Physics
Physics
3rd Edition
ISBN: 9780073512150
Author: Alan Giambattista, Betty Richardson, Robert C. Richardson Dr.
Publisher: McGraw-Hill Education
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Chapter 9, Problem 72P
To determine

The viscosity of the liquid.

Expert Solution & Answer
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Answer to Problem 72P

Viscosity is 2.4Pas

Explanation of Solution

Radius of sphere is 1.0cm, mass of sphere is 12.0g, density of liquid is 1200kg/m3, and the terminal speed is 0.15m/s.

There will be no acceleration for sphere moving with terminal velocity. That means, the net force on sphere in vertical direction is zero.

The free body diagram is shown below in figure 1.

Physics, Chapter 9, Problem 72P

Write the equation for net force on sphere in vertical direction.

FDFBmsg=0. (I)

Here, FD is the viscous drag force on the sphere,FB is the buoyant force, ms is the mass of sphere, and g is the gravitational acceleration.

Write the equation for FB.

FB=mlg                                                                                                                   (II)

Here, ml is the mass of liquid displaced.

Write the equation for FD.

FD=6πηrvt                                                                                                                   (III)

Here, η is the coefficient of viscosity of the fluid, r is the radius of sphere, and vt is the terminal velocity of the sphere.

Rewrite equation (I) by substituting equations (II) and (III).

6πηrvtmlgmsg=06πηrvtg(msml)=0 (IV)

Write the equation for ml in terms of volume and density.

ml=43πr3ρl

Here, ρl is the density of liquid.

Rewrite equation (IV) by substituting the above relation for ml.

6πηrvtg(ms43πr3ρl)=0

Rewrite the above relation in terms of η.

η=g(ms43πr3ρl)6πrvt

Conclusion:

Substitute 9.8m/s2 for g, 12g for ms, 3.14 for π, 1.0cm for r, 1200kg/m3 for ρl, and 0.15m/s for vt in the above equation to find η.

η=(9.8m/s2)[(12g(103kg1g))(43(3.14)((1.0cm(102m1cm)))3(1200kg/m3))]6(3.14)(1.0cm(102m1cm))(0.15m/s)=0.06790.0283Pas=2.4Pas

Therefore, the viscosity is 2.4Pas

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Chapter 9 Solutions

Physics

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