Relation of Pressure and Weight of Air.

[las2vc]

The problem is in the context of your being a volleyball team manager and having to fill up the balls before a match...

The question itself reads as follows:

The game is only an hour away, so you start putting air in the first of your volleyballs. You open the ball's inlet valve and the ball fills with ordinary air at normal atmospheric density and temperature. The air in the volleyball now has a real (i.e., gravitational) weight of 0.1 Newtons. When you place the ball on a scale, what measured weight does the scale report for the volleyball? Briefly explain the value reported by the scale.

I cannot determine whether or not the ball would have any mass or not because in the opener of the problem set, my professor has stated that the skin of the ball has zero weight. Does this mean that the ball would weigh, in fact, zero? I find it hard to believe that air would weigh nothing, but I was discussing this with a friend and they tried to use the analogy of a vase-- technically there's still air in the vase since it's not a vacuum, but would that weight register on a scale?

I tried thinking of air as a fluid and buoyant forces, but since the ball isn't floating, I'm not sure. I'm leaning toward zero weight just because the ball has same pressure as the weight around it, but I'm not sure this is the correct weight, or if it is the right answer, I can't articulate the logic behind it very well.

Thanks for your help!

Laura.

 

[Pythagorean]

Think about what medium you're measuring it in. If you're measuring the weight of air in air, does it have any meaning?

What about more dense air in less dense air (the case of the basketball)?

 

[kyle8921]

I would say that the weight of the air inside the volleyball is directly related to the pressure inside the ball. This is because the weight of the air is a result of the force of gravity acting on the mass of the air molecules. Therefore, as the pressure inside the ball increases, so does the weight of the air inside the ball.

In the context of filling up volleyballs before a match, it is important to consider the relationship between pressure and weight of air. This is because the amount of air needed to fill the ball to the desired pressure will also determine the weight of the ball. A ball filled with more air will have a higher pressure and therefore a higher weight.

Now, to address the question of whether the ball would have any mass or not, it is important to understand that air does have mass, but it is very small. The weight of air is usually measured in grams or kilograms, and in this case, the weight of the air inside the volleyball is 0.1 Newtons. This weight would be registered on a scale, but it may not be significant enough to make a noticeable difference in the overall weight of the ball.

In terms of the analogy of a vase, it is important to note that the air inside the vase is not under pressure, as it is free to move and expand. However, in the case of a volleyball, the air is confined and under pressure, which is why it can affect the weight of the ball.

In conclusion, the weight reported by the scale for the volleyball would be the combined weight of the ball and the air inside it. The weight of the air may be small, but it is still present and contributes to the overall weight of the ball. As a volleyball team manager, it is important to ensure that the balls are filled to the correct pressure, as this can affect the weight and performance of the ball during the game.