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 60angle in just 0.28 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--long, 9.0 rigid rod with a 9.0 anther sac at the end. Although oversimplifying, we'll assume a constant angular acceleration

a) How large is the straightening torque?

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

Explanation / Answer

OK, I'll give this a shot. I am going to ASSUME that:

length of rod = 1.00 mm = 0.001 meter

mass of rod = 9.00 mg = 9x10^-6 kg

mass of pod = 9.00 mg = 9x10^-6 kg

time = 0.28 milliseconds = 0.00028 seconds

Then...

angular displacement = 60 degrees = 1.0472 radians

angular acc = 2 * displacement / time^2 = 2*1.0472 / 0.00028^2 = 2.6714x10^7 N-m

moment of inertia = (1/3) m L^2 + mL^2 =

= (4/3) * 9x10^-6 * .001^2 = 12 x 10^-12

torque = inerta * angular acc = 12 x 10^-12 * 2.6714 x 10^7 =

= 0.0003206 N-m

angular speed = acc* time = 2.6714x10^7 * 0.00028 = 7480 rad/sec

linear speed = w*L = 7480 * 0.001 = 7.48 m/s

Note that my answers are based on my assumptions about the units. If my assumptions are wrong, my answers might be wrong. Check the units you are given against my assumptions stated at the top of my solution.

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