246 Chapter 9 Mass and Mass-Related Parameters
Refer to Equations (9.10) through (9.13) for appro-
priate relationships. If you were to place these objects
alongside of each other on an inclined surface, which
one of the objects would get to the bottom first, pro-
vided that they all have the same mass and diameter?
9.11. The use of ceiling fans to circulate air has become quite
common. Suggest ways to correct the rotation of a
wobbling fan using the concept of mass moment of in-
ertia. As a starting point, you can use pocket change
such as dimes, nickels, and quarters and chewing gum.
How would you stop the fan from wobbling? Exercise
caution!
9.12. Determine the mass moment of inertia of a steel shaft
that is 1 m long and has a diameter of 5 cm. Deter-
mine the mass of the shaft using the density informa-
tion provided in Table 9.1.
9.13. Determine the mass moment of inertia of steel balls
used in ball bearings. Use a diameter of 2 cm.
9.14. Determine the mass moment of inertia of the earth
about its axis of rotation, going through the poles. As-
sume the shape of the earth to be spherical. Look up in-
formation such as the mass of the earth and the radius
of the earth at the equatorial plane.
9.15. Next time you put gasoline in your car, measure the
mass flow rate (kg /s) of gasoline at the pumping sta-
tion. Record the amount of gas in gallons (or liters
if you are doing the experiment outside the United
States) that you placed in your car’s gas tank and the
time that it took to do so. Make the appropriate con-
version from volume flow rate to mass flow rate using
the density of gasoline.
9.16. Measure the mass flow rate of water coming out of a
drinking fountain by placing a cup under the running
water and by measuring the time that it took to fill the
cup. Measure the mass of the water by subtracting the
total mass from the mass of the cup.
9.17. Obtain a graduated beaker and accurate scale from a
chemistry lab and measure the density of the follow-
ing liquids:
a. a cooking oil
b. SAE 10W-40 engine oil
c. water
d. milk
e. ethylene glycol, antifreeze
Express your findings in kg /m
3. Also determine the
specific gravity of each liquid.
9.18. Obtain pieces of steel, wood, and concrete of known
volume. Find pieces with simple shapes so that you can
measure the dimensions and calculate the volume
quickly. Determine their mass by placing each on an
accurate scale, and calculate their densities.
9.19. Take a 500-sheet ream of computer paper as it comes
wrapped. Unwrap it and measure the height, width,
and length of the stack. Determine the volume, and
measure the mass of the ream, and obtain the density.
Determine how many reams come in a standard box.
Estimate the total mass of the box. Discuss your as-
sumptions and estimation procedure.
9.20. In this assignment you will investigate how much
water may be wasted by a leaky faucet. Place a large
cup under a leaky faucet. If you don’t have a leaky
faucet at home, open the faucet so that it just drips
into the cup. Record the time that you started the
experiment. Allow the water to drip into the cup for
about an hour or two. Record the time when you re-
move the cup from under the faucet. Determine the
mass flow rate. Estimate the water wasted by
100,000 people with leaky faucets during a period of
one year.
9.21. Obtain a graduated beaker and accurate scale from a
chemistry lab and measure the density of SAE 10W-
40 engine oil. Repeat the experiment ten times. De-
termine the mean, variance, and standard deviation for
your density measurement.9.22. Referring to Figure 9.5, how much water is stored
after 20 minutes in each of the tanks? How long will
it take to fill the tanks completely provided that
the volume of tank (a) is 24 m
3
and tank (b) has a
volume of 36 m
3
? Assume the density of water is
1000 kg /m
3
.9.23. Investigate the size of the storage tank in a gas sta-
tion. Apply the conservation of mass statement to the
gasoline flow in the gas station. Draw a control vol-
ume showing appropriate components of the gaso-
line flow system. Estimate how much gasoline is
removed from the storage tank per day. How often
does the storage tank need to be filled? Is this a steady
process?
9.24. Calculate the mass moment of inertia of the thin ring
shown in the accompanying diagram. Express your
answer in lbmft
2
, lbmin
2
, and slugsft
2
.Copyright 2010 Cengage Learning. All Rights Reserved. May not be copied, scanned, or duplicated, in whole or in part. Due to electronic rights, some third party content may be suppressed from the eBook and/or eChapter(s).圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀圀圀圀⸀夀䄀娀䐀䄀一倀刀䔀匀匀⸀䌀伀䴀