The bunchberry flower has the fastest moving parts ever seenin a plant. Initiall

Question

The bunchberry flower has the fastest moving parts ever seenin a plant. Initially the stamens are held by the petals in abent position storing elastic energy liked a coiled spring. As the petals release the tips of the stamens act like medievalcatapults flipping through a 60 degree angle in just .30 ms tolaunch pollen from the anther sacs at their ends. We canmodel a stamen tip as a 1 mm long 10 ?g rigid rod with a 10?g anther sac at one end and a pivot point at the oppositeend. Assuming that the angular acceleration is constantthroughtout the motion

a) what is the trangential acceleration of the anther sacduring the motion

b) what is the speed of the anther sac as it relases itspollen

c)How large is the straightening torque? neglect gravitationalforces

d) compute the gravitational torque on the stamen tip(including the anther sac) in its initial orientation. was itreasonable to neglect the gravitational torque in part c?

Explanation / Answer

a) you can use aT=?r where (?) is angularacceleration and (r) is the length of the stamen and aT=tangential acceleration.

(?) can be found by using?f=.5?(?t)2 where?f= ?/3 or 600 ,?=2.327x107, aT=2.327x104

b) can be found by using?f=?(2???) once you have(?f) you can convert it to linear speed byvt=r?f ,  vt=(.001)(6981)=6.98m/s

c)without gravitational forces the torque (?)=rFt=mr2?

so(.001m)2(2.0x10-8kg)(2.327x107)=4.65x10-7Nm

D) is -mg?x so-(2.0x10-8)(-9.81)(.001)=1.962x10-10Nm

if you subtract the gravitational torque from the tangentialtorque you basically get the tangential torque back due to the factof the pollen being so minute in weight.

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