Question

A hollow microtubule is held to a rigid support on one end and is twisted at the other end until it fails at 2 μm from the rigid end. This microtubule is 10μm in length with an outside diameter of 10nm and an inside diameter of 5nm. As depicted in the plot below, measurements at the free end show that torque increases with the angle of twist, until failure occurs at an angle of 25° with a torque of 5x102N-m. Failure occurs at L 2um Tmar-5x 10-22 Theta max 25 deg Determine the following: (10Pts.) Maximum shear strain and shear stress at fracture site a) b) (3 Pts) Shear modulus Another microtubule with the same dimensions and properties is subjected to two parallel opposite forces of 2.5pN that act in the z-direction at the outermost edge of the microtubule, The combination of these two forces result in a net torque 2.5pN 2.5pN Determine the following: c) (Pts Maximum shear stress achieved in this microtubule d) (5Pts) Distance that point A rotates around point O before fracture. (ie. find the arc length that point A traverses, in microns.) Now, you discover that this microtubule actually has an inner diameter of 7nm. If the ultimate shear stress that it can withstand is 150kPa, e) (7Pts) Determine whether microtubule will fail. (show calculations then comment on what those calculations indicate)

Answer 1

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Sheor modu lus θニ twist angee = 25. = o.VXrad,'an 丁 -9 9 19 x lo 3 Shee tsess Also AIso, Ge 丁 ラ -2 2 Sheen modulus G 28 x o N/m

(CHene dim en Son ae Same -31 m pro pes te Torque can he calco lated 2 x Couple x radius аха.rx(0-12 x , 5xto. д Torq ue= - 20 a 2.5 lo Nm 品 1: T 丁 -9 d) Fir St ue wiln CalCobte twist,8 radius