If someone gets this right...

[SaintJude]

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If someone gets this right and has a rationale behind it, I will convince myself this is not the most random question I have ever seen

A baseball is hit identically by a batter in two locations, both at the same elevation. One in Arizona and one in Florida where the air is 80% more humid. All other things being equal (STP), which ball will travel farther, Arizona or Florida?

A. Arizona
B. Florida
C. Same
D. The humidity is negligible







Answer (white) : B

 

[pfaction]

I'm going to take a stab at it. More humid = more dense. More dense = more buoyant force. I have no idea about air resistance here. Bouyant force = rhogvol, so more dense = more boyant...so I'll guess A, but i'll prob be wrong. And I am! Probably because of air resistance or the fact there's more force against it, so the Fnet is decreased...

 

[MedPR]

If someone gets this right and has a rationale behind it, I will convince myself this is not the most random question I have ever seen

A baseball is hit identically by a batter in two locations, both at the same elevation. One in Arizona and one in Florida where the air is 80% more humid. All other things being equal (STP), which ball will travel farther, Arizona or Florida?

A. Arizona
B. Florida
C. Same
D. The humidity is negligible







Answer (white) : B

Florida. Humid air is lense dense than dry air.

 

[pfaction]

Oh wow, I was wrong but on the right track. How do you know more humid is less dense? I thought since the water concentration was more in humid, it would be more dense.

 

[MedPR]

Oh wow, I was wrong but on the right track. How do you know more humid is less dense? I thought since the water concentration was more in humid, it would be more dense.

Air is N2 and O2, both of which have greater mass and lesser volume than H2O.

More volume and less mass = less dense.

 

[gettheleadout]

I guessed A. This was my thinking: The only two ways the distance traveled by the ball could be affected is if the increased humidity results in water vapor keeping the ball in the air longer (increasing distance) or providing enough inertial resistance (essentially adding to air resistance) to reduce the force of its forward motion (decreasing distance.) Not knowing if humidity would actually result in the former, but reasoning that it must at least (to some extent) result in the latter (I mean the ball has to push water molecules out of the way now in addition to the air), I guessed A. I have no better rationale.

Air is N2 and O2, both of which have greater mass and lesser volume than H2O.

More volume and less mass = less dense.

Ah, brilliant.

 

[SaintJude]

Call me clueless BUT

1. How did you know more humid = more N2 and O2? (and not more H2O)

2. Also how is density of air related to how far something will travel?

P.s. MedPr, it's no wonder you're conquering the practice exams right now!

 

[pfaction]

If we take 80% to be humid as water content, then the partial pressures of oxygen and nitrogen are decreased, so we're decreasing heavier mass and increasing lighter mass %wise, meaning the ball will have less resistance?

 

[MedPR]

Call me clueless BUT

1. How did you know more humid = more N2 and O2? (and not more H2O)

2. Also how is density of air related to how far something will travel?

P.s. MedPr, it's no wonder you're conquering the practice exams right now!

1. I didn't, but if you are assuming STP, you know that any given volume of air will have the same number total of molecules of gas. More humid must mean more water, and at STP, more of one thing means less of everything else.

2. The drag equation has fluid density in the denominator. Bigger density = smaller drag coefficient = less friction.

 

[milski]

Florida. Humid air is lense dense than dry air.

Air is N2 and O2, both of which have greater mass and lesser volume than H2O.

More volume and less mass = less dense.

👍👍

 

[pfaction]

Seriously, you're doing ****ing awesome, keep it up. I would have thought that the introduction of other things at STP would keep everything proportional but I guess not.

 

[milski]

Call me clueless BUT

1. How did you know more humid = more N2 and O2? (and not more H2O)

2. Also how is density of air related to how far something will travel?

P.s. MedPr, it's no wonder you're conquering the practice exams right now!

More humid does mean more H2O. H2O is lighter than either N2 or O2 (18 vs 28/32 g/mol)

 

[chiddler]

More humid does mean more H2O. H2O is lighter than either N2 or O2 (18 vs 28/32 g/mol)

oh damn! I didn't know that!

 

[MedPR]

For what it's worth, I think this would be one of the more difficult discretes if it appeared on an actual MCAT. It completely goes against intuition, it involves multiple concepts from both physics and gen chem, and the answer choices all seem plausible so you couldn't even do POE.

 

[pfaction]

I have to ask you though, could buoyancy play an effect here? The air is lighter, so could one say since the buoyancy is less it'll also travel less?

 

[MedPR]

I have to ask you though, could buoyancy play an effect here? The air is lighter, so could one say since the buoyancy is less it'll also travel less?

The buoyancy force is negligible considering the mass and velocity of the ball.

 

[pfaction]

Cool beans. I'll have to think about this more carefully next time. N2 and O2(g) are more dense than water(g) due to masses. Rho=M/V, V is same, therefore M up Rho up and the ball would travel slower. Thanks.

 

[milski]

I have to ask you though, could buoyancy play an effect here? The air is lighter, so could one say since the buoyancy is less it'll also travel less?

Extremely unlikely. The buoyancy force in dry air is about 0.003 N which is about 0.002% of the weight of the ball. Replacing all the gasses in air with water vapor will result in decreasing that force by less than a half, so you're talking about 0.001% change here. If that's not negligible, I don't know what is. 😉

Edit: For what it's worth, the change of air density between dry and 80% humid air at 25 C is about 2%.

 

[gettheleadout]

Cool beans. I'll have to think about this more carefully next time. N2 and O2(g) are more dense than water(g) due to masses. Rho=M/V, V is same, therefore M up Rho up and the ball would travel slower. Thanks.

Just because I'm curious, is humidity actually a measure of gaseous water? Wouldn't that mean the air would have to be over 100C?

 

[MedPR]

Just because I'm curious, is humidity actually a measure of gaseous water? Wouldn't that mean the air would have to be over 100C?

The average temperature of the molecules has to be 100C to boil. Boiling is the temp at which vapor pressure exceeds atmospheric pressure. Any vaporization below that temp is evaporation. You could leave a glass of water on your kitchen counter and even if the temperature never exceeds 100C, given enough time, the entire glass would evaporate.

Here's a great explanation of the difference between boiling and evaporating.

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/vappre.html

 

[cloak25]

1. I didn't, but if you are assuming STP, you know that any given volume of air will have the same number total of molecules of gas. More humid must mean more water, and at STP, more of one thing means less of everything else.

2. The drag equation has fluid density in the denominator. Bigger density = smaller drag coefficient = less friction.

so if humid air = less dense wouldn't that = bigger drag coefficient = more friction = shorter distance traveled?? or am I missing something...

 

[MedPR]

so if humid air = less dense wouldn't that = bigger drag coefficient = more friction = shorter distance traveled?? or am I missing something...

Ah, no I typed the wrong thing. The fluid's density is in the numerator of the drag force equation.

Smaller = less drag.

It's something like Drag = density*v^2*area*drag coefficient.

 

[gettheleadout]

The average temperature of the molecules has to be 100C to boil. Boiling is the temp at which vapor pressure exceeds atmospheric pressure. Any vaporization below that temp is evaporation. You could leave a glass of water on your kitchen counter and even if the temperature never exceeds 100C, given enough time, the entire glass would evaporate.

Here's a great explanation of the difference between boiling and evaporating.

http://hyperphysics.phy-astr.gsu.edu/hbase/kinetic/vappre.html

Wow duh, sorry about that.

 

[ipodtouch]

Wait, question. Why does the H2O have to replace the N2 and the O2?


I was under the assumption that:
(arbitrary numbers per square inch)

Dry Air:
10 O2, 10 N2

Humid Air:
8 O2, 8 N2, and 9 H2O



The point is that there is no reason H2O/N2/O2 are exclusive?

 

[chiddler]

Wait, question. Why does the H2O have to replace the N2 and the O2?


I was under the assumption that:
(arbitrary numbers per square inch)

Dry Air:
10 O2, 10 N2

Humid Air:
8 O2, 8 N2, and 9 H2O



The point is that there is no reason H2O/N2/O2 are exclusive?

At STP, you have some amount of moles per volume. If you add some water, you remove something else to keep volume the same.

 

[milski]

Wait, question. Why does the H2O have to replace the N2 and the O2?


I was under the assumption that:
(arbitrary numbers per square inch)

Dry Air:
10 O2, 10 N2

Humid Air:
8 O2, 8 N2, and 9 H2O



The point is that there is no reason H2O/N2/O2 are exclusive?

From PV=nRT. If P,V,R & T stay the same, n will have to stay the same as well.

 

[MedPR]

Wait, question. Why does the H2O have to replace the N2 and the O2?


I was under the assumption that:
(arbitrary numbers per square inch)

Dry Air:
10 O2, 10 N2

Humid Air:
8 O2, 8 N2, and 9 H2O



The point is that there is no reason H2O/N2/O2 are exclusive?

10 + 10 = 20

8 + 8 + 9 = 25

At STP there is 1mol of gas in 22.4L. Can't add more into the same volume without taking some out.

 

[Fortisbariatric]

Sorry, i am totally confused to read this random question. i think Florida is a correct one.

 

[dontbeanegaton]

Yeah, I got this one wrong when I first did it. Good problem. You kick yourself when you read the answer.

 

[gtbROX]

Arizona
Since it's more humid in Florida, there are more water molecules in the air, and since there are more water molecules, the air behaves less like an ideal gas since it exhibits stronger intermolecular interactions deccelerating the ball as it travels through the humid air. Stronger intermolecular interactions because of stronger intermolecular forces of the water molecules, which can hydrogen bond to the surface of the ball. Lower speed, less distance covered since it still hits the ground at the same time as the ball in Arizona, just Arizona ball was faster.

 

[BoxVersionAce]

Arizona
Since it's more humid in Florida, there are more water molecules in the air, and since there are more water molecules, the air behaves less like an ideal gas since it exhibits stronger intermolecular interactions deccelerating the ball as it travels through the humid air. Stronger intermolecular interactions because of stronger intermolecular forces of the water molecules, which can hydrogen bond to the surface of the ball. Lower speed, less distance covered since it still hits the ground at the same time as the ball in Arizona, just Arizona ball was faster.

I was under the impression that this question was already answered. Of which the answer is Florida and didn't mention hydrogen bonding of GAS molecules at STP. I'm not sure that intermolecular forces of vapor will play too much of a role in this situation. I think you're thinking too much about chemistry and not enough about physics.

Also, where did you get the idea that the balls would hit the floor at the same time in this question? Again, drag force <---> projectile motion. This relationship does what to the range (the primary parameter we are observing in this question) and thus the timing of the ball in the air?

 

[gtbROX]

I was under the impression that this question was already answered. Of which the answer is Florida and didn't mention hydrogen bonding of GAS molecules at STP. I'm not sure that intermolecular forces of vapor will play too much of a role in this situation. I think you're thinking too much about chemistry and not enough about physics.

Also, where did you get the idea that the balls would hit the floor at the same time in this question? Again, drag force <---> projectile motion. This relationship does what to the range (the primary parameter we are observing in this question) and thus the timing of the ball in the air?

I just wanted to try my hand at the problem. It makes sense that drag would counter the effect that intermolecular forces would have though.