In order to shoot 2 forces are involved:

Force from pulling stick backwards with bottom hand and
force from pushing forward with the top hand- creating a lever arm (see figure
below).

**How does stick length affect the magnitude of force/work required for shooting the ball at 70 mph?**

**Measurements**

Stick length regulation- 35.5 in-43.25 in (0.912 m-1.10m)

Stick: ~0.50 kg

Ball: ~0.14 kg;

**Assumption:**

The stick travels in a perfect circle in an overhand shot
from the axis of rotation in center of the stick- (calculations ignores all
momentum from body movement)

Assume stick is a uniformed rod and ball is a point mass

Assume shortest/longest stick has small mass

Forces are 0.1m away for the axis

Assume F are equivalent

Assume Δt= 0.3 seconds

Ball sits 0.05m from top of stick (r= 0.912-0.05= 0.862 m

__and__1.10-0.05 = 1.05 m)
No translational motion (only rotational)

Ball travels Δ θ= π/2 before released

Velocity of ball at the top of the shot (aka when released) = 70.0
mph (31.3 m/s)

Non-conservative
forces are ignored (F

_{AR}, F_{G}, etc.)**Calculations- shortest stick**

v/r=Ѡ

Ѡ=(31.3 m/s)(0.912m-0.05m) = 27 rad/s

α = ΔѠ/ Δt

α = (27-0 rad/s)/(.3 s) = 90 rad/s

^{2}
Στ =Σ I Ѡ = ΣFr

I

_{ball}= m_{b}r^{2 }= (0.14 kg)(0.862 m)^{2}= 0.104 kgm^{2}
I

_{stick}= 1/12 m_{s}l^{2 }= 1/12 (0.50 kg)(0.912 m)^{2}= 0.0347 kgm^{2}
(0.104+0.0347 kgm

^{2})(27 rad/s) = F (0.1 m) + F (0.1 m) = ΣF(0.2)
ΣF =

**18.7 N**
W= τ Δ θ

W=
(3.74 mN) (π/2 rad) =

**5.88 J****Calculations- longest stick**

v/r=Ѡ

Ѡ=(31.3 m/s)(1.10m-0.05m) = 33 rad/s

α = ΔѠ/ Δt

α = (33-0 rad/s)/(.3 s) = 110 rad/s

^{2}
Στ =Σ I Ѡ = ΣFr

I

_{ball}= m_{b}r^{2 }= (0.14 kg)(1.05 m)^{2}= 0.154 kgm^{2}
I

_{stick}= 1/12 m_{s}l^{2 }= 1/12 (0.50 kg)(1.10 m)^{2}= 0.0504 kgm^{2}
(0.154+0.0504 kgm

^{2})(33 rad/s) = F (0.1 m) + F (0.1 m) = ΣF(0.2)
ΣF =

**33.7 N**
W= τ Δ θ

W=
(6.75 mN) (π/2 rad) =

**10.6 J**
THEREFORE,
less force/input of work is required to shoot a ball at a certain speed with a
shorter stick than a longer stick (it is no surprise then that attackers
generally have shorter sticks than defenders). But we have to remember in reality that is a lot more
physic/biometrics to consider when determining the velocity and overall
mechanics of a shot.

Here’s
a video of the NCAA finals from last year. You can check out some shots and see why these calculations
above are insufficient:

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