Correct statement about movement of curve ball in a fluid

[songoku]

Homework Statement

In a curve ball, the movement of air can be shown below. For each statement, check whether it is true or false
(i) Upward force will act on the ball
(ii) If the rotation of the ball is reversed, then the force acting on the ball is also reversed.
(iii) In the picture, as it rotates, the ball is also moving to the left
(iv) The air below the ball is moving faster than the air above the ball

Relevant Equations

Not sure

(i) Not really sure about this statement but my answer is TRUE because from the picture the air layers on the bottom part of the ball are closer so it means there is force from the ball to push the layers to be closer. Since the ball gives downward force to the air, by Newton's 3rd law, the air will exert upward force on the ball

(ii) I would say this statement is FALSE. Even though the rotation is reversed, there is possibility that the bottom air layers are squeezed closer so direction of force is not reversed.

(iii) Can we determine the direction of movement of the ball from the picture? I mean maybe the ball can move upward, downward, left, right

(iv) This statement is TRUE because at the bottom part the direction of air flow and rotation of the ball is the same while at the top they have opposite direction so at the top part of the ball, the rotation of the ball will obstruct the air movement, causing it to move slower


Are my answers correct and how to determine the direction of movement of the ball?

Thanks

 

[haruspex]

(i) Not really sure about this statement but my answer is TRUE because from the picture the air layers on the bottom part of the ball are closer so it means there is force from the ball to push the layers to be closer. Since the ball gives downward force to the air, by Newton's 3rd law, the air will exert upward force on the ball

Yes, and the reasoning you give is ok. I would have described it as the flow lines are compressed below so the air pressure is greater.

(ii) I would say this statement is FALSE. Even though the rotation is reversed, there is possibility that the bottom air layers are squeezed closer so direction of force is not reversed.

Surely the flow lines are as they are because of the ball's rotation.
To see the effect of opposite spin, just flip the picture upside down.

(iii) Can we determine the direction of movement of the ball from the picture? I mean maybe the ball can move upward, downward, left, right

I think you are supposed to assume the ball has been pitched at a speed rather greater than the wind speed.

(iv) This statement is TRUE because at the bottom part the direction of air flow and rotation of the ball is the same while at the top they have opposite direction so at the top part of the ball, the rotation of the ball will obstruct the air movement, causing it to move slower

Another argument I've seen used is to consider how far the air has to move in the two paths, but I think yours is ok.

 

[songoku]

Surely the flow lines are as they are because of the ball's rotation.
To see the effect of opposite spin, just flip the picture upside down.

I see, so statement (ii) is TRUE

I think you are supposed to assume the ball has been pitched at a speed rather greater than the wind speed.

Sorry I don't understand this. Do you mean the ball is moving against the wind so it is moving to the right?

Another argument I've seen used is to consider how far the air has to move in the two paths, but I think yours is ok.

What do you mean by "how far the air has to move in the two paths"?

Thanks

 

[kuruman]

See Magnus effect.

 

[haruspex]

I have a feeling I have misled you on statement 1. From experience, there should be downward pressure on the ball. And if the air is moving faster under the ball the pressure must be lower there.

I see, so statement (ii) is TRUE

Yes.

Sorry I don't understand this. Do you mean the ball is moving against the wind so it is moving to the right?

I mean the ball is moving sufficiently fast that you can ignore the wind and treat the air as still.

What do you mean by "how far the air has to move in the two paths"?

That the lower stream has further to go around the ball to rejoin the upper stream. Why does it need to rejoin its original neighbours in the upper stream? The ball is not very wide. There needs to be some continuity with the lateral neighbouring air masses.

 

[songoku]

I have a feeling I have misled you on statement 1. From experience, there should be downward pressure on the ball. And if the air is moving faster under the ball the pressure must be lower there.

Ah I see, so statement (i) is FALSE, the force must be downward. This matches the explanation in link in post#4

I mean the ball is moving sufficiently fast that you can ignore the wind and treat the air as still.

I thought the ball would move to the right since the drag is to the left but if we treat the air as still, how to determine the direction of motion?

Thanks

 

[haruspex]

Ah I see, so statement (i) is FALSE, the force must be downward. This matches the explanation in link in post#4


I thought the ball would move to the right since the drag is to the left but if we treat the air as still, how to determine the direction of motion?

Thanks

The arrows on the airflow show the relative motion. If the air is actually still, which way is the ball moving?

 

[songoku]

The arrows on the airflow show the relative motion. If the air is actually still, which way is the ball moving?

I would say to the right

 

[haruspex]

I would say to the right

Right

 

[songoku]

Thank you very much for the help haruspex and kuruman