The bunchberry flower has the fastest-moving parts ever observed in a plant. Ini

Question

The bunchberry flower has the fastest-moving parts ever observed in a plant. Initially, the stamens are held by the petals in a bent position, storing elastic energy like a coiled spring. When the petals release, the tips of the stamen act like medieval catapults, flipping through a 60? angle in just 0.31 ms to launch pollen from anther sacs at their ends. The human eye just sees a burst of pollen; only high-speed photography reveals the details. As in the following figure shows, we can model the stamen tip as a 1.0-mm-long, 11 ?g rigid rod with a 11 ?g anther sac at the end. Although oversimplifying, we'll assume a constant angular acceleration.(Figure 1)

Q1

How large is the "straightening torque"?

Express your answer to two significant figures and include the appropriate units.

Q2

What is the speed of the anther sac as it releases its pollen?

Express your answer to two significant figures and include the appropriate units.

Explanation / Answer

It is an intersting question.

Lets start with moment of inertia of the system. then we'll find the angular acceleration and then we ll find torque.
I = mrodl2/3 + msacl2
I = (.11/3 + .11)*10^-12 kgm2
Now, for acceleration use second equation of motion in rotational frame:
s = ut+ 0.5*a*t^2
So, 60*(pi/180) = 0 + 0.5*a*.31*.31*10^-6
angular acc = (pi/3)/(0.5*.31*.31*10^-6) = 21,793,913.657 rad/sec2

So torque = .1466*21,793,913.657*10^-12 = 3.19 * 10^-6 Nm

Now speed of sac = angular velocity* length from pivot
angular velocity = alpha*t
angular velocity = 21,793,913.657 * 0.31*10^-3 = 6756.113 rad/sec
So speed = 6756.113*10^-3 = 6.756 m/s

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