1. Engineering
  2. Mechanical Engineering
  3. problem 1 50 points consider a neutrophil in a micropipette...

Question: problem 1 50 points consider a neutrophil in a micropipette...

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Problem 1 (50 points): Consider a neutrophil in a micropipette that is being pulled away from a stationary bead by a suction force Force in tether, Fe(t) Suction force Stationary bead Neutrophil Micropipette The suction force is rsuctionー where Uo is the velocity the cell would have if it were not tethered. The neutrophil is attached to the bead by an elastic tether that lengthens over time, so that the separation between bead and cell obeys the relationship x(t) -inal 1- e where t is time and τ is a constant. 1.1) [10 points] Calculate the initial velocity of the neutrophil 1.2) [10 points] Draw a free-body diagram of the neutrophil and label the forces acting on it and its result- ing acceleration. 1.3) [10 points] Compute the force in the tether as a function of time, Fe(t). Note that Uoo is the same as the initial velocity computed in (1.1) 1.4) [10 points] In some studies, the inertia of the cell, mcellacell, may be assumed to be negligible. Consider the error in the calculation of the tether force that would result from this assumption. What is the error at t-0? At t = oo? When is the error the largest? 1.5) [10 pointsl When the cells inertia is small, what is the effective spring constant of the tether?

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