Exploring Projectile Motion with Compressors

[knightryder]

Homework Statement

Hello everyone - here's my question: I am doing an assignment on projectile motion and I will be launching some balls from a compressor (that I have not seen yet!). I know how to calculate how much work will be done by the air expanding (will obv. depend on how much pressure is in the compressor); but i do not know how to go from there:

do i say that the work done will equal the kinetic energy of the ball and just use the simple projectile motion formulae? If i do, isn't that neglectling the time taken for the ball to accelerate?
If I take acceleration into account, i guess i would use momentum of air hitting ball = momentum of ball (elastic collision) then use f=ma on the ball. This will give me the acceleration of the ball. But how do I use the acceleration of the ball upwards with gravity taken into account? This would mean the acceleration would be highest at the launch, be 0 somewhere midair, decrease to 9.8 m/s then stay there? Perhaps there is an easy equation that I am forgetting (I would never rule that out!)

Homework Equations

ummm.. that's what I am wondering..
if my first guess is right, then I use Ke= 1/2 m v2,
if my second guess is right , then I use Newton's 3rd.

The Attempt at a Solution

Please read part 1.



Thanks for your help.
P.S. If possible use metric units- I am Grade 11 Australia.

 

[LowlyPion]

Welcome to PF.

I suspect you already know, but here are the kinematic equations for motion once the ball is in flight.
https://www.physicsforums.com/showpost.php?p=905663&postcount=2
And they an also be used to calculate your acceleration and initial velocity depending on what you are measuring.

As to your question about how complex ... that can be as complicated as you want it to be.

Your biggest problem will likely be in getting accurate measurements and determining your error tolerances. The easiest way to get a good crack at what your initial velocity is would be to fire the ball straight up and time its total time of flight. That of course ignores air resistance, which is certainly a factor, but it can give you a ball park working initial velocity.

Good luck.

 

[thomate1]

Hello there, it sounds like you have an interesting assignment! Projectile motion with compressors can be a bit tricky, but I can help guide you through it. First, let's review the basic principles of projectile motion.

Projectile motion is the motion of an object that is launched into the air and then moves under the influence of gravity. The path of the object is called its trajectory and it follows a parabolic shape. The motion of the object can be described using equations for displacement, velocity, and acceleration.

In this case, the compressor is providing a force on the ball, causing it to accelerate and launch into the air. As you mentioned, the work done by the air expanding will depend on the pressure in the compressor. This work will then be converted into kinetic energy as the ball is launched.

To calculate the trajectory of the ball, you can use the equations for projectile motion. This will give you the position, velocity, and acceleration of the ball at any given time. However, as you pointed out, this neglects the time taken for the ball to accelerate.

To take acceleration into account, you can use the principle of conservation of momentum. This means that the momentum of the ball after it is launched will be equal to the momentum of the air hitting the ball. You can then use the equation F=ma to calculate the acceleration of the ball.

To account for gravity, you can use the equation for gravitational acceleration, which is 9.8 m/s^2. This means that the acceleration of the ball will decrease as it moves upwards, and then will be 9.8 m/s^2 as it falls back down.

In summary, to calculate the trajectory of the ball launched from the compressor, you will need to use equations for projectile motion, conservation of momentum, and gravitational acceleration. I hope this helps and good luck with your assignment!