This would either belong in here of math odds and ends, but here is probably better. I have a trebuchet to be built, it's kind of like a seesaw, with something to be thrown on one end, and a counterweight on the other. I'll ignore friction for the time being. So the formula for Torque is given in terms of the weights of the beam, the current angle and both end objects. Inertia is constant.
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It looks like that a bit. So I'll let m3 and m4 be the two weights, and m1 and m2 be thee mass of the two parts of the beam, left to right. l1 and l2 are the lengths. x is the angle it's at, from the beam to the vertical, 90 being the angle in the picture. v is the angular velocity, and a is angular acceleration. t is time. And m4 is the object being thrown, so the beam will turn counter clockwise.
Torque=T=9.8sin(x)[(m3)(l1)-(m4)(l2)+((l1)/2)(m1)-((l2)/2)(m2)]
Inertia=I
a=T/I
T/I can really be simplified to k*sin(x)
dv/dt=a
dx/dt=v
So k*sin(x)=x`` which probably isn't solvable if I'm right. But I really hope not, but if I am, can it be solved?
Also, there's been ideas of the object being in a sling attached by a string, to somehow increase the centrifugal force. I would have a hard time illustrating this, but I have no idea for the equations in that case. Wheels have also been suggested, which even further complicate this. So hopefully someone can help. Thank you!
to see what a trebuchet looks like, go to
http://www.trebuchet.com/
*==========^==========*
(spacespace)|
(spacespace)|
It looks like that a bit. So I'll let m3 and m4 be the two weights, and m1 and m2 be thee mass of the two parts of the beam, left to right. l1 and l2 are the lengths. x is the angle it's at, from the beam to the vertical, 90 being the angle in the picture. v is the angular velocity, and a is angular acceleration. t is time. And m4 is the object being thrown, so the beam will turn counter clockwise.
Torque=T=9.8sin(x)[(m3)(l1)-(m4)(l2)+((l1)/2)(m1)-((l2)/2)(m2)]
Inertia=I
a=T/I
T/I can really be simplified to k*sin(x)
dv/dt=a
dx/dt=v
So k*sin(x)=x`` which probably isn't solvable if I'm right. But I really hope not, but if I am, can it be solved?
Also, there's been ideas of the object being in a sling attached by a string, to somehow increase the centrifugal force. I would have a hard time illustrating this, but I have no idea for the equations in that case. Wheels have also been suggested, which even further complicate this. So hopefully someone can help. Thank you!
to see what a trebuchet looks like, go to
http://www.trebuchet.com/