Physics question

RoadHustler

RoadHustler

AzB Silver Member
Silver Member
I was wondering about something we all experience at least once and didn't know how to figure it out so I thought I would put it to you folks. Someonewill know the answer ehem Mr. Jewett?

If released from straight up and allowed to fall flat on the floor how fast is the tip of a pool cue moving when it hits the floor. Does it change with weight and balance?

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Doesn't it accelerate until it reaches terminal velocity? I dunno ... but I think how far it is dropped from makes a difference regarding how fast it goes until it gets to that speed. :scratchhead: LOL, don't go by me though ... :smile:
 
Right... its not all that simple also the end sitting on the floor should affect acceleration. I think?

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So the butt is sitting on the floor, and the tip is pointed straight up at the ceiling, and then the cue falls over?

Yeah, that can be calculated (ignoring air resistance), but you would need to know the length of the cue, center of mass of the cue, and initial angular velocity. It's not too difficult, but it's been waaaaay too many years since I graduated, so it I'll defer to someone like Dr, Dave. :grin-square:




Just to add: This isn't as simple as calculating linear velocity. We are basically dealing with an inverted, physical (solid) pendulum. So solving for angular velocity is the key to the problem. And I'm not up to it anymore.
 
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Its been years since I did a physics problem. Someone needs to double check my work! lol. I got about 9.25 meters per second, or 21 miles per hour. This is with the stick standing on its bumper, vertically, and let go, to drop on the ground so it ends up horizontal.

Screen Shot 2015-10-04 at 2.37.55 PM.jpg

Edit, I was going to calculate the cg of the trapezoid pool cue mathematically, that's why I had the width of the tip and butt. Then, I decided just to measure my own cue's balance point with my finger and a tape measure. So I never used the width numbers in these calculations.
 
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If my thought process is correct, no, the mass of the cue will not affect the velocity of the tip when it strikes the ground. The only things that matter are the center of gravity of the cue (balance point) and the total length of the cue. The mass cancels out when doing the conservation of energy equations (that's why a bowling ball and a pool ball will fall at the same rate when dropped).
 
It would depend.
If the cue belonged to someone other than yourself then by my precise calculations the cue would hit the floor only slightly ahead of the time it would take for the owner to shit his pants. Now bear in mind that this time could change depending upon the relative value of the cue to said owner.
In either case it would behoove you, as the conductor of this noble experiment, to see how fast you can find an exit. A worthwhile experiment in it's own right. :smile:
 
expectations

I expected slower than break speeds. So less than 20 mph I was surprised by 3 mph that one sounds pretty slow.

But what the hell do I know I had absolutely nothing to base my feeling on. Just watched a guy forget he was holding his cue this weekend and had a unobstructed view of it hitting the floor. Spent the day thinking about how surprised he was when the tip popped off. It festered the question.
 
If released straight down, 32 feet per second, per second, until terminal velocity. If some part is already on the floor or other object (pool table) it depends. An 18 oz. cue and a 25 oz. cue falls at the same rate.
 
RoadHustler said:
I expected slower than break speeds. So less than 20 mph I was surprised by 3 mph that one sounds pretty slow.

But what the hell do I know I had absolutely nothing to base my feeling on. Just watched a guy forget he was holding his cue this weekend and had a unobstructed view of it hitting the floor. Spent the day thinking about how surprised he was when the tip popped off. It festered the question.
Click to expand...

The tip popped off when the shaft off the cue whipped after the fall -
All of the energy that is built in the fall is released in the whip at the tip - pretty violent
Most of the time a cue falls flat and there is no whip - pick it up and chalk it


bill
 
When the side of the tip hits the floor, there's a very strong impact.

Now, you would think that the tip stands through impacts all the time, but there is a difference. When the tip hits the cue ball the impact is carried by the materials more so than the adhesive. It's a compression load so the glue pretty much just go's along for the ride.

But, when the side of the tip hits the floor, it's a shear load that's carried virtually 100% by the adhesive holding the tip on. CA, or cyanoacrylate is known to be brittle when it comes to impacts. In many cases, the CA just gives up and the tip comes off. In some cases, the adhesive is fractured, but the tip is still on. Often, these come off very soon after the cue was dropped, but I've seen them come off days later as well.


Royce
 
RoadHustler said:
If released from straight up and allowed to fall flat on the floor how fast is the tip of a pool cue moving when it hits the floor. Does it change with weight and balance?
Click to expand...
Here's my analysis:

cue_tip_floor_speed.JPG

Assuming a cue is approximately a long, thin cyclinder, the result depends only on cue length. To get a more accurate answer, the result would depend on cue length (L), weight (m), mass moment of inertia (Iend), and balance point (h).

Regards,
Dave
 
dr_dave said:
Here's my analysis:

cue_tip_floor_speed.JPG

Assuming a cue is approximately a long, thin cyclinder, the result depends only on cue length. To get a more accurate answer, the result would depend on cue length (L), weight (m), mass moment of inertia (Iend), and balance point (h).

Regards,
Dave
Click to expand...

It looks like I forgot all about rotational kinetic energy in my analysis. I will do it again later.

You are approximating the cue as a long cylinder, and have its center of mass at L/2, which is used or the starting potential energy height. A typical 58" cue with a balance point about 19" from the bumper would be more like L/3 for h. That may be a significant differnce. Don't kill me, I'm very rusty! lol.

Edit, never mind my question. I have to rework it for myself and figure it out. Thanks.
 
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Ha .. here's how shot I am, I totally misunderstood the question. Here I am thinking you are dropping the cue out of your hand with the tip facing down toward the floor like you were trying to spear a spider walking across the floor.

Now that I understand .... I completely concur with all those calculations, and if there's any pie left over I want some. :grin:
 
That's the exact method I used to arrive at the numbers in my previous post. Good to see I still remember something from those physics classes! Thanks for the confirmation.

dr_dave said:
Here's my analysis:

cue_tip_floor_speed.JPG

Assuming a cue is approximately a long, thin cyclinder, the result depends only on cue length. To get a more accurate answer, the result would depend on cue length (L), weight (m), mass moment of inertia (Iend), and balance point (h).

Regards,
Dave
Click to expand...
 
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