Tennis Ball Launcher Predicted Distance Help

[imusion]

For our physics class we have to make a tennis ball launcher and we are also responsible for doing calculations to predict the distance our launcher will be able to launch the tennis ball.

I have done the calculations here and can be seen in this PDF file:
http://imusion.net/backup/yahoo.pdf

The diagram of our launcher can be seen in here:
http://imusion.net/backup/yahoo.jpg ...

I have looked through it but I know it is wrong. For u = 0.5kx^2 which is the first equation, x is the distance we can stretch the bungee cord which is supposed to be 1.2m and not 1.2-0.955(0.955 being the "slack " length of the cord). The problem is if I use 1.2m for x and follow through with everything else I get a ridiculous number like 500m. Which I know is not right.

Just a short explanation of what else I did for the calcs. After I found the PE of our bungee cord I plugged it into E=0.5mv^2 to figure out the velocity of the ball. With E being the potential energy present in the bungee cord. After I found the velocity I used projectile motion equations to solve for time. Because of the polynomial I had to use the quadratic equation to find out the time the ball is in the air. Then afterwards I plugged it into the horizontal distance.

If anyone can look through what I did and see if you can find what I did wrong I would appreciate that. I have looked through it numerous times already but I still dont' know what I'm doing wrong.

 

[tyco05]

I have looked through it but I know it is wrong. For u = 0.5kx^2 which is the first equation, x is the distance we can stretch the bungee cord which is supposed to be 1.2m and not 1.2-0.955(0.955 being the "slack " length of the cord). The problem is if I use 1.2m for x and follow through with everything else I get a ridiculous number like 500m. Which I know is not right.

I'm not sure what you mean here. Can you stretch the cord 1.2m or is that the final length of the cord?
Remember that with Hooke's Law, the force comes from the spring (cord) being displaced from the equilibrium position.

Also, are your cords in line with the direction of shooting? Or are they at an angle?
How many cords do you have? Where did you get the k value from? Did you measure it, or estimate, or from a book or similar?

Another thing to consider (but at your level you probably won't have to calculate) is the reality of air resistance and it's effect on the flight path and distance. (Worth at least a mention in your report).Your picture looks like you have a 'platform' for the ball to sit on... don't forget that this has mass too.

 

[imusion]

I'm not sure what you mean here. Can you stretch the cord 1.2m or is that the final length of the cord?
Remember that with Hooke's Law, the force comes from the spring (cord) being displaced from the equilibrium position.

Also, are your cords in line with the direction of shooting? Or are they at an angle?
How many cords do you have? Where did you get the k value from? Did you measure it, or estimate, or from a book or similar?

Another thing to consider (but at your level you probably won't have to calculate) is the reality of air resistance and it's effect on the flight path and distance. (Worth at least a mention in your report).


Your picture looks like you have a 'platform' for the ball to sit on... don't forget that this has mass too.

From the equilibrium position, I can stretch the cord 1.2m MORE to the ground. So in reality x should equal 1.2m in my calculations.

The cords are at a 45 degree angle to the horizontal. 2 bungee cords are one one side and 2 bungee cords are on the other. The k value was found by doing a force/distance graph by putting different masses on the 2 bungee cords. Then the k value is doubled to account for the other 2 bungee cords on the other side.

Yes correct, we are told to neglect air resistance etc.

The platform has turned out just to be a small yogurt cup, so I don't think it has much significant mass.

 

[tyco05]

The cords are at a 45 degree angle to the horizontal.

OK, I figured this much, but what I was really asking was how wide is your apparatus? You may need to resolve your forces for this as well (see attachment for a diagram).

Is the mass of the bungee cords significant? This could also affect things.

 

[imusion]

The cords are lined up to shoot forwards. Our launcher is probably 75cm wide. At most 1m wide. The bungee cords do not have much mass either.

 

[imusion]

No one can provide insight on this? I know it has been awhile but I still want to figure this out haha.