Calculating Trebuchet Mechanics

[andy343]

Can someone please explain to me how to calculate Trebuchet mechanics?
I know it involves lever mechanics with torque, angular velocity and projectile motion but I
just can't seem to put these things together.

 

[DennisN]

Hi andy343! There's quite a lot of mechanics going on when dealing with trebuchets, so they are pretty good as physics examples.

A trebuchet uses potential energy which gets converted to kinetic energy. First you do do work on the system by pulling back the throwing arm (analogous with compressing a spring). When you release the arm, the potential energy will be transformed to kinetic energy (of both the projectile+throwing arm).

The potential energy can be calculated by W=mgh where m=mass of counterweight being lifted, g=standard gravitation≈9.81 m/s² and h=the height to which the counterweight is lifted to (or rather, height difference). See gravitational potential energy.

Some of this energy (not all) will be transformed to kinetic energy of the projectile. See formula for kinetic energy.

For trajectories of the projectile, these formulas can be used (range of trajectory, height of trajectory, time of flight etc.) For trajectory calculations you need initial velocity, initial angle and standard gravitation g≈9.81 m/s².

 

[andy343]

Umm, how bout lever mechanics and the angular velocity when the counterweight falls since it does not falls perfectly down and how would I convert the PE to KE, don't I have to use lever mechanics and torque since its a first class lever.

 

[DennisN]

It depends on what you exactly are interested in calculating (you did not specify this); I described the basic energy mechanism for a trebuchet, some energy relations and projectile formulas.

To set up a basic model, we would need a couple of more parameters; lever length and at which height the lever releases the projectile. The lever mass would also be good to know. As I said, trebuchets are good examples with quite a lot of mechanics going on .

The initial velocity of the projectile (when it finally is released by the arm) is needed to calculate the trajectory.

You can make approximate calculations of this without using forces. The actual movement of the counterweight is not particularly important; the important thing is the height difference from max to min height of the counterweight.

You'll need these parameters:

• mass of projectile
• mass of counterweight
• height difference of counterweight
• lever length
• lever mass
• height at which the lever releases the projectile

Step suggestions:

• calculate potential energy stored (W_p) (this is the energy that will be conserved during the operation)
• calculate work done (W_d) by raising the lever+projectile to the release height (hint: this will involve two calculations)
• calculate resulting kinetic energy of the projectile (W_k); W_k ≈ W_p-W_d (since energy is conserved)
• use W_k to calculate initial velocity of projectile (when the projectile is released it will cease to be accelerated by the lever)
• the initial velocity, release angle and g can be used to calculate the trajectory

(of course there are other factors involved like mechanism friction and air drag, but it all depends on how accurate you want to be, so it might be good to ignore this at this point)

So I suggest putting up some numbers for the parameters and do some calculations. This will involve mechanics and some trigonometry .