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hollow cylinder with outer diameter of 12.5 nm and thickness 2.5nm.

a) If one end of the microtubule is clamped down, and is the other end is free to wobble.

Estimate the work that must be done to displace the free end of the microtubule by an amount

y in a direction perpendicular to the microtubule itself.

b) Thermal fluctuations will bend the microtubule spontaneously. Estimate the value of y under

thermal energy of room temp.

c) How much energy is needed to curve this microtubule by 60 degrees? Express your result in units of

kBT.

Any help is much appreciated!