How mass affects projectile motion

[xp8nter]

Hi, I am a mechanical engineering student and I am currently taking Dynamics.

We have been assigned a project that basically revolves around the dynamics of a vacuum cannon. The cannon we have designed shoots ping-pong balls and we have found that shooting the balls without any added mass will make the ball travel in random directions and go a short distance. We also found that when mass was added it shot over a 100 yards. I can only assume that is due to the balls mass and its relationship with air resistance.

Basically my question is how can I determine the optimal mass of the ping-pong ball to make it travel the furthest distance.

Anything would help because I am having trouble finding thing online.

Thanks A Lot

-Jason

 

[dulrich]

I think you are right is saying that air resistance is the key factor here. Air drag can be quite complicated to calculate from first principles. Here is a wikipedia link to get started:

http://en.wikipedia.org/wiki/Drag_(physics)

You have two extremes. On the one hand is the ping pong ball with low mass. By Newton's second law we know that a = F/m. Since the air drag does not depend on the mass of the ball, the lower the mass the higher the acceleration (or deceleration).

On the other hand if your mass is too large, the force of the cannon is the limiting factor. Again a = F/m (where F is the force from the cannon), but now you want to maximize the acceleration.

These are the two competing forces in play. The latter should be easy to measure (maybe start by measuring the speed out of the cannon). The former is more difficult due to the complex nature of air drag, but you might be able to get some estimates based on average speed, time in flight and get some bounds around its magnitude.

 

[SimonRoberts]

I would guess (and it is a guess, not being a golfer myself) - that a golf ball probably has the density it has to maximise this very problem. Maybe that would be a good starting point? Of course, golf balls have more complicated surface patterns with dimples and whatnot, but might give you a ballpark figure.

,Simon

 

[hotvette]

This kind of problem gets to the heart of what engineering is all about. Perform experiments based on theoretical knowledge only to find out that many additional factors come into play that you may or may not be able to readily define or account for. Example: depending on how you add weight to the ping pong ball, you could get strange rotations of the ball (due to imbalance) after it is launched that will affect the trajectory. Refine the experiments based on observed behavior (and engineering judgement). Plot a curve of distance vs weight and estimate the optimal situation based on the shape of the curve.

I think the golf ball (SimonRoberts) is a great example. It was no doubt refined over years of trials. Often the theoretical understanding comes alongside or even after the experimentation.

 

[PJC01]

Hello Jason,

I would first like to commend you on your project and your curiosity about the dynamics of projectile motion. It is a fascinating subject and I am glad to see your interest in it.

To answer your question, the optimal mass for a projectile to travel the furthest distance depends on various factors such as the initial velocity, angle of launch, and air resistance. However, in general, increasing the mass of the projectile will increase its momentum, making it more resistant to air resistance and allowing it to travel further.

In your case, adding mass to the ping-pong ball increased its momentum, allowing it to overcome air resistance and travel over 100 yards. To determine the optimal mass for your cannon, you can conduct experiments by gradually increasing the mass of the ping-pong ball and measuring the distance it travels. This will give you an idea of the relationship between mass and distance in your specific setup.

Another approach could be to use mathematical equations such as the projectile motion formula or the drag force equation to calculate the optimal mass. However, keep in mind that these calculations may not account for all the variables and may not be as accurate as experimental data.

I would also suggest consulting with your dynamics professor or a physics expert for further guidance and resources in determining the optimal mass for your project. Good luck with your project!