Tennis Ball Throwing Question

[dolphinboy]

I like to play fetch with my Jack Russell Terrier. I have one of those ‘Chuck It’ ball launchers that I use to throw tennis balls that he chases after and returns. Here’s what a Chuck It looks like if you’ve never seen one before. I get tennis balls from a variety of sources, and contrary to popular belief not all tennis balls are alike. Some are fuzzier than others, some are smaller than others, and some weigh more than others. They mostly weigh about 2 ounces, but I have some that only weighs 1.4 ounces. I’ve discovered that all things being equal I can chuck the 1.4 oz. balls a lot further than the 2.0 oz balls. I thought that was because they weighed less, but both types of balls are relatively light and easy to throw. The lighter one just tends to fly a lot further. I would think the added weight would help the heavier balls travel further due to their increased momentum once in flight, but perhaps gravity is pulling them down to the ground faster due to their additional weight.

So why exactly can I throw the lighter tennis balls considerably further than the heavier ones? How is Newtonian physics working in this real world example?

[bob_2]

Someone will no doubt explain the physics, but think if the difference was more extreme. You can easily see that the energy needed to throw a heavy ball the same distance as a light one would be much greater.Of course air resistance comes into play but it won’t have a big effect until the light ball is really light.

[dolphinboy]

@bob_2

Someone will no doubt explain the physics, but think if the difference was more extreme. You can easily see that the energy needed to throw a heavy ball the same distance as a light one would be much greater.Of course air resistance comes into play but it won’t have a big effect until the light ball is really light.

I thought of that, but let’s say I had ping pong ball the size of a tennis ball. It would be so light that I doubt I could sling it half as far as a tennis ball. Of course something that light would be greatly affected by air resistance. So why doesn’t that matter in my simple example?

[Cheesesteak]

@dolphinboy

So why exactly can I throw the lighter tennis balls considerably further than the heavier ones? How is Newtonian physics working in this real world example?

All other things equal (and with tennis balls, they mostly are) the heavier ball will travel further, due to air resistance (which is unchanged) having less effect on the speed of the ball.

Since the heavier ball is not traveling further, one of the ‘other’ things must not be equal, I suspect it’s the initial speed. Let’s imagine you have a ball of lead the size of a tennis ball. If you try to throw it with that wibbly skinny arm (the Chuck It’s arm, not yours) the arm will just flex and the ball will have very little speed.

The heavier ball causes the throwing arm to flex more, and it imparts a lower initial speed to the tennis ball.

Another possibility is that the difference in weight causes a difference in spin upon release, a difference that happens to favor the lighter ball.

[RedSwinglineOne]

Are the light ones also the less fuzzy ones? Brand new fuzzy tennis balls are tough to get through the air. The “fuzz” adds a lot of air resistance. Old bald ones probably fly farther.

[dolphinboy]

@RedSwinglineOne

Are the light ones also the less fuzzy ones? Brand new fuzzy tennis balls are tough to get through the air. The “fuzz” adds a lot of air resistance. Old bald ones probably fly farther.

I tried this with two bald tennis balls to eliminate the fuzziness factor.

I guess my arm speed would be somewhat slower with the heavier ball, but I don’t have any way to check that. Again, the difference in weight is only 6 ounces, yet the difference in distance is considerable (20 feet or more). So gravity plays no part in this particular case? Or whatever part it plays would be negligible?

[Ornery_Bob]

My WAG would be the heavier ball causes the Chuck It to flex more, which effectively makes it shorter and reduces the arc.

[Baracus]

@dolphinboy

I tried this with two bald tennis balls to eliminate the fuzziness factor.

I guess my arm speed would be somewhat slower with the heavier ball, but I don’t have any way to check that. Again, the difference in weight is only 6 ounces, yet the difference in distance is considerable (20 feet or more). So gravity plays no part in this particular case? Or whatever part it plays would be negligible?

Not gravity, per se, because the acceleration due to just gravity is the same regardless of the weight of the object. However, just as the lighter ball will slow down faster in the horizontal direction due to its higher surface area to mass ratio, it will also accelerate more slowly while coming back to the ground due to that greater air resistance. Of course, it also experiences more resistance on the upward portion of its arc and should peak at a lower altitude for a given throwing angle, so it will have less distance to fall.

Overall I am reasonably sure that given two objects of the same diameter launched at the same angle and speed, the more dense one will go farther. Thus I am inclined to think that either the heavier one is getting launched with less speed or perhaps a less useful angle for whatever reason.

[dolphinboy]

@Baracus

Not gravity, per se, because the acceleration due to just gravity is the same regardless of the weight of the object. However, just as the lighter ball will slow down faster in the horizontal direction due to its higher surface area to mass ratio, it will also accelerate more slowly while coming back to the ground due to that greater air resistance. Of course, it also experiences more resistance on the upward portion of its arc and should peak at a lower altitude for a given throwing angle, so it will have less distance to fall.

Overall I am reasonably sure that given two objects of the same diameter launched at the same angle and speed, the more dense one will go farther. Thus I am inclined to think that either the heavier one is getting launched with less speed or perhaps a less useful angle for whatever reason.

The angle is the same since I have to clear some trees to get maximum distance. I think it must be due to lunch speed differences. I can launch the lighter ball further because I can throw it faster. Mystery solved.

[dolphinboy]

@dolphinboy

The angle is the same since I have to clear some trees to get maximum distance. I think it must be due to lunch speed differences. I can launch the lighter ball further because I can throw it faster. Mystery solved.

That should be ‘launch’ speed, not lunch speed.

[Irishman]

@dolphinboy

I would think the added weight would help the heavier balls travel further due to their increased momentum once in flight, but perhaps gravity is pulling them down to the ground faster due to their additional weight.

No, gravity pulls equally. The difference is as you surmise. Distance comes from energy and momentum at departure, air resistance, and angle of departure.

If you use the same physical size and both bald to negate air resistance differences, that puts it down to the other two. Throwing the same manner and having the same departure angle eliminates the last.

That leaves the energy and momentum. Momentum is mass times velocity, energy is mass times velocity squared.

p = m x v
E = m x v[sup]2[/sup]

In this situation, I believe energy is the important factor.

Since the heavier item is falling shorter, that suggests that it has lower kinetic energy. Since the mass is higher, the velocity must be lower. Since velocity squares for energy, a smaller change in the velocity will have a bigger effect than a change in mass.

The energy the ball gets is the energy you put in. Since you try to throw consistently, we will assume the average effort you put in is the same, which translates to your input energy being the same. If the energy in is the same, the mass is higher, then it is taking more of that energy to get the mass accelerated, and thus the velocity is lower.

Or think about it this way: how far the ball goes before it hits the ground is determined by the initial speed, the launch angle, air resistance, and the acceleration of gravity. Since g stays the same, and their size and shape and surface are the same, that leaves only two factors. If you are certain the launch angle is not any different, then that leaves only one factor.

[dolphinboy]

@Irishman

No, gravity pulls equally. The difference is as you surmise. Distance comes from energy and momentum at departure, air resistance, and angle of departure.

If you use the same physical size and both bald to negate air resistance differences, that puts it down to the other two. Throwing the same manner and having the same departure angle eliminates the last.

That leaves the energy and momentum. Momentum is mass times velocity, energy is mass times velocity squared.

p = m x v
E = m x v[sup]2[/sup]

In this situation, I believe energy is the important factor.

Since the heavier item is falling shorter, that suggests that it has lower kinetic energy. Since the mass is higher, the velocity must be lower. Since velocity squares for energy, a smaller change in the velocity will have a bigger effect than a change in mass.

The energy the ball gets is the energy you put in. Since you try to throw consistently, we will assume the average effort you put in is the same, which translates to your input energy being the same. If the energy in is the same, the mass is higher, then it is taking more of that energy to get the mass accelerated, and thus the velocity is lower.

Or think about it this way: how far the ball goes before it hits the ground is determined by the initial speed, the launch angle, air resistance, and the acceleration of gravity. Since g stays the same, and their size and shape and surface are the same, that leaves only two factors. If you are certain the launch angle is not any different, then that leaves only one factor.

Q.E.D.

[puddleglum]

They are several different types of tennis balls. There is the standard ball, Type 2, which is what most people play with. There is a faster ball for clay courts and a slower ball for grass courts. There are also red, orange, and green balls for kids.
If you have a ball that is different than the type 2 ball then it would have a different circumference, weight, and a different type of fuzz. All those would influence how far the ball goes.

[trmptgn]

This isn’t an answer with regards to the physics of it all, but I can speak to this from the position of being a pretty experienced tennis player. When I use the lighter tennis balls the spin tends to have a greater effect on the flight path as well. If you are releasing the ball with a great amount of backspin, that may keep the ball aloft longer than with the heavier balls. Slices with the lighter balls do float longer, but they have less “drive” once they hit the court than the heavier balls.

[Troy_McClure]

I’m going to go with trmptgn on this one. The lift generated by a spinning sphere is not dependent on its mass.

https://www.grc.nasa.gov/WWW/K-12/airplane/beach.html

When you chuck the lighter ball, it will spin quite a bit faster (all other things being equal) because it has a lower moment of inertia. The faster the spin, the greater the lift, and since the ball is lighter it will get more benefit from the lift.

Obviously there are limits where, if the ball is too light, the drag will overwhelm the forward momentum too quickly.