How to find the height where two same marbles have the same velocity?

In summary: Then for the second part, you would use that velocity and solve for the height on the moon.In summary, to find the height where two same marbles have the same velocity when dropped from different atmospheres, first find the terminal velocity of the marble on Earth. Then, use that velocity to solve for the height on the Moon where the marble would have the same velocity upon hitting the ground. This can be done using kinematic equations and taking into account the effects of air resistance on Earth and the absence of air resistance on the Moon.
  • #1
mwahx3
19
0

Homework Statement



How do you find the height where two same marbles have the same velocity when one marble is dropped from the Earths atmosphere (g=9.8) and the other is dropped from the Moons atmosphere (g=1.6)? Both are dropped from the same height

Homework Equations



kinematic equations

The Attempt at a Solution



I have absolutely no idea where to start...
 
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  • #2
Is that the question exactly?
 
  • #3
yes.
 
  • #4
mwahx3 said:
yes.

Are they saying the velocity is the same as they hit the ground?

That's a strange question... because if they are dropped from exactly the same height, then when they hit the ground they'll both always have different velocities because the g's are different... unless the height they are dropped from is 0...
 
  • #5
yea that was what i was wondering...no it doesn't say that.
maybe the velocity is the same right when they are released?
the only possible reason i can think of...
 
  • #6
mwahx3 said:
yea that was what i was wondering...no it doesn't say that.
maybe the velocity is the same right when they are released?
the only possible reason i can think of...

Do they give any other numbers... like the height at which they're released?
 
  • #7
no they dont. they just say at height 'H'.
 
  • #8
mwahx3 said:
no they dont. they just say at height 'H'.

Hmmm... that gives the impression that the answer can be given in terms of H... do they also say velocity V or anything like that?
 
  • #9
no, since they ask for the velocity in one part of the problem...
 
  • #10
mwahx3 said:
no, since they ask for the velocity in one part of the problem...

Do they give drag or air resistance for this question?
 
  • #11
F=-kv

and k= 0.1854
 
  • #12
mwahx3 said:
F=-kv

and k= 0.1854

Ah... ok, now I think I understand... a marble is dropped from a height on earth... due to air resistance it reaches its terminal velocity before hitting the ground... when it hits its terminal velocity, the net force on it is 0... so its acceleration is 0 at that point... and it stays at that terminal velocity...

On the moon, there's no atmosphere... so there's no air resistance to think about.

So, first find the terminal velocity of the marble on earth... then find the height that the marble needs to be dropped from on the moon, so that it reaches that velocity just as it hits the ground.
 
  • #13
ohh okay thank you. I think I got the terminal velocity...but I'm having trouble finding the height the marble needs to be dropped from the moon. What velocity should I use?
 
  • #14
mwahx3 said:
ohh okay thank you. I think I got the terminal velocity...but I'm having trouble finding the height the marble needs to be dropped from the moon. What velocity should I use?

The terminal velocity that you get for the Earth marble.
 
  • #15
ahhh okay! thank you! would that just be my answer?
 
  • #16
mwahx3 said:
ahhh okay! thank you! would that just be my answer?

Yeah, the terminal velocity would be your answer for that part.
 

1. What factors affect the velocity of two marbles?

The velocity of two marbles can be affected by factors such as the force of gravity, air resistance, and the mass and size of the marbles.

2. Is there a mathematical equation to determine the height where two marbles have the same velocity?

Yes, there is a mathematical equation known as the Law of Conservation of Energy that can be used to calculate the height where two marbles have the same velocity.

3. Can the surface or material of the marbles affect their velocity?

Yes, the surface or material of the marbles can affect their velocity due to differences in friction and air resistance.

4. How can I conduct an experiment to find the height where two marbles have the same velocity?

To conduct an experiment, you will need two identical marbles, a ruler, and a tall surface such as a staircase. Drop the marbles from different heights and measure their velocities using a stopwatch. Keep increasing the height until the velocities of the two marbles are the same.

5. Why is it important to know the height where two marbles have the same velocity?

Knowing the height where two marbles have the same velocity can help us understand the principles of physics and the behavior of objects in motion. It can also be useful in designing experiments and predicting the outcomes of certain scenarios.

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