I think you are confused or I misunderstand something.
iron wrote on Jun 25
th, 2019 at 2:57pm:
Indeed, but imagine you only know the strength of the thrower (Fn) and the characteristics of both the sling (L, ms) and the projectile (mw). There should be a way to figure out how much of L x Fn is converted into kinetic energy.
How do you measure the strength of the thrower in such a complex and dynamic movement ?
L of sling and the L in W=L*Fn is not the same also it's a vector dot product not just a multiplication of numbers, what it means is that any force perpendicular to motion is not contributing as work, so centrifugal force has nothing to do with work, only that it redirects the projectile, also the trajectory of the projectile during the throw is not straight in any way, the radius which you need to use in the centrifugal force formula is constantly changing.
for the formula to be used you need stupid long slings.Or measure the radius and force just when you release which would be much easier if you measured the "muzzle" velocity with a camera.The formula can work on what comes once you accelerate
to accelerate a projectile into a "perfect" circular motion, the pull on the sling must first be off center of the circle and at that moment is when you put energy into the system .and any more energy you put in the same manner once in circular motion is to fill energy losses
the best way to measure the efficiency of slinging is use a 3D tracker and track every movement of the joints and body so you can somehow know(if you can find the mass of every joint) how much energy you put to move yourself and the projectile , at the same time you measure the "muzzle" speed of the projectile which is your output energy and then divide the two and you got efficiency.