[LawrenceC]

In pendulum type motion, energy is conserved. The pendulum bob follows an arc so it rises and falls. You have potential energy being converted to kinetic energy as it falls, the KE converts to PE as the bob rises for the second half of its trip. There is a loss. It is air resistance. Once again the force on the bob due to air multiplied by the distance it travels is the work done on the air. The force is not constant because the bob speeds and slows.

With a ball dropping from a height, potential energy is continually being converted to kinetic energy. When it's halfway to the ground, half of the PE is converted to KE, etc,etc. When it hits the ground, all the PE has been converted to KE.

Energy is transformed when the ball hits the ground. Some is used up due to the deformation of the ball - the gas inside will warm slightly, work is being done deforming the ball and the ground and some heat is generated.

If you drop a ball on a hard surface, it never bounces as high as it was before dropped. This is because the collision is inelastic and energy is transformed into other forms.