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 0.30ms 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, 10?g rigid rod with a 10?g anther sac at the end. Although oversimplifying, we'll assume a constant angular acceleration.(Figure 1)

Part A

How large is the "straightening torque"?

Express your answer to two significant figures and include the appropriate units.

3.1

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 0.30ms 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, 10?g rigid rod with a 10?g anther sac at the end. Although oversimplifying, we'll assume a constant angular acceleration.(Figure 1)

Part A

How large is the "straightening torque"?

Express your answer to two significant figures and include the appropriate units.

3.1

Explanation / Answer

ength of rod = 1.00 mm = 0.001 meter

mass of rod = 9.00 mg = 9x10^-6 kg

mass of pod = 9.00 mg = 9x10^-6 kg

time = 0.28 milliseconds = 0.00028 seconds

Then...

angular displacement = 60 degrees = 1.0472 radians

angular acc = 2 * displacement / time^2 = 2*1.0472 / 0.00028^2 = 2.6714x10^7 N-m

moment of inertia = (1/3) m L^2 + mL^2 =

= (4/3) * 9x10^-6 * .001^2 = 12 x 10^-12

torque = inerta * angular acc = 12 x 10^-12 * 2.6714 x 10^7 =

= 0.0003206 N-m

angular speed = acc* time = 2.6714x10^7 * 0.00028 = 7480 rad/sec

linear speed = w*L = 7480 * 0.001 = 7.48 m/s

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.