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 0.32ms 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, 9.0?g rigid rod with a 9.0?g anther sac at the end. Although oversimplifying, we'll assume a constant angular acceleration

Q: How large is the "straightening torque"?

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 0.32ms 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, 9.0?g rigid rod with a 9.0?g anther sac at the end. Although oversimplifying, we'll assume a constant angular acceleration How large is the "straightening torque"?

Explanation / Answer

a) alpha = 2theta/ t^2 = 2(60*2pie/360)/(0.32*10^-3)^2 = 2.04*10^7 rad/s^2

at = alpha *R = 2.04*10^7 *10^-3 = 2.04*10^4

b) v = v0 +at *t = 2.04*10^4*0.32*10^-3 = 6.5 m/s

c) torque = I alpha = 1/3 mR^3 + mr^2

1/3(9*10^-9(0.32*10^-3)^2 + 9*10^-9(0.32*10^-3)^2

= 1.2288*10^-15 kg/m^2

torque = 1.2288*10^-15*2.04*10^7 = 2.5*10^-8 kg.m

d) xcm = 9 mue (0.5mm) + 9mue*1mm / 18 mue

= 0.75 mm = 7.5*10^-4m

torque = mg xcm = 18*10^-9 *9.8 *7.5*10^-4 = 1.323 *10^-10 kg.m

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