Is the Final Velocity of a Fly Impacted by an Elephant's Mass?

[cxza]

Homework Statement

This homework was given by my teacher. Assume we have an elephant that is moving in one dirction and a fly that is stationary. Find the speed of the fly after the colision and express it in terms of u

Relevant Equations

The answer is only supposed to contain the velocity and some integers. I hope this is the right place, thx in advance.

My solution was that the final velocity of the fly is equal to the mass of the elephant divided by the mass of the fly, and then multiplies by the delta in the elephant's velocity. My teacher said it was the wrong answer and that the calculations are presumably pretty long

 

[berkeman]

Homework Statement: This homework was given by my teacher. Assume we have an elephant that is moving in one dirction and a fly that is stationary. Find the speed of the fly after the colision and express it in terms of u
Relevant Equations: The answer is only supposed to contain the velocity and some integers.

My solution was that the final velocity of the fly is equal to the mass of the elephant divided by the mass of the fly, and then multiplies by the delta in the elephant's velocity. My teacher said it was the wrong answer and that the calculations are presumably pretty long

Welcome to PF.

Please show your work on this, and also let us know to how many decimal places your instructor wants this solution. It is a pretty easy calculation to 3 decimal places or so...

EDIT/ADD -- is there any chance that your instructor is pranking your class? Or maybe you are pranking us?

 

[cxza]

Welcome to PF.

Please show your work on this, and also let us know to how many decimal places your instructor wants this solution. It is a pretty easy calculation to 3 decimal places or so...

EDIT/ADD -- is there any chance that your instructor is pranking your class? Or maybe you are pranking us?

He told us it is a question that was given to him by his teacher, so I am pretty sure he's for real. 3 decimal places is definitely enough. I don't have a lot of working because I have no idea how to approach this problem. He also mentioned we should assume it is an elsatic collision, so I tried solving it with conservation of momentum, I suppose I have to cancel the mass out somehow.

 

[berkeman]

He also mentioned we should assume it is an elsatic collision

Oh, that's different. Poor fly.

What are the Relevant Equations?

 

[cxza]

Oh, that's different. Poor fly.

What are the Relevant Equations?

I am not sure, I guess conservation of kinetic energy and conservation of momentum. I am an IB Physics student and it's the first semester so it's not very advanced.

 

[berkeman]

conservation of momentum

This...

 

[berkeman]

Can you write the Conservation of Momentum equation for the Elephant and the fly, and plug in some numbers...?

 

[cxza]

Can you write the Conservation of Momentum equation for the Elephant and the fly, and plug in some numbers...?

Well, can we assume that the change in momentum of the elephant on negligible? But this would mean that the momentum of the fly will also not change. I took me=6000kg, ue=10m/s, ve=9.9m/s, mf=0.045g If I use these values I get that the speed of the fly is more than 13 000m/s.

 

[cxza]

Well, can we assume that the change in momentum of the elephant on negligible? But this would mean that the momentum of the fly will also not change. I took me=6000kg, ue=10m/s, ve=9.9m/s, mf=0.045g If I use these values I get that the speed of the fly is more than 13 000m/s.

My teacher didn't give us any values, the solution is supposed to be "theoretical" if that makes sense. Not using any values.

 

[PeroK]

Homework Statement: This homework was given by my teacher. Assume we have an elephant that is moving in one dirction and a fly that is stationary. Find the speed of the fly after the colision and express it in terms of u
Relevant Equations: The answer is only supposed to contain the velocity and some integers. I hope this is the right place, thx in advance.

My solution was that the final velocity of the fly is equal to the mass of the elephant divided by the mass of the fly, and then multiplies by the delta in the elephant's velocity. My teacher said it was the wrong answer and that the calculations are presumably pretty long

If you are expected to model an elephant and a fly as an elastic collision, then I think your teacher has lost the plot and needs to think carefully about the fact that physics is supposed to provide a realistic model of natural phenomena. Asking students to calculate nonsense can't do anyone any good.

 

[cxza]

If you are expected to model an elephant and a fly as an elastic collision, then I think your teacher has lost the plot and needs to think carefully about the fact that physics is supposed to provide a realistic model of natural phenomena. Asking students to calculate nonsense can't do anyone any good.

So what if I take it as an inelastic collision, then of course the energy will no be conserved, so I can only use the fact that the momentum will be conserved.

 

[PeroK]

So what if I take it as an inelastic collision, then of course the energy will no be conserved, so I can only use the fact that the momentum will be conserved.

A totally inelastic collision where the fly is squashed on the elephant is more realistic.

 

[cxza]

A totally inelastic collision where the fly is squashed on the elephant is more realistic.

So in this case the velocity of the fly will be the same as the velocity of the elephant, which my teacher has said is not the answer he is looking for.

 

[berkeman]

A totally inelastic collision where the fly is squashed on the elephant is more realistic.

Poor fly.

we should assume it is an elsatic collision,

So in a totally elastic collision, what is the final velocity of the fly? Doink!

 

[haruspex]

If you are expected to model an elephant and a fly as an elastic collision, then I think your teacher has lost the plot and needs to think carefully about the fact that physics is supposed to provide a realistic model of natural phenomena. Asking students to calculate nonsense can't do anyone any good.

I disagree. We can take it as perfectly elastic, perfectly inelastic or some specified point in between (coefficient of restitution between 0 and 1). By assuming that the elephant's speed barely changes, all cases can be answered sensibly.

 

[PeroK]

So in this case the velocity of the fly will be the same as the velocity of the elephant, which my teacher has said is not the answer he is looking for.

I guessed as much. If your teacher doesn't believe physics should be even remotely realistic, then there's not a lot anyone can do.

 

[PeroK]

I disagree. We can take it as perfectly elastic, perfectly inelastic or some specified point in between (coefficient of restitution between 0 and 1). By assuming that the elephant's speed barely changes, all cases can be answered sensibly.

You've have about as much chance of getting a lump of putty to bounce elastically off an elephant!

 

[PeroK]

Poor fly.

I was cycling round Regent's Park yesterday and one got in my mouth. I wish it had bounced elastically off my tongue and out again!

 

[kuruman]

A totally inelastic collision where the fly is squashed on the elephant is more realistic.

If you want to insist on "realistic", how many flies have you met that will just hover in mid air waiting for an elephant to collide with them, elastically or inelastically? They will either move away or alight on the elephant attracted by something or other on it.

 

[berkeman]

You guys are making me cry now...

 

[cxza]

I'm think my first step will be to get rid of the mass in the equation as the answer is supposed to be in terms of v

 

[cxza]

I'm think my first step will be to get rid of the mass in the equation as the answer is supposed to be in terms of v

I gotta go now, i will read your answers tomorrow, thank you all for the help

 

[PeroK]

If you want to insist on "realistic", how many flies have you met that will just hover in mid air waiting for an elephant to collide with them, elastically or inelastically? They will either move away or alight on the elephant attracted by something or other on it.

Lots have got in my mouth and eyes while I'm cycling. I don't know their state of motion before the collision, but they don't just bounce off.

If I was teaching physics, I wouldn't have elephants and flies in the first place. I'd choose a scenario that made sense.

There is no place in physics for "theory" that bears no relation to experiment. An approximation is one thing. There's a Veritasium video where he asks college students about something and one says something like: "in physics, this is what you are told happens, but in reality, something else happens". That's the result of this sort of teaching, IMHO.

I'll get off my soap-box and go to bed.

 

[haruspex]

You've have about as much chance of getting a lump of putty to bounce elastically off an elephant!

Depends on the fly. Blowflies (UK bluebottle?) are pretty resilient. Swatting them mid air may stun them but never crush them.
At the same time, elephant hide is a lot stiffer than human skin. I can easily imagine a blowfly colliding with an elephant and bouncing off. Making the fly stationary and the elephant the mover doesn't change that.

 

[Orodruin]

I'm think my first step will be to get rid of the mass in the equation as the answer is supposed to be in terms of v

You don’t need to do any math whatsoever. At least not anything harder than addition of integers. Use your intuition instead.

What would be the rebound velocity of the fly if instead the fly was moving straight towards the elephant at velocity v? Considering that the mass of the elephant is much larger than that of the fly.

(Ignoring for the moment the issues regarding the collision actually being elastic or not …)

 

[kuruman]

I'm think my first step will be to get rid of the mass in the equation as the answer is supposed to be in terms of v

All jesting aside, assuming that the collision is perfectly elastic, you can write two equations, one conserving momentum and one conserving kinetic energy. You have two unknowns, the final velocities of the fly and the elephant so you can find expressions for them in terms of the mass $m$ of the fly and $M$ of the elephant. You don't know what they are, but you know that the mass of the fly is much much smaller than the mass of the elephant. See what happens to your expression at that limit. You can also look up on the web a typical mass of each and substitute. Either way you will get the same answer.

 

[cxza]

All jesting aside, assuming that the collision is perfectly elastic, you can write two equations, one conserving momentum and one conserving kinetic energy. You have two unknowns, the final velocities of the fly and the elephant so you can find expressions for them in terms of the mass $m$ of the fly and $M$ of the elephant. You don't know what they are, but you know that the mass of the fly is much much smaller than the mass of the elephant. See what happens to your expression at that limit. You can also look up on the web a typical mass of each and substitute. Either way you will get the same answer.

That seems good, just I am not sure how to do it exactly

 

[PeroK]

That seems good, just I am not sure how to do it exactly

We need to see your best attempt to solve the problem. At least write down the equations for an elastic collision between a particle of mass $M$, which may or may not be an African elephant, and an object of mass $m$, which may or may not be a tse-tse fly.

 

[Orodruin]

which may or may not be an African elephant,

What about swallows and coconut shells?