Two containers are connected by a cord(of negligible mass) passing over a fricti

Question

Two containers are connected by a cord(of negligible mass) passing over a frictionless pulley (also ofnegligible mass). At time t = 0 container 1 has m1 and container 2has mass m2 with m1 < m2, but container 1 is losing mass(through a leak) at the constant rate r. (a) At what rate is themagnitude of acceleration of the containers changing at time t? (b)When will container 2 reach maximum acceleration?Expressyour answers in terms of the variables given andg. Two containers are connected by a cord(of negligible mass) passing over a frictionless pulley (also ofnegligible mass). At time t = 0 container 1 has m1 and container 2has mass m2 with m1 < m2, but container 1 is losing mass(through a leak) at the constant rate r. (a) At what rate is themagnitude of acceleration of the containers changing at time t? (b)When will container 2 reach maximum acceleration?Expressyour answers in terms of the variables given andg.

Explanation / Answer

m2 g - T = m2 dv/dt T - m1 g = d(m1 v) / dt = r v +m1 dv/dt (m2 - m1) g = r v + m1dv/dt      adding equations  Error here forgot to include m2 (m2 - m1) g / m1 = r v /m1 + dv/dt       r should be negative here Let (m2 - m1) g /m1 = M and r / m1 =R   temporarily M = R v + dv/dt M - R v = dv/dt dt = dv / (M - R v) -1 / R ln (M - R v) = t + C C = -1 / R ln M     if v = 0 at t =0 t = -1 / R [ln ((M - R v) / M)] M e-Rt = M - R v v = M (1 - e-Rt) a = dv/dt = M R e-Rt This has some errors as noted above but I think theapproach should be OK a would go to zero in the equation obtained here instead ofapproaching g This has some errors as noted above but I think theapproach should be OK a would go to zero in the equation obtained here instead ofapproaching g

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