3 upvotes, 3 direct replies (showing 3)
View submission: Ask Anything Wednesday - Physics, Astronomy, Earth and Planetary Science
[removed]
Comment by B_zark at 26/04/2023 at 19:32 UTC
6 upvotes, 0 direct replies
I think that depends on how you throw a ball! Do you throw by rotating your totally straight and rigid arm? When using a stick, you're probably using your wrist too to dramatically increase the acceleration at the end of the stick. This will give the ball a lot more kinetic energy than a simple lever.
Comment by SonOfOnett at 27/04/2023 at 03:45 UTC*
3 upvotes, 2 direct replies
If we assume that you throw like a windmill, perfectly rotating your arm about a fixed point on your shoulder, then we can determine how the lever arm length affects the launch velocity. Let's call the lever arm length "R". Assuming you have the same rotational speed regardless of your lever arm then we can translate your rotational motion to linear via (omega)x(R) = V, where omega is that rotational rate and V is your launch velocity. So the impact on your lever arm length is linear to your launch velocity: **twice the lever arm results in twice the launch velocity**
Ignoring air resistance and assuming you always release at the same angle, we now need to know how your launch velocity affects your throw distance. Some re-arranging of kinematics equations eventually yields that for a initial velocity V and launch angle (theta), the distance of a throw is equal to: (V^2 )xsin(2xTheta)/(g) where g is the acceleration due to gravity. So that means that **twice the launch velocity results in four times the distance thrown**
Putting it all together your experiment seems correct! Ignoring air resistance and all other factors held constant, **Doubling a lever arm will result in a throw four times as far**
Comment by TanteTara at 27/04/2023 at 09:18 UTC
1 upvotes, 0 direct replies
The stick helps you by making your throw more efficient, However, your muscles still have to spend the energy to get the ball moving, so with ever longer sticks you get diminishing returns.