Yr 11 Trebuchet Project Calculations

[darkblade4]

Homework Statement

I have a physics project in which I need to find a relationship between the distances from each side of the throwing arm of a trebuchet and the actual throwing distances. Let's call the distance from the counter-weight side of the throwing arm to the axle variable 'A' and the distance from the object basket to the axle variable 'B'. I had to investigate the effect changing the values of these had on throwing distance. I kept everything else constant.

3. The Attempt at a Solution +relevant equations

-Firstly I found the distance that the counterweight dropped before the arm became perpendicular to the floor (at which point the object is flung, btw there is no sling), this would be the vertical displacement. I then used Energy(Potential)=mgh using this value of h. I equated this to E(potential)=Energy(kinetic)=0.5mv^2 (when the counter-weight had been displaced the full vertical displacement of h) and then solved for the velocity the counter-weight should be at the point when the arm is perpendicular to the floor and the object is thrown. I multiplied this velocity by B/A because the velocity would be amplified by the ratio of the arm lengths. Then I calculated the time before the object hit the floor by using: s=distance from the floor when the object is released=ut+0.5at^2 and I used a=9.8ms^-2 . I solved for t to find the time before the object hit the floor. This value of t was then substituted into v=s/t s=vt using the horizontal velocity (horizontal component of the velocity) as 'v' and the time the object was air-born for as the value for 't' and this returned the horizontal displacement.

I hope you can understand what I just said and btw these are going to be approximations, not exact distances thrown because I don't know how to use torque and moment because this is just yr 11.

I also have another question, how can I graph this? I tried to use A/B as the x-axis and the throw distance as the y-axis but since the x values are A/B the gradient is not linear because each step in x is different to the previous, ie, when X=1, A=B, when X=2, A=2B which is a factor of two, however when X=3, A=3B which is not the same as the step from X=1 to X=2. If any of that makes sense, can you please help me.

thankyou for your help

 

[Stevedye56]

I have a quick question about the actual trebuchet. Is it a fixed arm on an A frame or is it a floating arm?

If it is floating this may help out.

http://students.eou.edu/~duyckj/treb-final/node4.html

 

[darkblade4]

the one i used was a fixed axle trebuchet, i followed this tutorial without using a sling: http://www.io.com/~beckerdo/other/trebuchet.html so it is a fixed axle trebuchet.

 

[TheHurler]

How about a computer simulator that can graph some kinds of data and can be used to test a whole variety of parameters. I have some very accurate simulators for both a traditional style machine and the FAT available at www.Trebuchet.com

Good luck, and try asking the folks at www.TheHurl.org too. I'm sure they can help!

 

[darkblade4]

I've tried a few simulators but they don't seem to work with my parameters seeing as i don't have a sling and the object is let out when the arm is perpendicular to the floor..can someone just confirm if the formulas in my previous post give the correct answer?
please!