Achieving Equal Velocity: Dropping 3 Ball Bearings

[sunbunny]

Homework Statement

Consider 3 ball bearings, one with a mass of 8g, one with 16g, and one with 32 g. What heights should the 3 ball bearings be dropped from so that all 3 ball bearings have the same velocity?

Homework Equations

I think that the relevant equation would be:

vf^2= vi^2 + 2ad

The Attempt at a Solution

I know what the initial velocity is 0m/s, and of course the acceleration. I thought that I could just solve for the distance easily by isolating d, the distance however i don't have the final velocity and I'm not sure if i need to be using the mass of the weights (since reglecting air resistance would have the same acceleration/ free fall regardless of mass).

If anyone can lead me in the right direction and show me where I'm going wrong that would be greatly appreciated!

Thanks a lot!

 

[Ja4Coltrane]

you wrote that they have the same acceleration--that means they should be dropped from the same height if you want them to land at the same time. Your question was unclear by the way. What do you mean by same velocity? same final velocity or what?

 

[Ja4Coltrane]

edit:if you want them to land at the same time with the same velocity.

 

[Kurdt]

It doesn't matter what the final velocity is. From the equation of motion you've provided you know the final velocity is v_f^2= 2ad.

What does this equation tell you?

 

[sunbunny]

the question that i have just states that they wasnt to know what heights the 3 ball bearings should be dropped from so that at impact all 3 have the same velocity.

I don't think that it matters whether or not they land at the same time, just the same velocity, or that's what it seems like to me

 

[AngeloG]

Here's an idea to think about: Throw an object up at 5 m/s and throw an object down at 5 m/s.

Which one will hit the ground at a faster velocity?

Also, does the weight matter when it comes to velocity [given there was no air resistance]?

Also, it would be a good idea to think about things with a force diagram and seeing if variables cancel out or think about it deeply to see relationships =).

Like does mass affect velocity?

 

[sunbunny]

so from the vf^2 = 2ad equation, I can find the height by isolating d getting vf^2/2a

But now where I'm confused at with this is how do i find the height if i do not know the final velocity?

 

[Kurdt]

so from the vf^2 = 2ad equation, I can find the height by isolating d getting vf^2/2a

But now where I'm confused at with this is how do i find the height if i do not know the final velocity?

You don't need to find a numerical distance. The equation is telling you something fundamental. The equation describes the motion of an object under uniform acceleration that starts from rest. What do you notice about the information given in the question and the equation of motion and thus what does this tell you about the height all three can be released from to reach the same velocity at impact.

 

[Ja4Coltrane]

this is silly--there is no need to interperet the formula. All you need is logic. You know that there is constant acceleration, and with this, you should be able to figure it out by thinking.

 

[Kurdt]

It generally helps if there is some physical justification. One could just think about the problem without using any physical formula whatsoever, however it is good practise to approach any problem using grounded physical concepts and then interpreting the results. Also I doubt there would be any physics lecturer out there that would accept an answer with no physical justification other than I thought about it, and they most certainly would prefer an algebraic explanation over a verbal one.

 

[Ja4Coltrane]

we are getting so off the point here, but I would like to politely disagree. A verbal explanation shows that one has conceptual understanding of the problem. There is no problem with having an algebraic justification, but that should come after a true understanding--it should be like a neat realization that it works that way mathematically as well as in the way that you already understood.

 

[Ja4Coltrane]

A formula is like a method of cheating and not truly understanding unless one understands the formula itself.

 

[Ja4Coltrane]

(I'm not talking about you not understanding, I'm talking more to the person trying to solve the problem)

 

[Kurdt]

If one is competent at mathematics many more nuances and truths become clear with a mathematical formula that you just can't get from visualising problems. That is the point of these problems though, to become familiar with manipulating the formula to extract obscure information. Also it is not an intuitive answer that can be merely plucked out of the air with this question. The meaning of the result runs very deep indeed and confuses people to this day. I bet 9/10 people would get this question wrong if they were just asked on the street and this is made apparent even in recent movies such as Addam's family values where they got it wrong.

Anyway I'll agree to disagree and not pursue any further off topic of the thread.

 

[Ja4Coltrane]

Sorry, one more thing. I thought this was an interesting discussion so I made a post outside of the homework section.
https://www.physicsforums.com/showthread.php?p=1210565#post1210565

 

[sunbunny]

Thank you everyone for your input