Question

Question 1 (CLO 1, PLO 2, C3): A flat plate with a surface area of 0.25 m moves above a parallel flat surface with a lubricant film of thickness 1.5 mm in between the two parallel surfaces. If the viscosity of the lubricant is 0.5 Pa-s, analyze the following: a. Damping constant b. Damping force developed when the plate moves with a velocity of 2 m/s. Question 2 (CLO 1, PLO 2, C3): A machine is subjected to the motion x(t)- A cos (50f + a) mm. The initial conditions are given by x (0) = 3 mm and (0) = 1.0 m/s. a. Find the constants A and a. b. Express the motion in the form x (1) = A1 cos of + A2 sin of and identify the constants Ai and A2.

Answer 1

1. given

Area of plate A=0.25 m2

thickness dy = 1.5 mm = 0.0015 m

Dynamic viscosity, $\mu$ = 0.5 Pa-s

Velocity , du = 2 m/s

According to Newton's law of viscosity

shear stress, $\tau$ = $\mu$ * (du/dy)

therefore $\tau$ = 0.5 * (2/0.0015) = 666.66 N/m2

a) Damping constant, C = ($\mu$*A)/ (dy)

therefore C = (0.5 *0.25) / 0.0015 = 83.33 N-s/m (Answer)

b) Damping force, F= shear stress * Area

that is F = $\tau$ * A

F = 666.66 * 0.25 = 166.66 N (Answer)