December 4, 2016

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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