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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^o颅 angle in just 0.30 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 FIGURE CP12.85 shows, we can model the stamen tip as a 1.0mm long, 10 渭g rigid rod with a 10 渭g anther sac at the end. Although oversimplifying, we鈥檒l assume a constant angular
acceleration.

a. How large is the 鈥渟traightening torque鈥�?
b. What is the speed of the anther sac as it releases its pollen?

Step by step solution

01

Part(a) Step1 : Given information

length of rod = 1 mm = 0.001 m

mass = 10^-8 kg

time = 3 x 10^-4sec

angular displacement = 60^o = 1.0472 rads

02

Part(a) Step2 : Explanation

Angular acceleration is calculated by
$$\begin{gathered} 伪=\frac{2\left(\text{displacement}\right(胃\left)\right)}{t^2} \\ 伪=\frac{2(1.0472rad)}{{\left(3脳{10}^{-4}s\right)}^2}=23.2脳{10}^{6}rad/s^2 \end{gathered}$$

We can calculate moment of inertia as

$I=\frac{1}{3}M{L}^2+M{L}^2$

$$\begin{gathered} I=\frac{1}{3}\left({10}^{-8}kg\right)(0.001m{)}^2+\left({10}^{-5}g\right)(0.001m{)}^2 \\ I=1.33脳{10}^{-14}kg.m^2 \end{gathered}$$

Calculate torque as $蟿=I伪$
Substitute values, we get

Torque $$\begin{gathered} =\left(1.33脳{10}^{-14}g.m^2\right)脳\left(23.2脳{10}^{6}rad/s^2\right) \\ =29.52脳{10}^{-8}\mathrm{Nm} \end{gathered}$$

03

Part(b) Step1 : Given information

length of rod = 1 mm = 0.001 m

mass = 10^-8 kg

time = 3 x 10^-4sec

angular displacement = 60^o = 1.0472 rads

04

Part(b) Step 2: Explanation

Angular velocity is given as

$$\begin{gathered} 蝇=伪t \\ 蝇=\left(23.2脳{10}^{6}rad/s^2\right)\left(3脳{10}^{-4}s\right) \\ 蝇=6960\mathrm{rad}/\sec \end{gathered}$$

and velocity is v= 蝇L
On substitution we get
$\mathrm{v}=(6960rad/s)脳(0.001m)=6.960m/s=7\mathrm{m}/\sec$

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