Homework Solutions
1 What is the difference between pound-mass and pound-force?
A pound mass is a unit of mass, which is equal to 0.45359237 kg. A pound-force is a unit of
force, which is equal to 4.44822 N. The pound-mass (lbm) and pound-force (lbf) are related by the
following expression.
2m
fs
ftlb174.32
lb1
2 A woman weighs 180 lbf at a location where g = 32.10 ft/s2. Determine her weight on the
moon where g = 5.47 ft/s2.
The mass of the woman is constant. Since weight is given by the equation W = mg we can write
the following equation for comparing a constant mass, m, in two different gravitational fields (g1
and g2) to determine the weights (W1 and W2) for each gravity. Doing this and using the data
given for this problem in that equation gives the following result.
2
2
1
12
2
2
2
1
110.32
180
47.5
s
ft
lb
s
ft
g
Wg
W
g
W
g
W
mf
W2 = 30.7 lbf
3 A 3 kg plastic tank that has a volume of 0.2 m3 is filled with liquid water. Assuming the
density of water is 1000 kg/m3, determine the weight of the combined system.
The weight of the combined system, Wtot, is the product of the total mass, mtot, and the
acceleration of gravity, g = 9.807 m/s3. The total mass is the sum of the tank mass, mtank = 3 kg,
and the mass of the water, mH2O. The mass of the water is the product of the tank volume, Vtank =
0.2 m3 and the density of the water, H2O = 1000 kg/m3. Translating these statements into
equations (and applying the unit conversion for newtons) gives the following result.
mtot = mtank + mH2O = mtank + H2O Vtank = 3 kg + (1000 kg/m3)(0.2 m3) = 203 kg
Wtot, = mtot g = (203 kg)(9.807 m/s2)[1 N•s2/(kg•m)] = 1,991 N
4 Determine the mass and the weight of the air contained in a room whose dimensions are
6 m X 6 m X 8 m. Assume the density of air is 1.16 kg/m3.
The weight of the air, Wair, is the product of the air mass, mair, and the acceleration of gravity, g =
9.807 m/s3. The mass of the air is the product of the room volume, Vroom = (6 m)(6 m)(8 m) =
288 m3 and the density of the air, air = 1.16 kg/m3. Translating these statements into equations
(and applying the unit conversion for newtons) gives the following result.
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