Chunking a potato - what happens to the speed if...?

[mssr7]

Let's say I'm riding in the back of a truck and decide to throw a potato at a passerby. Note: Passerby is walking with slumbering gait, so consider him practically motionless.

Question applies to each scenario: 1.) passerby is ahead of the truck 2.) passerby is directly beside (me in) the truck 3.) passerby is behind the truck.

1. Does the air wake of the truck increase, decrease, or have no effect on the velocity of my thrown potato?

Forgive me if I haven't presented the question well, if I've used the wrong terminology, or if this is a stupid question. I'm an old lady, who never cared for science, or took classes, other than the basics necessary to graduate high school.

Anxious to read your responses.

[ghariman]

Hi there,

No questions are stupid questions. What is stupid is not to ask a question for then you will always have no answer to it.

I am not an expert in this field (ie. fluid mechanics) but here is my take on it. Someone correct me if I am wrong.

The potato in your hand will be travelling at the same velocity and direction as you and the truck in which you are sitting in. At the instant you throw it out of your hand it will still be at the same velocity and direction you throw it at. So let's take an example to clarify things.
Say the truck, you and the potato are travelling north at 60mph. And the truck has a wake (which I think goes to the south) of 5mph.
And say you managed to throw the potato with your hands and get 100mph.

And to make things simple say the person you are trying to 'chunk-down' is very close to your hands and so the distance doesn't matter as the potato will eventually slow down and hit the ground.

Scenario 1:
As the unfortunate lad is in front of the truck the total velocity and direction of the potato = 60mph + 100mph - 5 = 155mph to the north.

Scenario 3 (number 2 is complicated):
The potato will travel = 60mph - 100mph - 5mph = -45mph (that is 45mph to the south).

Scenario 2:
Now you're throwing the potato perpendicular to both the truck (north) and the wake (south). To first order the only component will be 100mph from your hand to the west/east. However in reality there should be an effect from the truck and wake on the potato in that it won't travel exactly perpendicular but it will sway (here more to the north, so north-west).

Anyway I think in the first case the potato will hit the lad faster than anycase. Then again I may wrong as I am not an expert in this.

Besides why throw the potato at a man on the side of the street if you could instead boil, mash it and make a good meal out of it.


Hope this helps.

[mssr7]

Besides why throw the potato at a man on the side of the street if you could instead boil, mash it and make a good meal out of it.

Hope this helps.

You had me going there... I thought you were concerned for the passerby, and all you were worried about was the potato...lol...J/K.

I think your answer for scenario no. 1 is the answer I need. I pretty much came to the same answer, but wasn't sure of myself, figuring there could be other factors I was leaving out.

Do you know if this has been tested? If yes, where do you think I might find the results?

BTW - thanks for taking a shot at it!

[awhite]

This intent of this forum is to provide guidance and help for students who are preparing for a science fair. There is the possibility a student could come across this post, and consider the material within as a potential topic for a science fair contest, so I'd like to add a supplemental opinion to ghariman's response.

The potato in your hand will be travelling at the same velocity and direction as you and the truck in which you are sitting in. At the instant you throw it out of your hand it will still be at the same velocity and direction you throw it at.

I agree.

So let's take an example to clarify things.
Say the truck, you and the potato are travelling north at 60mph. And the truck has a wake (which I think goes to the south) of 5mph.
And say you managed to throw the potato with your hands and get 100mph.

I believe it may be confusing to say "The wake will travel south at 5 mph." A more accurate statement would be that the air behind the truck has been sufficiently beat up (from the fast moving truck that recently passed through it), and that an object in that air, moving at the speed of the truck, would feel less deceleration due to that body of air, than if it were not behind the truck. This is like race cars or bicyclists drafting (following close behind one another).

And to make things simple say the person you are trying to 'chunk-down' is very close to your hands and so the distance doesn't matter as the potato will eventually slow down and hit the ground.

A good assumption, but in my approach, perhaps we simply assume that we're so good at throwing potatoes, that we know how to compensate for all the forces that will act on the potato after it leaves our hands; we can put it right-on-target with a similar flight path everytime. Further, we'll ignore gravity--pretend we throw the potato horizontal, and it doesn't gain or lose velocity in the vertical direction.

Scenario 1:
As the unfortunate lad is in front of the truck the total velocity and direction of the potato = 60mph + 100mph - 5 = 155mph to the north.

First, we'll assume the person we're aiming at is directly in the path of the truck's travel, so we are throwing the potato straight ahead. The potato's velocity, after it leaves the thrower's hands, will not be affected by the turbulent wake behind the truck. Instead, it the potato will travel at 160 mph due north. In this case, the potato will be slowed by the full frictional force af a 160 mph headwind, and will thus slow fairly rapidly, it's final speed depending on how long the potato is aloft. Assuming a short time-of-flight, this is the scenario in which our potato is traveling the fastest when it hits the target.

Scenario 3 (number 2 is complicated):
The potato will travel = 60mph - 100mph - 5mph = -45mph (that is 45mph to the south).

In scenario 1, we assumed we could through the potato at a speed of 100 mph. In scenario 3, then, when the potato leaves our hands, it will leave a truck traveling at 60 mph to the north at a speed of 100 mph, to the south, and have a net speed of 40 mph to the south. Here the effect of the "wake" will be pronounced; the potato traveling to the south will be subject to an airstream that has a net velocity to the north (pulled by the truck that just passed through). So, the potato will travel at 40 mph, and be exposed to a somewhat-greater-than-40 mph frictional headwind. Assuming a short time-of-flight, this scenario gives the slowest speed with which the potato will hit the target.

Scenario 2:
Now you're throwing the potato perpendicular to both the truck (north) and the wake (south). To first order the only component will be 100mph from your hand to the west/east. However in reality there should be an effect from the truck and wake on the potato in that it won't travel exactly perpendicular but it will sway (here more to the north, so north-west).

In this case, the potato has two components of motion as it leaves the thrower's hands: along the direction of the truck, at 60 mph, and perpindicular to the truck, at 100 mph. It will be subject to the effects of friction in both directions; but since the total speed of the potato is around 117 mph (sqrt(60^2+100^2)) it will face less of a decelerating force than the potato in scenario 1, but more than that from scenario 3. It will likely (again--under the assumption of the a similar time-of-flight with the other scenarios) strike the target with a total speed less than that of the first potato, but more than that of the third potato.

Anyway I think in the first case the potato will hit the lad faster than anycase. Then again I may wrong as I am not an expert in this.

Besides why throw the potato at a man on the side of the street if you could instead boil, mash it and make a good meal out of it.


Hope this helps.

Agreed. A tomato might carry the same message, without the same potential for injury.

I also am also not in the field of fluid mechanics, but I don't believe I've made any gross oversights. However, I believe the original response may have been somewhat misleading in stating the velocity of the potato would change by +/-5 mph due to a wake that purportedly travels both ahead, and behind, the truck. Certainly, the wake will have a net effect on the velocity of the potato, but only when the potato is thrown behind the truck, and--with our throwing speed greater than the speed of the truck--this wake would slow the potato more than if the wake were ignored.

Adam

[deleted-71572]

Fluid Mechanics! They printed those words on my degree. I will chime in, mainly because I can't resist a food-throwing problem. Regarding the potato lateral:

Assuming that the truck is, well, truck-like, as opposed to sleek and streamlined like a Formula 1 racecar, there will be substantial turbulence to the side of the truck as well. A turbulent boundary layer, as we fluid mechanics like to call it. Its thickness will depend on how fast you are going, and the shape of the (front of the) truck. Thus, I think it would be important to include the effects of the wake (the turbulent buffeting) in this scenario as well. Also, in this classic kinematics problem, I would like to point out that I choose to be the pedestrian directly beside Mrs. Potato Head in her truck. If she throws her spud directly at me as she passes me, it won't actually hit me, because the potato will have a forward component of velocity away from me. Then I could pick up the potato, brush it off (10 second rule! There's a science fair project idea for you...), and make myself some nice hash browns.

As for mssr7's follow-up question:
Not sure if this exact experiment has been tested, but there has been lots done with turbulent wakes, this being an important topic for people designing cars and boats and airplanes and such. Come to think of it, there must be lots of research on what happens to things you release from airplanes too, but some of that might be classified. I know there are empirical relationships that have been developed for how thick a boundary layer is, and also equations describing projectile motion through turbulent air (rather than still air), but I can't cite them off the top of my head.

But, you should check out the Van Dyke's Album of Fluid Motion for cool pictures (well, okay, I'm a science geek, but I think they're cool) of what flow looks like around things. There must be websites with pictures of flow around objects in wind tunnels too. (In a wind tunnel, the idea is to keep the object still and move the air around it. Same effects, but easier to observe, since you don't have to run around after a car in your lab.)

[awhite]

Assuming that the truck is, well, truck-like, as opposed to sleek and streamlined like a Formula 1 racecar, there will be substantial turbulence to the side of the truck as well. A turbulent boundary layer, as we fluid mechanics like to call it. Its thickness will depend on how fast you are going, and the shape of the (front of the) truck. Thus, I think it would be important to include the effects of the wake (the turbulent buffeting) in this scenario as well. Also, in this classic kinematics problem, I would like to point out that I choose to be the pedestrian directly beside Mrs. Potato Head in her truck. If she throws her spud directly at me as she passes me, it won't actually hit me, because the potato will have a forward component of velocity away from me.

Good point about the turbulent boundary layer along the side of the truck; I chose to ignore it because I couldn't clearly state the impact it would have on a potato traveling laterally through it (increase drag on the potato vs the case with no boundary layer, or decrease drag vs that case).

As to the comment regarding the lateral throw missing, remember--I stated we were expert potato-throwers, and hit everytime. The potato would be leaving our hands a bit before a normal line from the truck and it's path would intersect the pedestrian.

So, still best to be behind the truck if someone's going to throw a potato at you; at least from an energy-at-impact point of view.

adam