Range Report Bowling Ball vs a Marble

[tictar]

I want to start off by saying this question is a little off topic but I don't know where to find the answer so I thought someone here who is good a ballistics would know the answer.

Here is the debated question here in the office:

Which would hit the ground harder? Dropping a bowling ball from 2 stories or dropping a marble off of the Empire State Building?


(To make note, I have $5.00 riding on the answer) I said the bowling ball.

I know a 223 bullet does not penetrate as well as a 500 Nitro for Elephant hunting, but I wanted to see what you guys think.

Thanks.

Edit, Sorry the bowling ball is falling from a 2 story building not a 3 story building. I don't know if that makes a difference.

Also a bowling ball weighs 16lbs and a marble weighs 5 grams.

 

[BigJohn141]

Re: Bowling Ball vs a Marble

Bowling ball for sure. I dont know the exact formulas but the marble would reach terminal velocity on the way down and I highly doubt that it would have enough speed to make up for the lack of mass over the bowling ball.

 

[kraigWY]

Re: Bowling Ball vs a Marble

The bowling ball of course. Both fall at the rate of 32fps per second. So speed is the same.

What makes a difference is weight. Figure the KE of both, Velocity squared X weight in grains / 450240 = KE.

Since the bowling ball is much heavier, its gonna hit harder.

Consider it something like this. A 150 grn bullet shot straight up is gonna have a KE about 30 ft lbs, returning to earth, it wont do much damage.

Now lets say you drop a 1000 lb bomb out of an airplane, its going to fall about the same speed as the 150 grn bullet but its gonna have the Ke of about 28,000,000 ft lbs.

 

[Pat M]

Re: Bowling Ball vs a Marble

but for the same energy use: you can throw the marble further than the bowling ball (outer space not figured in)

 

[shooterone]

Re: Bowling Ball vs a Marble

The best reasoning that I can use without digging out my physics book is the following: if you could wear a Kevlar reinforced steel alloy hard hard, would you choose to have the marble or bowling ball dropped on you head.

 

[csi:cyberspace]

Re: Bowling Ball vs a Marble

Hummm.... I would <span style="font-style: italic">think</span> the bowling ball simply due to the ostensibly insurmountable mass difference between the two. However, the two would not fall at the same speed. In a vacuum, yes. In a fluid environment such as the Earth's atmosphere, no. Drag and by extension mass do play a role in the determination of "terminal velocity", which is the second major factor in the kinetic energy upon impact. To accurately determine the KE of both, you'd have to know the mass of each, as well as the drag coefficient of each. I'm guessing the sheer mass of the bowling ball - 16 lbs - compared to mere grams for the marble would make it a no-brainer, so I suppose my entire posting here is moot, save for making the point that objects don't really travel at the same speed via acceleration due to gravity in a fluid environment. So what does all this mean? It means I have entirely too much time on my hands, as do you and your buddy

 

[Greg Langelius *]

Re: Bowling Ball vs a Marble

The terminal velocity is most directly related to sectional density, all other variables being rather close to identical.

Define "hits harder". If the answer is defined in terms of terminal energy, the answer is obvious.

 

[tomcatfan]

Re: Bowling Ball vs a Marble

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: kraigWY</div><div class="ubbcode-body">The bowling ball of course. Both fall at the rate of 32fps per second. So speed is the same.

What makes a difference is weight. Figure the KE of both, Velocity squared X weight in grains / 450240 = KE.

Since the bowling ball is much heavier, its gonna hit harder.

Consider it something like this. A 150 grn bullet shot straight up is gonna have a KE about 30 ft lbs, returning to earth, it wont do much damage.

Now lets say you drop a 1000 lb bomb out of an airplane, its going to fall about the same speed as the 150 grn bullet but its gonna have the Ke of about 28,000,000 ft lbs. </div></div>

The above is completely wrong. Both things have the same gravitational force acting on them (assuming they are at similar places on earth) not terminal velocity. Two things accelerate towards the surface of the earth at the same rate, but not at the same speed. For example drop a feather and a pen or pencil. I bet the pen or pencil hits the ground first.

The force of gravity at sea level is about 32.2 ft per second^2. The marble and bowling ball are going to hit the ground at very different speeds. Neglecting drag for the bowling ball, which is a pretty good assumption being as it will only go 28.19 ft/sec or 19.2 mph once dropped from a height of 20 ft. This has a kinetic energy of 6357 ft lbs of energy. The marble will go significanly faster than that. But you really have to ask which marble you are talking about. A shooter will be larger in diameter and more mass. This will effect the terminal velocity of the marble.

But to answer your question a 5 gram or .011023 lbs marble will have to travel at a speed of 1074 ft/sec or 732 miles per hour to reach an equivalent kinetic energy. This is roughly mach .9 at sea level so this is very unlikely (impossible).

I don't know which side of the argument you were on, but the bowling ball will hit with more kinetic energy than the marble. Now if you want to talk about stress concentration applied to the ground by the bowling ball vs. the marble, that is also a different conversation as you have to discuss the surface areas now interacting with the ground.

If you want to fact check my work reference: newtonian equations of motion and laws of kinetic energy.

 

[kraigWY]

Re: Bowling Ball vs a Marble

We need to go back and study our "NEWTON"

Find a copy of Hatcher's Notebook, the section on "Bullets from the Sky" will explain this.

You'll also find a better explanation from Hatcher's "Machine Guns 1916" though that book is gonna be hard to find.

 

[csi:cyberspace]

Re: Bowling Ball vs a Marble

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Greg Langelius *</div><div class="ubbcode-body">The terminal velocity is most directly related to sectional density, all other variables being rather close to identical.

Define "hits harder". If the answer is defined in terms of terminal energy, the answer is obvious. </div></div>
What HE said.

 

[csi:cyberspace]

Re: Bowling Ball vs a Marble

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: kraigWY</div><div class="ubbcode-body">We need to go back and study our "NEWTON"

Find a copy of Hatcher's Notebook, the section on "Bullets from the Sky" will explain this.

You'll also find a better explanation from Hatcher's "Machine Guns 1916" though that book is gonna be hard to find. </div></div>

See the following:

http://www.grc.nasa.gov/WWW/k-12/airplane/termv.html

Note the following:

<div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">
Objects do <span style="text-decoration: underline">NOT</span> fall at the same rate through the atmosphere.
</div></div>

Of course, I'm just assuming that NASA knows what they're talking about here.....

 

[tomcatfan]

Re: Bowling Ball vs a Marble

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: csi:cyberspace</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: kraigWY</div><div class="ubbcode-body">We need to go back and study our "NEWTON"

Find a copy of Hatcher's Notebook, the section on "Bullets from the Sky" will explain this.

You'll also find a better explanation from Hatcher's "Machine Guns 1916" though that book is gonna be hard to find. </div></div>

See the following:

http://www.grc.nasa.gov/WWW/k-12/airplane/termv.html

Note the following:

<div class="ubbcode-block"><div class="ubbcode-header">Quote:</div><div class="ubbcode-body">
Objects do <span style="text-decoration: underline">NOT</span> fall at the same rate through the atmosphere.
</div></div>

Of course, I'm just assuming that NASA knows what they're talking about here..... </div></div>

It really makes sense if you think about it. Things do not fall at the same speed regardless of their size and shape. If that were the case, there would be no point in parachutes.

The reason we use parachutes is that people typically fall through the atmosphere at about 120 mph depending on size and position of the person falling. In the case of Col. Joseph Kittinger he fell in a free fall at over Mach 1. The only person to break the sound barrier in free fall but I digress.

Now one can imagine what would happen if you hit the ground at 120 mph, it wouldn't go to well. So by using a parachute we drastically increase drag thus reducing the speed of descent. Even with a parachute, your subject to the 32.2 ft/sec^2 acceleration due to gravity, you just have a bunch of drag holding you up. I would rather not reference the books you mentioned. What I'm talking about is in any high school level physics book. I'm not trying to argue, its just the way it is.

 

[tomcatfan]

Re: Bowling Ball vs a Marble

So the marble looses to the bowling ball, but I think you can take some peoples money if you bet them about a bowling ball at 20 ft. vs. a good sized steel ball bearing at 500 ft. You can easily get a ball bearing heavy enough to create more kinetic energy than a bowling ball. But lets for the sake of argument go with a 12 pounder rather than 16. My little girly wrists don't like bowling with 16 pounders.

 

[5RWill]

Re: Bowling Ball vs a Marble

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Savage 10fp</div><div class="ubbcode-body">

The above is completely wrong. Both things have the same gravitational force acting on them (assuming they are at similar places on earth) not terminal velocity. Two things accelerate towards the surface of the earth at the same rate, but not at the same speed. For example drop a feather and a pen or pencil. I bet the pen or pencil hits the ground first.

The force of gravity at sea level is about 32.2 ft per second^2. The marble and bowling ball are going to hit the ground at very different speeds. Neglecting drag for the bowling ball, which is a pretty good assumption being as it will only go 28.19 ft/sec or 19.2 mph once dropped from a height of 20 ft. This has a kinetic energy of 6357 ft lbs of energy. The marble will go significanly faster than that. But you really have to ask which marble you are talking about. A shooter will be larger in diameter and more mass. This will effect the terminal velocity of the marble.

But to answer your question a 5 gram or .011023 lbs marble will have to travel at a speed of 1074 ft/sec or 732 miles per hour to reach an equivalent kinetic energy. This is roughly mach .9 at sea level so this is very unlikely (impossible).

I don't know which side of the argument you were on, but the bowling ball will hit with more kinetic energy than the marble. Now if you want to talk about stress concentration applied to the ground by the bowling ball vs. the marble, that is also a different conversation as you have to discuss the surface areas now interacting with the ground.

If you want to fact check my work reference: newtonian equations of motion and laws of kinetic energy.
</div></div>

Would you measure "hits harder" through force or energy? I was approaching it with newton's second law (ignoring air resistance).

If going strictly by energy wouldn't gravitational potential energy come into play as well for the marble?

 

[tomcatfan]

Re: Bowling Ball vs a Marble

I don't think potential energy would come into play here. Realistically potential energy only comes into play when evaluating the energy state of something when its converted to something useful. I mean everything has potential energy all the time, well everything with mass any way.

Typically when looking at collisions, which I think is what we are talking about here, kinetic energy is used. When bullets are compared to each other I think kinetic energy is used as well. I think some ammo comes with kinetic energy ratings on the box. Wiki references the muzzle kinetic energy usually with its muzzle velocity of various rounds. I guess if you don't want to use kinetic energy you could use momentum. but momentum is also a function of mass and velocity. In which case the bowling ball would win again. But you are right it completely depends on how you define "harder".

 

[The Mechanic]

Re: Bowling Ball vs a Marble

Sectional density and aerodynamics (drag). If the sectional density is the same and they are both spherical objects their terminal velocity would be the same but the mass will be the difference.

 

[sandwarrior]

Re: Bowling Ball vs a Marble

This pretty simple. If the two were dropped from the same distance from the ground to their nearest point on the falling object then they would both hit the ground at the same time. Due to the mass (weight) of the bowling ball, it would hit harder.

Now, if the center of the bowling ball and the center of the marble were lined up equidistant from the earth and dropped then the bowling ball would hit first. Not because the bowling ball is heavier but, because it's radius is many times more than that of a marble.

 

[5RWill]

Re: Bowling Ball vs a Marble

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: sandwarrior</div><div class="ubbcode-body">This pretty simple. If the two were dropped from the same distance from the ground to their nearest point on the falling object then they would both hit the ground at the same time. Due to the mass (weight) of the bowling ball, it would hit harder.

Now, if the center of the bowling ball and the center of the marble were lined up equidistant from the earth and dropped then the bowling ball would hit first. Not because the bowling ball is heavier but, because it's radius is many times more than that of a marble.</div></div>

But they're at different heights marble from the empire state building and bowling ball from 2 stories.

 

[TiroFijo]

Re: Bowling Ball vs a Marble

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: The Mechanic</div><div class="ubbcode-body">Sectional density and aerodynamics (drag). If the sectional density is the same and they are both spherical objects their terminal velocity would be the same but the mass will be the difference.</div></div>

Mass of a sphere changes with the third power of the diameter, and frontal area with second power. Sectional density is mass/frontal area, so a 8.5" diameter bowling ball has 17 times the sectional density of a 0.5" marble.

As pointed above by others, you can safely neglect air drag to calculate terminal velocity for a bowling ball dropped from a third floor, but the marble dropped from the top of a very tall building eventually reaches its equilibrium velocity (air drag against gravity) of about 130 mph.

You can do the calculations (it's physics 101), but the bowling ball wins by far

 

[Temp9]

Re: Bowling Ball vs a Marble

For those too lazy to calculate it:

Potential (gravitational, in this case) energy will directly convert to kinetic energy in the absence of air resistance (drag). I think we've already determined that air resistance is negligible for the bowling ball from 20 feet (6.1m), which is 2 stories for a short-ish building. A 12lb bowling ball has a mass of 5.44kg.
Gravitational Energy = (mass)*(gravitational acceleration)*(height)
which equates to 325.2 joules of energy for the bowling ball.

Now let's say the marble NEVER hits terminal velocity (you'll see in a second). This means its potential energy will also be equal to its eventual kinetic energy. Let's also say the marble weighs 4 grams (.004kg) which is a very generous rounding. Let's also toss the marble from the top of the antenna spire of the Empire State Building (443.2m). This gives us a whopping 17.4 joules of energy, again being generous with the rounding. The real values will be much lower because I bet it will hit terminal velocity.

Again in the absence of air resistance, the marble would have to be dropped from a height of 8296 meters, or 5.15 miles, to gain the same kinetic energy as the bowling ball. Of course, it'll hit terminal velocity far before this. Likewise, you could load the sucker into a muzzle loader and launch it at just over 400m/s to get that much kinetic energy.

The bowling ball would have to be dropped from a mere .33 meters (1.1ft) to top the marble off the Empire State Building (with no air drag).

So air drag is really not an important factor. Your friend may have lost $5, but there's so little competition, his pride should be a bit sore as well.

 

[tobias]

Re: Bowling Ball vs a Marble

I did some calculations.
Starting with the bowling ball: m = 5,4 kg, diameter = 21 cm, height = 6 m

Without drag: v = 10.85 m/s thus an energy of 318 J
With drag: v = 10.80 m/s thus an energy of 315 J
You can neglect drag.

Marble: m = 0.004 kg, diameter = 1 cm, height = 443 m
Without drag: v = 93.23 m/s thus an energy of 17.4 J (Time of flight: 9.50 s)
With drag: v = 44.4146 m/s thus an energy of 3.9 J (Time of flight: 13.05 s)

The marble reaches a terminal velocity of 44.704 m/s after t = 27 s.

The question “Which would hit the ground harder?” can actually not be answered by examining the kinetic energy. You have to calculate the force, when the ball or marble is hitting the ground and slowed down. The formula is F = delta p / delta t. Delta p is the change in momentum p = m*v and delta t is the time, that is needed for this change. The (change of) momentum is much bigger for the bowling ball and the time depends on the material and is not known. I would assume it is comparable in magnitude for both, so the ball hits harder.

 

[GrantB]

Re: Bowling Ball vs a Marble

Define (Hit the ground Harder)

 

[HeathenRifleman]

Re: Bowling Ball vs a Marble

So if I drop a styrofoam cup and depleted uranium ball out of a plane they both hit the ground at the same time right?

 

[csi:cyberspace]

Re: Bowling Ball vs a Marble

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: HeathenRifleman</div><div class="ubbcode-body">So if I drop a styrofoam cup and depleted uranium ball out of a plane they both hit the ground at the same time right? </div></div>
WOW! You <span style="font-weight: bold">really</span> haven't been paying attention, have you...

 

[abizdafuzz]

Re: Bowling Ball vs a Marble

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: HeathenRifleman</div><div class="ubbcode-body">So if I drop a styrofoam cup and depleted uranium ball out of a plane they both hit the ground at the same time right? </div></div>

Theoretically in a perfect vacuum that might be the case, but that has nothing to do with the problem at hand being in open air which is a viscous fluid. The cup looses too...

 

[HeathenRifleman]

Re: Bowling Ball vs a Marble

<div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: Abizdafuzz</div><div class="ubbcode-body"><div class="ubbcode-block"><div class="ubbcode-header">Originally Posted By: HeathenRifleman</div><div class="ubbcode-body">So if I drop a styrofoam cup and depleted uranium ball out of a plane they both hit the ground at the same time right? </div></div>

Theoretically in a perfect vacuum that might be the case, but that has nothing to do with the problem at hand being in open air which is a viscous fluid. The cup looses too... </div></div>

Just a joke guys lol

 

[XTR]

Re: Bowling Ball vs a Marble

Wow, 7 posts before anyone even got yo the 32ft/sec^2 part.

By the way, as I recall wasn't it Apollo 11 when they dropped what was it, a hammer and a feather on the moon to show that w/o atmosphere it really works?

Yes, in this case it it the bowling ball.

Now for fun,calculate the speed required by a mosquito to stop a loaded Kenworth assuming an inelastic collision. (Hey we were bored one night during Nuke School)

 

[MitchAlsup]

Re: Bowling Ball vs a Marble

Slightly different question:

Take a piece of mild steel 1" thick and place it so the bowling ball will land upon it and the marble will land upon it.

Which landing will forge a tiny swath of the steel plate to a higher tensile strength?

Here, the cross-sectional area of the bowling ball is a definate disadvantage to the smaller (and more dense) steel ball bearing.

 

[TRAAV]

Re: Bowling Ball vs a Marble

I actually feel dumber than I did before I read this