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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 degree angle in just 0.34ms 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, 12ug rigid rod with a 12ug anther sac at the end. Although oversimplifying, we'll assume aconstant angular acceleration.PART A: How large is the "straightening torque"?PART B: What is the speed of the anther sac as it releases its pollen?

Respuesta :

Answer:

A)     τ = 1,222 10⁻⁶ N m , B) w = 0.24 rad / sec ,   v = 2.88 10⁻³ m / s

Explanation:

Part A

We can get the torque

              τ=  F x r

    bold are vector

             τ = F r sin θ

Let's use according to Newton's law

               F - W = 0

               F = mg

               τ  = mg r sin θ

Let's reduce the magnitudes to the SI system

             m = 12 ug = 12 10⁻⁶ kg

             r = 12 mm = 12 10⁻³ m

Let's calculate

               τ  = 12 10⁻⁶ 9.8 12 10⁻³ sin 60

                τ = 1,222 10⁻⁶ N m

Part B

Let's use Newton's law for rotational movement

             τ = I α

The moment of inertia of the antero that we approximate as a particle is

              τ = m r² α

              α = τ / m r²

              α = 1,222 10⁻⁶ / (12 10⁻⁶ (12 10⁻³)²)

              α = 0.70718 10³ rad / s²

Angular velocity is

              w = w₀ + α t

              w = 0 + 0.70718 10³ 0.34 10⁻³

              w = 0.24 rad / sec

Angular and linear variables are related.

         v = w r

         v = 0.24 12 10⁻³

        v = 2.88 10⁻³ m / s

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