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

[Lida]

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??

 

[Hootenanny]

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?

 

[Lida]

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. :)

 

[Hootenanny]

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?

 

[Lida]

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!

 

[Hootenanny]

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.

 

[chislam]

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).

$$y = \frac{1}{2}at^2$$

 

[Lida]

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).

$$y = \frac{1}{2}at^2$$

With this formula I got 192.08m for the tower and 48.02m/s for my velocity. Closer?

 

[Lida]

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.

 

[Hootenanny]

With this formula I got 192.08m for the tower and 48.02m/s for my velocity. Closer?

I'm afraid it's still incorrect. Have you tried looking in your text for kinematic (SUVAT) equations? A summary of these equations can be found https://www.physicsforums.com/showpost.php?p=905663&postcount=2".

 

[Lida]

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?

 

[Lida]

I think the answer is 78.4 now...hopefully.

 

[Hootenanny]

I think the answer is 78.4 now...hopefully.

Correct

 

[Lida]

Finally!

Thanks!