Supersonic ping pong ball cannon

In summary, a supersonic ping pong ball cannon is a device that uses compressed air to launch ping pong balls at supersonic speeds, typically exceeding the speed of sound. It works by using compressed air to accelerate the ball through a barrel and requires materials such as PVC pipe, a valve, an air compressor, and a trigger mechanism to build. While it can be used for educational and recreational purposes, proper precautions should be taken to ensure safety. It can also be used for scientific research on high-speed projectiles and their effects.
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voko
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Description: http://arxiv.org/ftp/arxiv/papers/1301/1301.5188.pdf

So I though I would do a back-of-envelope check if that was even possible. I decided to model that as adiabatic expansion from the pressure plenum into the barrel, ignoring any effect the nozzle could make.

So ##p_i V_i^{\gamma} = p_f V_f^{\gamma}##, yielding ## p_f = p_i (\frac {V_i} {V_f})^{\gamma} ##. Then, the internal energy is ## U = \hat{c}_V n R T = \hat{c}_V p V ##, so ## U_i - U_f = \hat{c}_V (p_i V_i - p_f V_f) = \hat{c}_V (p_i V_i - p_i (\frac {V_i} {V_f})^{\gamma} V_f) = \hat{c}_V p_i V_i (1 - (\frac {V_i} {V_f})^{\gamma - 1}) ##.

From the dimensions given I computed ## V_i = 0.0042 m^3, \ V_f = (0.0042 + 0.0028) = 0.007 m^3 ##; two pressure values were mentioned, so I took ## p_i = 500 kPa ##. I assumed air is a diatomic ideal gas, so ## \gamma = 7/5, \hat{c}_V = 5/2 ##, so the final result is ## U_i - U_f = 970 J ##.

Then the mass of the ping pong ball is 2.7 g, the reported speed was 406.4 m/s, thus its kinetic energy was 223 J, which is quite a bit less than the diff in the air's internal energy, which makes the whole thing plausible - at least in this model.

Now, my question is, is there any obvious problem with the model and, perhaps, the computation? How would one model the effect of the nozzle?
 
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An obvious problem with the model is that it does not take into account the effect of the nozzle. The nozzle has a significant influence on the air's speed and pressure, and this should be taken into account when computing the decrease in internal energy. One way to do this would be to use the Bernoulli equation to relate the pressure and velocity of the air at different points in the barrel, and then use the ideal gas law to calculate the temperature and internal energy of the air at those points. This would give a more accurate result for the difference in internal energy.
 

1. What is a supersonic ping pong ball cannon?

A supersonic ping pong ball cannon is a device that uses compressed air to launch ping pong balls at supersonic speeds, typically exceeding the speed of sound (343 meters per second).

2. How does a supersonic ping pong ball cannon work?

A supersonic ping pong ball cannon works by using compressed air to accelerate a ping pong ball through a barrel. The pressure from the compressed air builds up behind the ball, propelling it forward at high speeds.

3. What materials are needed to build a supersonic ping pong ball cannon?

To build a supersonic ping pong ball cannon, you will need a PVC pipe for the barrel, a valve to release the compressed air, an air compressor, and a trigger mechanism. You may also need some additional materials for stability and safety, such as a sturdy base and protective gear.

4. Is a supersonic ping pong ball cannon safe to use?

Like any other scientific experiment or project, proper precautions should be taken when using a supersonic ping pong ball cannon. It is important to wear protective gear, follow safety guidelines, and use the cannon in a controlled and safe environment to avoid any potential hazards.

5. What are the potential applications of a supersonic ping pong ball cannon?

A supersonic ping pong ball cannon can be used for educational purposes, such as demonstrating the principles of air pressure and projectile motion. It can also be used for recreational purposes, such as launching ping pong balls at targets. Additionally, it can be used for scientific research on high-speed projectiles and their effects.

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