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Chapter 15: Homework Problems
12.1 Stealing Buddhas Dinner is a poignant memoir written by Bich Minh Nguyen (a Purdue professor) that captures her experiences leaving Vietnam and growing up in the
Midwestern United States. Her ability to simultaneously describe complex events from
a childs perspective and capture the emotional complexities of the adults around her is
one particularly noteworthy aspect of this elegant work. One of the themes throughout
the book is central role of food in shaping her identity and one of the more interesting
foods described therein is Cha Gio, a type of crispy spring roll fried in oil.
For this problem, each spring roll will be modeled as a square cross section (1.5 cm on
a side) and they are 6 cm long (distance into the page). The mass of the spring roll is
approximately 10.8 grams, and the density of the oil is 0.922 g/cm3 .
1.5 cm
d
Draw a free body diagram of the spring roll.
Determine how deep within the hot oil the spring roll will sit when it is cooking (denoted
by the variable, d in the figure).
If one were to heat the oil, causing its density to decrease, would the spring roll sink
deeper or rise upward?
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12.2 Imagine an iceberg in the North Atlantic. Icebergs are giant blocks of ice formed from
fresh water floating in saltwater. They are usually named according to their size. A
Growleris less than 1 m in height and 5 meters long. A Bergy Bitis 1-5 m high and
5-15 meters long. Small, Medium, Large, and Very Large icebergs are accurately (if
not interestingly) named. The height of a Small iceberg can be up to 15 m (and 60 m
long) while Medium icebergs are 15-45 m high (and up to 120 m long). Large icebergs
get us up to 75 m high and 200 m in length while anything bigger is considered a Very
Largeiceberg.
For this problem, you may assume that we are dealing with the biggest possible Bergy
Bit, the density of ice is 916.7 kg/m3 and the density of seawater is 1,025 kg/m3 .
H
L
L
We’ll assume it has a pyramidal shape (the volume of a pyramid is 13 AH, where A = L2
is the cross-sectional area of the base and H is the height of the pyramid. What is the
height of hte iceberg above the water? What percentage of the iceberg’s volume sits
above the water?
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Chapter 15: Homework Problems
12.3 The USS Enterprise is the first nuclear powered aircraft carrier, commissioned in 1961.
She weighs 94,781 tons (93,284 tonnes).
Figure 15.1: The USS Enterprise sailing along side the FS Charles de Gaulle
If the USS Enterprise has a length, L = 342m and the cross-section shown below,
determine the depth it sits in the water. You may assume that w = 40.5m and H = 5m.
The density of saltwater is 1,025 kg/m3 .
Deck
w
Water line
h
H
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12.4 Driving on the ice. In Northern Minnesota (and likely other places as well) people will
drive their ice houses out onto frozen lakes (please do not try this - it is terrifying and
surprisingly dangerous if not done at the right time of the year). This habit seems
problematic, especially if the ice were to give way. The goal of this problem is to see if
there are any cars that could float (assuming the doors and trunk were sealed properly).
We shall begin with the Volkswagen Jetta. According to Wikipedia it is 4.64 m long,
1.78 m wide, and 1.45 m tall. Determine whether or not the Jetta sinks in freshwater
if it weighs 14.4 kN.
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Chapter 15: Homework Problems
12.5 In October of 2010, there was a breach in the wall of a reservoir that stored chemical
waste from an alumina processing plant in Hungary. The red sludge that it held back
was mostly iron oxide and when the wall of the reservoir failed, it dumped 1 million
cubic meters of chemical waste into the surrounding countryside. The sludge, mostly
iron oxide, is extremely alkaline and able to burn the skin. To date, the failure has
killed four people, injured over 100, left several missing, and contaminated the Danube.
The walls of the reservoir were approximately H = 80 meters tall and 25 meters wide
(the distance b in the figure). There is a stop at the origin to prevent it from sliding
to the left. The density of the concrete is 2400 kg/m3 and the density of the sludge is
1760 kg/m3. For this problem, you may assume that we are considering a section of
the wall and sludge that extends 1 meter into the page.
Determine the weight of the concrete wall.
How much force will the sludge exert on the wall in terms of its height, h?
Where is the resultant force of the sludge located relative to its height, h?
Determine the height, h, at which the block will tip about the origin.
y
H
h
x
b
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12.6 A spring-loaded water gate. Determine the value of the spring coefficient, k needed to
ensure that the gate will open to the drain when the water height reaches 1.5 m. The
distance, x is 0.2 m.
x
k
h
Drain
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Chapter 15: Homework Problems
12.7 Determine the x and y forces exerted by the water on the dam shown below if D = 3m
and the water is filled to the top.
y
D
y = 0.5x 3
Water
H
x
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12.8 A submerged gate is shown below. You may assume that the angle θ = 40o the gate
has a weight, W , and a length of 5 ft. If there is minimal friction between the bottom
of the gate and the river bed, how much does the gate have to weigh to ensure that
it makes contact with the bottom of the river bed and what is the reaction at the pin
joint? You may assume that h = 6f t. and H = 15f t. and the gate extends 3 ft. into
the page.
Water
L
W
h
θ
H