Question

The bunchberry flower has the fastest-moving parts ever seen in a plant. Initially, the stamen are held by the petals in a bent position, storing elastic energy like a coiled spring. As the petals release, the tips of the stamen act like medieval catapults, flipping through a 60 ∘ angle in just 0.30 ms to launch pollen from the anther sacs at their ends. The human eye just sees a burst of pollen; careful photography(Figure 1) reveals the details. As shown in the figure, we can model a stamen tip as a 1.0-mm-long, 10 μg rigid rod with a 10 μg anther sac at one end and a pivot point at the opposite end. Although oversimplifing, we will assume that the angular acceleration is constant throughout the motion.(Figure 2)

a) What is the tangential acceleration of the anther sac during the motion?

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

c)How large is the "straightening torque"? Neglect gravitational forces in your calculation.

D) Compute the gravitational torque on the stamen tip (including the anther sac) in its initial orientation. Was it reasonable to neglect the gravitational torque in part c?

Answer 1

let ongular acceleration = 2 of wat toat² woo o= 60 = 7 rad ✓ = Ź «x 0. 3 x163)2 x=23.26x100 rad is? acceleration a= la= lxlo3 x 23.26x16 a= 23.26 x 103 m/s² so v = Vot at v= 23.26x10² x 0.3x10 3 = 6.98 mis Torque T = I a I= mee + me = u Sac loxloxIxloo = 13.33x10 12 kg m² (c) = loxio 20 yl OX T= 13.33x102x 23.26x106 = 310.13x10 6 Nm T = mg & + mol = loxlo x 9.8 x 23 x 1x103 = 147x10 = 0.147x10 6 Non yes it is reasnable to neglect it s