July 1, 2015

Homework Help: physics

Posted by pramoda on Sunday, September 4, 2011 at 6:19pm.

A 10-kg block slides down a smooth inclined surface. Determine the terminal velocity of the block if the 0.1-mm gap between the block and the surface contains SAE 30 oil at 60 F. Assume the velocity distribution in the gap is linear, and the area of the block in contact with the oil is 0.1 m^2.

(the diagram shows a slope downward 20 degrees from the horizontal)
What I did:
T = 60 F = 15.56 C
Looked up viscosity of SAE 30 oil at 15.56 C:
mu = 0.8 N*s/m^2
h (height) = 0.1 mm = 1 * 10^-4 m

tau = F/A = mu * dv/dy
F = sin theta * mg

Rearranging with assumption that dv/dy is constant (linear velocity gradient mentioned in problem):

velocity = (tau * h)/mu = (sin (theta) * mgh)/(A * mu)
= (sin (20*pi/180)*10*9.8*10^-4)/(0.1*0.8) = 0.0419 m/s

The official textbook answer is 0.0883 m/s.

How do I get the correct answer?

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