How do I find the necessary height for a shot tower in this problem?

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Ball bearings can be made by leting shperical drops of molten metal fall inside a tall tower - called a shot tower- and solidify as they fall.

If a bearing needs 4.0s to solidify enough for impact, how high must the tower be?
What is the bearing's impact velocity?



I've never taken a physics course before. I have no idea how to figure out the height of the shot tower, I think I'm supposed to know from the 4 seconds that the tower is a certain height, but I'm totally clueless. If someone could even just tell me how to figure that out I'd really appreciate it.



I saw an old post with a near identical question from 2 years ago, but looking at the answer given there didn't help me figure out what to do here.

Help??
 

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  • #2
Hootenanny
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Ball bearings can be made by leting shperical drops of molten metal fall inside a tall tower - called a shot tower- and solidify as they fall.

If a bearing needs 4.0s to solidify enough for impact, how high must the tower be?
What is the bearing's impact velocity?



I've never taken a physics course before. I have no idea how to figure out the height of the shot tower, I think I'm supposed to know from the 4 seconds that the tower is a certain height, but I'm totally clueless. If someone could even just tell me how to figure that out I'd really appreciate it.



I saw an old post with a near identical question from 2 years ago, but looking at the answer given there didn't help me figure out what to do here.

Help??
Welcome to PF Lida,

What is the acceleration of the shot?
 
  • #3
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Welcome to PF Lida,

What is the acceleration of the shot?


I dooooon't knooooow! :(
Should it be obvious from the problem? I'm so confused by this.


And thanks for the welcome. :)
 
  • #4
Hootenanny
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I dooooon't knooooow! :(
Should it be obvious from the problem? I'm so confused by this.

And thanks for the welcome. :)
No problem, I see from your initial post that this is your first physics class, do you have a class text? Have you come across kinematic (SUVAT) equations before?
 
  • #5
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Ok. I have a book called "How to Solve Physics Problems" and it uses 9.8 a lot for free falling objects, so I'm guessing that might be the acceleration of a falling object?

If that's the case, then the shot tower is 39.2 m right?

And I got that the velocity was 9.8 m/s, but I'm not so sure about that. Is it right?

Thanks!
 
  • #6
Hootenanny
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Ok. I have a book called "How to Solve Physics Problems" and it uses 9.8 a lot for free falling objects, so I'm guessing that might be the acceleration of a falling object?
Correct. 9.8 m/s2 is the acceleration due to gravity or the acceleration of an object in freefall.
If that's the case, then the shot tower is 39.2 m right?

And I got that the velocity was 9.8 m/s, but I'm not so sure about that. Is it right?
Not quite, perhaps if you detailed you calculations we could point out where you're going wrong.
 
  • #7
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If that's the case, then the shot tower is 39.2 m right?

And I got that the velocity was 9.8 m/s, but I'm not so sure about that. Is it right?

Thanks!

No, that's incorrect. Use this equation, and solve for y (height). Make sure that you plug in your known variables: a (acceleration), t (time).

[tex]y = \frac{1}{2}at^2[/tex]
 
  • #8
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No, that's incorrect. Use this equation, and solve for y (height). Make sure that you plug in your known variables: a (acceleration), t (time).

[tex]y = \frac{1}{2}at^2[/tex]

With this formula I got 192.08m for the tower and 48.02m/s for my velocity. Closer?
 
  • #9
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Not quite, perhaps if you detailed you calculations we could point out where you're going wrong.

I multiplied 9.8 by 4 in an attempt to reverse the equation for acceleration.
 
  • #10
Hootenanny
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Last edited by a moderator:
  • #11
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Now I figured 39.2 as my velocity and got 348.88 for the tower. This doesn't seem right, but I did that using the x-x0= v0t + 1/2at^2 equation. ( I'm using 192.08 for 1/2at^2)

Using 19.6 instead of 192.08, because I think that might be where I'm going wrong, I end up with 176.4.

Are either of my answers right?

How do I figure out the difference between x and x0?
 
Last edited:
  • #12
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I think the answer is 78.4 now...hopefully.
 
  • #13
Hootenanny
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I think the answer is 78.4 now...hopefully.
Correct :approve:
 
  • #14
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Finally!

Thanks! :biggrin:
 

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