A slice causes a tennisball to spin and deviate from its normal parabolic path.

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Homework Statement


A tennis player slices the ball to spin and deviate from its normal parabolic path. What is an explanation for this phenomenon?

I am having trouble visualizing the phenomena that is occurring with the slice and as well as the explanation give by the book.

How is the velocity changing?



Homework Equations


On Earth, a tennis player can hit a tennis ball normally causing the ball to travel on a path that is a symmetrical parabola. A tennis player can also hit a tennis ball with a “slice” which causes the ball to spin and deviate to one side of its normal path. What is the best explanation for this deviation?
A. There is an additional acceleration on the ball. Or
B. The spin on the ball used energy so the ball could not travel in a straight line.
The correct answer is A.
Here is an explanation from the book.
The sliced ball travels off to the side, so there must be an acceleration causing the velocity to change. Since gravity is always directed down toward the earth, there must be an additional acceleration from another source (other than gravity) causing the ball’s velocity to deviate to the side.




The Attempt at a Solution

 

Discussion

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This is actually a fluid dynamics problem. The balls spins - thus, as it moves through the surrounding air the flow of air will move faster around one side of the ball and slower on the other. By Bernoulli's principle a faster flow means a lower pressure. Thus we end up with a reduced air pressure on one side of the ball and a correspondingly increased air pressure on the opposite side. This pressure gradient is what causes the ball to deviate from the parabolic trajectory.
 
Oh, so the pressure gradient creates a new horizontal acceleration while in the air?
 
It's called Magnus effect, and one explanation is that the flow on the downwind spinning side remains attached longer, causing the air to be deflected, and the ball to be curved. Wiki article (with a diagram showing a ball with top spin):

http://en.wikipedia.org/wiki/Magnus_effect
 
Just quickly, from the answer given to me by the textbook, it says that an additional acceleration is occurring. Is this due to the magnus effect? Where is the additional acceleration occurring? I know that there is a constant -9.80 m/s^2 downward acceleration, but I just can't seem to visualize or know where the additional acceleration is pointing in which direction.
 
jlyu002@ucr.e said:
Just quickly, from the answer given to me by the textbook, it says that an additional acceleration is occurring. Is this due to the magnus effect?
yes

jlyu002@ucr.e said:
Where is the additional acceleration occurring?
In the case of a ball with back spin (slice), the ball exerts a downwards force on the air, diverting the air downwards, coexistant with the air exerting an upwards force on the ball. It's relatively small in the case of a tennis ball, but a ping pong ball can be made to rise with enough speed and backspin to generate more lift (force) than the weight of the ball.
 
Last edited:
OOOO thanks rcgldr. There is an upward acceleration.
 
jlyu002@ucr.e said:
OOOO thanks rcgldr. There is an upward acceleration.
A ping pong ball can have upwards acceleration, but in the case of a tennis ball, I'm don't know if upwards acceleration is possible, versus just reduced downwards acceleration due to gravity being opposed by a upwards but weaker aerodynamic force.
 
woah, crazy my head hurts. lol. thanks rcgldr I'm going to try and digest this.