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Physics / College Physics 1 / Chapter 12 / Problem 29

College Physics | 1st Edition | ISBN: 9781938168000 | Authors: Paul Peter Urone, Roger Hinrichs

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(a) Calculate the retarding force due to the viscosity of

Chapter 12, Problem 29

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QUESTION:

Problem 29PE

(a) Calculate the retarding force due to the viscosity of the air layer between a cart and a level air track given the following information—air temperature is 20º C , the cart is moving at 0.400 m/s, its surface area is 2.50×10−2 m 2 , and the thickness of the air layer is 6.00×10−5 m . (b) What is the ratio of this force to the weight of the 0.300-kg cart?

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QUESTION:

Problem 29PE

(a) Calculate the retarding force due to the viscosity of the air layer between a cart and a level air track given the following information—air temperature is 20º C , the cart is moving at 0.400 m/s, its surface area is 2.50×10−2 m 2 , and the thickness of the air layer is 6.00×10−5 m . (b) What is the ratio of this force to the weight of the 0.300-kg cart?

ANSWER:

a.)

Step 1 of 2

The retarding force (F) due to the viscosity of the air layer is given by the expression,

$F=$ $\eta{}$ $\frac{vA}{L}$

where, $\eta{}=$ viscosity of the air at 20 oC in Pa $\cdot{}$ s

v = velocity of the cart in m/s

A = Surface area in m2

L = thickness of the air layer in m

Substituting 15.11 $\times{}$ 10-6 Pa $\cdot{}$ s for $\eta{}$ , 0.400 m/s for v, 2.50 $\times{}$ 10-2 m2 for A and 6 $\times{}$ 10-5 m for L

$F=$ $15.11\ \times{}{10}^{-6}$ $\frac{(\ 0.400)(\ 2.50\times{}{10}^{-2})}{6\times{}{10}^{-5}}$

= $15.11\times{}{10}^{-6}\times{}166.67$

=0.00252 N

Therefore, the retarding force due to the viscosity of the air layer between a cart and a level air is 0.00252 N

b.)

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