SpudFiles

When i think of school i think of a place of mature, intelectual nd able teachers who teach either hopeless wastes of time or intelegent people who will achieve something in life. IF you think of latter student and the teacher then really a school would be a great place for a slightly more difficult or dangerous eyperiment...

Seeign reality is different from the above i undestand your concern.

jimmy101 wrote:

willarddaniels wrote: A fair question that I anticipated.
Without details, the references and numbers can be seen and derived by using both Bernoulli's equation and Pascal's principle.

Hmmm, I think I'll have to call Shenanigans on this one.

Not going to get supersonic, certainly not mach 2 outside the barrel.

Best I can find puts the velocity at roughly mach 0.8.
http://www.physics.ubc.ca/~outreach/phy ... Lesson.ppt

using a balistic pendulum they measure ~260m/s (Mach 0.78 ).

Not anywhere near Mach 1, let alone Mach 2.

Use it with the numbers I had suggested: 2m barrel and a lighter (cheap) ping pong ball of 1 gram. (I didn't mention this weight before). This will provide you with 676.7 m/s. Mach 2 is 662-686 m/s, depending on temp and humidity.
Conclusion: yes, mach 2 is quite possible if you calculate your numbers correctly using the powerpoint presentation you provided and set up your experiment properly.

EDIT: great video as well. Unfortunately, there is not a good method for calculating the final velocity of the ping pong ball; the are many external forces acting on this experiment that the teacher will conveniently ignore for the sake of teaching the desired information: coefficient of friction of the pendulum against the paper or around the fulcrum will be part, but not all of these items. There is also not a 100% (or anywhere close to it) energy transfer in this conservation of energy experiment because the ball bounces back off of the bloc, taking a significant amount of energy with it. With the difference in masses, probably between 25 and 50%. They probably also did not take into account I (moment of inertia) of the contraption nor can you have a perfect or even near perfect arm in such a setting, losing energy to sound and heat.
Also, notice they were using heavier ping pong balls that will travel slower than the ultra light, cheap ones. You can be fairly certain they used these so they could reuse them in such destructive experiments (smashing them against blocks and cans (though very cool).

Any more questions? Thanks for helping to prove my point with your powerpoint and video.

willarddaniels wrote:

jimmy101 wrote:

willarddaniels wrote: A fair question that I anticipated.
Without details, the references and numbers can be seen and derived by using both Bernoulli's equation and Pascal's principle.

Hmmm, I think I'll have to call Shenanigans on this one.

Not going to get supersonic, certainly not mach 2 outside the barrel.

Best I can find puts the velocity at roughly mach 0.8.
http://www.physics.ubc.ca/~outreach/phy ... Lesson.ppt

using a balistic pendulum they measure ~260m/s (Mach 0.78 ).

Not anywhere near Mach 1, let alone Mach 2.

Use it with the numbers I had suggested: 2m barrel and a lighter (cheap) ping pong ball of 1 gram. (I didn't mention this weight before). This will provide you with 676.7 m/s. Mach 2 is 662-686 m/s, depending on temp and humidity.
Conclusion: yes, mach 2 is quite possible if you calculate your numbers correctly using the powerpoint presentation you provided and set up your experiment properly.

EDIT: great video as well. Unfortunately, there is not a good method for calculating the final velocity of the ping pong ball; the are many external forces acting on this experiment that the teacher will conveniently ignore for the sake of teaching the desired information: coefficient of friction of the pendulum against the paper or around the fulcrum will be part, but not all of these items. There is also not a 100% (or anywhere close to it) energy transfer in this conservation of energy experiment because the ball bounces back off of the bloc, taking a significant amount of energy with it. With the difference in masses, probably between 25 and 50%. They probably also did not take into account I (moment of inertia) of the contraption nor can you have a perfect or even near perfect arm in such a setting, losing energy to sound and heat.
Also, notice they were using heavier ping pong balls that will travel slower than the ultra light, cheap ones. You can be fairly certain they used these so they could reuse them in such destructive experiments (smashing them against blocks and cans (though very cool).

Any more questions? Thanks for helping to prove my point with your powerpoint and video.

Nope, still have to call shenanigans.

In order to get a supersonic ball you must get the air pushing it supersonic. That ain't going to happen in a small diameter tube. Doesn't matter how much energy you put into the system the air won't go supersonic. In addition, as the air expands (which it does) it cools off. The speed of sound is very dependent on the air temperature (but not the density). As the temp drops the speed of sound also drops. So Mach 1 in the tube isn't even ~700FPS, it is significantly less.

If you actually read the PPT on slide 13 it says you also have to take into account the mass of the air column that also has to be accelerated. Since the ammo is so light, the mass of the air column is significant. The PPT puts the maximum velocity at 241.8m/s, well below the speed of sound. On slide 15 (with the crappy backgound color) is a plot of velocity versus barrel length. As you can see, the velocity is going asymptotic to a speed less than Mach 1. No matter how long the barrel is you won't ever get the ping pong ball up to Mach 1.

A 1 gram ping pong ball traveling at mach 2 has about 220J of kinetic energy.

Now, maybe my calculations are wrong, but I found that to draw a vacuum in a tube 1 inch in diameter by 2 meters you need about 75 ft-lbs of force, or 101 joules.

So we have an energy efficiency of 220% ?

***

Edit: I just saw in an earlier post this was 1.5" pvc. In that case this design doesn't break any energy laws if the weight of air isn't considered.

If it is, and we have 3 grams of air going mach 2, the total energy released is around 900 J with an efficiency of 360%.

willarddaniels wrote:Unfortunately, there is not a good method for calculating the final velocity of the ping pong ball; the are many external forces acting on this experiment that the teacher will conveniently ignore for the sake of teaching the desired information: coefficient of friction of the pendulum against the paper or around the fulcrum will be part, but not all of these items. There is also not a 100% (or anywhere close to it) energy transfer in this conservation of energy experiment because the ball bounces back off of the bloc, taking a significant amount of energy with it. With the difference in masses, probably between 25 and 50%.

Actually, the ball bouncing off the block causes exactly the opposite problem.
It's not energy transfer that matters here, it's momentum transfer (because kinetic energy is not conserved in collision. Momentum is).

The fact that the ball has bounced back (i.e. It's velocity change has exceeded it's original speed) has increased the impulse on the pendulum, which will cause it to read over, particularly with such a light pendulum relative to the projectile.

With ballistic pendulums, if the projectile comes to a complete halt (or is trapped by the pendulum), you get an accurate result.
If it punches through the pendulum, it reads under velocity. If it bounces back, it will read over velocity. Simple rules of momentum.


The other thing is that because the pendulum was pressed against the end of the muzzle, the air that was behind the projectile - which itself has momentum - will have continued moving into the pendulum and will have had some further effect on increasing the results.

You are right, the result doesn't mean much, but you're then compensating in the wrong direction.

They probably also did not take into account I (moment of inertia) of the contraption nor can you have a perfect or even near perfect arm in such a setting, losing energy to sound and heat.

I can confidently tell you that with those things considered, the projectile was going slower than they calculated, even were you to consider your other complaints, which are of far smaller magnitude than the points I have brought up.

The friction in the system has little effect on the result. Ballistic pendulums are VERY reliable pieces of kit - at least, this is as long as they're used right (which this one wasn't).
If used properly (i.e. the projectile is trapped in the pendulum and the muzzle blast does not affect the pendulum), although they're not very precise (that being that you will struggle to determine a result to better than a few metres per second), they are accurate (That being that they will never give you a result that is outright wrong)