Question

2) Problem 5-3. Freely Settling Hinge. A plate of density pm, thickness d, and width W (you may consider the third dimension to be infinite - it is a 2D problem - and d/W «1) is hinged at one edge in contact with the bottom of a tank filled with a viscous liquid. The angle separating the plate and the plane is given by a. If we release the plate it will settle toward the plane (e.g., a will decrease in time). In the limit a«<, develop an equation governing a as a function of time. w the torque that is due to lubrication forces Host: The net torque on the plate will be zero will balance the torque that is due to gravity

Answer 1

sol. Given, for rectangular plate, 10 ༡༩ E G em If pressure force) 2 free body Diagram G-scentre of gravity of plate ng weight of plate. a velocity of plate sind. ng moving downward. ng ng cosa 5 Distance of Centre of gravity from bottom of pertank. t time taken to reach the botton. Torque due to Lubrication forces = Torque due to gravity. (egAh) x h* (mg Cash x W) + (maxw) → 0 (Ion = htt IG sind th centre of pressure, h* 11 Ah h = W sind. * Wd² sin22. 12 (wxd) W sind + W / W sind. JK = d²sind 6W + W sind. * d² - Sind ( + W GW

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