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Help needed in this question - falling feathers

Feathers are dropped from a height of 100m on The Earth, mars and venus. surface gravities r - 975,860,378 cm/sec2 respect. The surface atmos. pressuree on Venus and mars r 90 times n 0.01 times that of earth respect. in which order will the feathers settle on the respective surfaces?

A- Mars-earth-ven
B-E-V-M
C-V-EM
D-V-M-E

pLZ GIVE REASONS AND WRKING?

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Reply 1

Sycren

I havent got any working, but surely in the order of greatest to smallest of gravitation. So depending on the size(which=larger mass) of the planets, if earth>venus>mars then in that order

I know that mars is smaller than earth so that knocks out A,D,

When it talks about surface atmosphere, is that about how dense the atmosphere is? I believe that its B

Reply 2

Morbo

Firstly, I think the gravities are:
E - 975
V - 860
M - 378

Not the order that you wrote in your first line.

This question is about terminal velocity. The famous thing about feathers is that they fall at terminal velocity for most of their descent, so the feather with the higher terminal velocity will reach the surface first.

Terminal velocity goes as:

v \propto \sqrt{\frac{g}{\eta}}

where

\eta

is the viscosity of the air.

Now, as far as the relation between pressure and viscosity goes, I seem to remember that viscosity is pretty much independent of pressure. However, there must some dependence, especially at low pressures.

If we say the viscosity of all the atmospheres is the same for this reason, then from my above equation, we should deduce that the order is - as Sycren says - purely determined by the relative gravities, thus the higher the gravity, the quicker the feather hits the ground.

So, B - EVM seems like the right answer from this analysis.

However, given the atmosphere of M has 100x less pressure than Earth, I don't know whether to include this. (I would say viscosity considerations preserve the relative order of Earth and Venus as EV, since I believe a higher pressure atmosphere would only serve to reduce terminal velocity further.)

So even though the gravity of Mars is 2.5x less than that of Earth, it would only take a viscosity of, say, 3x less than that of Earth, to give Mars the highest terminal velocity, and thus make A - MEV the correct answer.

Tough one.

Reply 3

Sycren

sorry Im on wrong exam board so above looks right.

Reply 4

Sidhe

The feather would never reach the ground on venus, the conditions would anihilate it before it was a few feet into the heavy pressurised sulphuric acid atmosphere.

However since they probably don't expect smartass replies then the rate of acceleration due to gravity is proportional to the gravitational constant and the mass of the planet.

{g}=-\frac{MG}{ r^2}

You can plug the numbers in here if you know them, but essentially this just means the higher the gravity the higher the acceleration due to gravity.

The feather will strike Earth first, then Mars, then Venus as their masses are respectively higher.

I think we need to know what level you are studying at. In simple conditions it's obvious, but in real conditions none of the answers are correct :smile:

Go with Worzos answer, that is correct assuming atmospheric conditions, were as mine is a simplistic model taking account of gravity alone.

For extra credit write a smart arse answer as well :smile:

Ie none of the above.

Reply 5

Morbo

Sidhe

{g}=-\frac{MG}{ r^2}

That's a useless equation for this question - you're given the values of g. The only possible point of this question is to illustrate terminal velocity.

The key thing we need to know is the pressure-viscosity relationship.

Another lower order effect would be the amount of water vapour in the atmosphere which might condense on the feather in the form of liquid or ice, increasing its terminal velocity by reducing its shape factor. Though I think you're supposed to assume that the atmosphere and feather have constant properties throughout the descent.

In reality, though, you are correct that the feather would be dissolved by Venus' atmosphere :smile:

And even if that didn't happen, it would probably not reach the surface anyway because it would get caught up in the horrific storm winds.

Reply 6

Sidhe

You mean it's useless if you take the atmosphere into consideration. It's far from useless though if you consider a vacuum or no atmosphere.

So given just the mass of the planet and no other factors as in the question, then you could answer the question with this equation alone ie if acceleration due to gravity Mars<Venus<Earth then you have an answer , you could rank them in order of that alone. That's kind of why I asked whether there was any atmosphere involved, since if there is there is no possible answer.

I do acknowledge your answer is better, I was just being a smart ass. My apologies, but I guess at least we now know that the acidic upper atmosphere of Venus is highly corrosive. It took five probes to Venus to get one to touch down and send back data, conditions are literally like hell :smile:

Reply 7

Morbo

Sidhe

So given just the mass of the planet and no other factors as in the question, then you could answer the question with this equation alone

No, you would need the mass and the radius of the planet in order to use Newton's Law. It saves you this hassle by giving you g. That's why Newton's Law is useless.

That's kind of why I asked whether there was any atmosphere involved, since if there is there is no possible answer.

There is a "possible answer" if the atmosphere is involved. And there is atmosphere involved - it tells you the value of the atmospheric pressures! That's why it's a feather and not a brick, in order to emphasise the fact that atmospheric viscosity is a factor in terminal velocity.

The fact that viscosity effects might be independent of pressure would mean that the terminal velocity is proportional to the square root of the gravitational force. If the viscosity is not independent of pressure, then it will play a part.

Simply put, if someone could tell me whether the viscosity is independent of pressure over this range of pressures then I could tell you the answer. I don't know this fact, so I can't answer the question, but that's not to say that "there is no possible answer".

Reply 8

phys981

Leaving aside the chemical arguments above, I think the only posible asnwer is A.

Since Venus has less gravity and greater atmospheric pressure, surely it will fall more slowly there.

I don't know enough to work out the relative speed on earth and mars, but since A is the only answer showing Venus as last, I'd go for that.

Edited to add - just noticed a correction to the gravities. is that correct or is your original correct? If the original post is wrong that makes my argument null and void....In that case all I can say that is that since Venus has similar gravity to earth but much more atmospheric pressure, it will land on earth before it does on Venus. That narrrows it down to A and B.

Reply 9

phys981

Oh Lord, can't believe I didn't see this earlier

Pressure = Force/Area so assuming feathers are of similar area, the upwards force on each is proprtional to the pressure.

So, Mars has downward force approx 2 or 3 times less than earth, but an upward force of 100 times less. So it lands on mars first, then earth then venus.

How come none of the other esteemed posters spotted it either?

Reply 10

Morbo

rsk

Because pressure doesn't act solely upwards. It acts from above as well. And in fact, from every direction. (Pascal's law of hydrostatics). Thus, when you have an object immersed in a fluid (where the pressure is more or less constant in the vicinity of the object), the net force on it due to the fluid's pressure is zero.

I'm afraid your physics is totally wrong there. If you don't believe me, try calculating the force that would be applied to your body if atmospheric pressure only acted on you in the upwards direction. It's about a tonne, and since this is greater than your downwards weight, you would be accelerated upwards! (As a similar consequence, all the fish in the ocean would be accelerated towards the surface)

rsk

Since Venus has less gravity and greater atmospheric pressure, surely it will fall more slowly there.

Are you even considering viscosity? As I have said twice in this thread now, the key to this problem is figuring out the relative viscosity of the fluids in question by considering the relative pressures.

Reply 11

phys981

Worzo

Because pressure doesn't act solely upwards. It acts from above as well. And in fact, from every direction.

Good point. But I still say MEV

And I really don't think viscosity is what this question is about. My fluid dynamics is more than a little rusty but as far as I can see there's no direct way to go from the information given in the question to viscosity. Is there?

Reply 12

Morbo

rsk

Good point. But I still say MEV

So it hits the surface of Mars first, even though Mars has the weakest gravity?

The only way this can be possible is if the viscosity of the Martian atmosphere is lower by a large enough factor that the terminal velocity of the feather is highest.

Reply 13

phys981

It may be. Pressure is 100x less, gravity only 2-3 times less.

As far as I know, the presure-viscosity coefficient isn't the same for all fluids, so we'd have to know the composition of the 3 atmospheres, which, unless the OP is hiding something from us, we don't.

So, like I said, I really don't think viscosity can be the issue here.

Reply 14

Morbo

rsk

So, like I said, I really don't think viscosity can be the issue here.

Then how do you explain your deduction that the feather on the planet with the weakest gravity hits its surface first? Surely weaker gravity --> slower feather --> longer time. Thus, M should be last?

rsk

As far as I know, the presure-viscosity coefficient isn't the same for all fluids

This is true. You would have to assume the compositions are similar. But this still doesn't get away from the fact that you need to know about viscosity in order to do this question.

Reply 15

phys981

Worzo

taking into account that the difference in air pressure is far greater than the difference in gravity.

OK, what about this.

At higher physics they do Upthrust. (i don't know of any a-levels where they do viscosity but then I don't know wherer this Q comes from) Edite* Yes I do, it comes from here

the upthrust on an object is directly related to the difference in pressure on its top and bottom surfaces. This pressure difference is rho.g.h, h being the distance between the top and bottom surfaces and rho the fluid density.

So g comes into the upthrust aswell....

and the resultant downwards force is mg - rho.g.h

Sorry sunnyguha, this isn't helping at all. I'd still put money on A even if I can't yet explain why....

Reply 16

Morbo

rsk

taking into account that the difference in air pressure is far greater than the difference in gravity.

I've just said that the air pressure produces no net force on the feather because it does not vary significantly over the height of the feather.

Upthrust is there, correct, but this is negligible too. Proof:
- Upthrust is proportional to the volume of fluid displaced by the object:

F_u = \rho_{fluid} V_{object} g

.

- The weight of an object goes as its mass:

F_w = mg = \rho_{object} V_{object} g

So the correction due to upthrust is:

\frac{F_u}{F_w} = \frac{\rho_{fluid}}{\rho_{object}}

Given that a gas is much less dense than a solid, for gaseous atmospheres:

\rho_{fluid} \ll \rho_{object}

So we see that the contribution of upthrust is negligible.

I will say again, the only relevant forces acting are:
- Gravity
- Viscous Drag

Reply 17

generalebriety

While I may be a physics amateur, I trust Worzo on this one... :p:

Reply 18

phys981

Worzo

Problem is, mass and therefore weight are also very small. Which is the more negligible force?

Reply 19

Morbo

rsk

Problem is, mass and therefore weight are also very small. Which is the more negligible force?

What?

Look. Weight is one force. This is related to the gravitational acceleration, which we all know about quite well. If this was the only consideration, the planet with the highest gravity would have its feather hit the ground first.

The problem is the second force - viscous drag. We don't know much about this, or how pressure might affect it.

If you think anything else is significant, you are wrong, I'm afraid.