H1-3: A heavy block is being pulled over a table by weight W = 10 N, as shown. T

Question

H1-3: A heavy block is being pulled over a table by weight W = 10 N, as shown. The block is in contact with an oil film with a viscosity of 5 times 10-4 Pa s. The bottom area of the block is A=1 m2, and the thickness of the oil film is h=0.01 mm. Find the steady velocity U of the block. Assume a linear velocity distribution in the oil film and neglect the cord weight, the pulley friction, and air resistance. Answer: 0.2 m/s. Hint: When the block has a steady velocity, from Newton's second law, the force on the block due to weight W is balanced by the force due to shear stress, i.e. W = tau A.

Explanation / Answer

shear stress = mu * (dv / dy ) = (5*10^-4 Pa-s) * ( U-0)/(0.01*10^-3 m) = 50*U

therefore force = shear stress * area

and from Newton 2nd law

force due to sear stress = weight

or 50*U * area = 10

or 50*U*1 = 10 , or U = 10/50 = 0.2m/s

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