Download Phys 201 - General Physics w/Algebra Homework 1

Phys 201 - General Physics w/Algebra
Homework 1
Units of Measure
Eastern Oregon University
Name:
Major:
Instructor: Anthony A. Tovar, Ph. D.
1. Unit Conversion
While the blood volume in the human body varies from person to person based on their age, body size,
sex, and genetics, a typical volume is about 5.0 L. Similarly, a typical number density of human red
blood cells (erythrocytes) is 5 billion cells/cm3 . Also, there are approximately 7.5 million circulating
white blood cells (leukocytes) per cm3 in the typical human body. The mass density of human blood
is about 1.05 g/cm3 .
(a) Use these values to determine the number of red blood cells in the typical human body. A “typical”
adult male has about 37.2 trillion cells total, so your answer should be smaller than 37.2 × 1012
and much larger than 100. Is it?
(b) If circulating leukocytes make up about 1/2 of the total number of leukocytes, about how many
total leukocytes are there in the human body? Again, this should be
100 << #totalwbc < 1013
(1)
is it?
(c) How much does this typical person’s blood weigh in pounds? Your answer should be less than a
persons body weight (say 200 lbs) and more than one pound, is it?
2. SI prefixes
Decode the following and rewrite it in conventional english:
Ned the Nerd had it all. He liked to read his favorite book “2 × 103 mocking bird” and play
solitaire with his 109 antic 101 cards. He looked forward to school where he could 10−1 mate
his 1018 minations. Afterwards, he would say to himself “10−18 boy”. However, sometimes
he felt 10−2 mental and would sing sweetly into his 10−6 phone.
3. Dimensional Analysis
(a) Your buddy needs the formula for the volume of a sphere. He thinks it’s V = 4πr2 . Is he right?
Use dimensional analysis to prove your answer.
(b) Consider the following equation: x(t) = a + bt + ct2 + dcos(et). If x(t) is in m, and t is in s, What
are the units of a, b, c, d, and e?
(c) Consider the following equation: F = −mg − cv 2 − µNy − kx where F is in kg · m/s2 , m is in kg,
v is in m/s, Ny is in kgm/s2 , and x is in m. What are the units of g, c, µ, and k?
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4. Unit Conversions
Consider the following automated cbc (complete blood count) from a Hematology Cell Analyzer for
Xena the Mom below. The left data panel gives information about the White Blood Cell count (WBC,
the uL is actually µL), the Red Blood Cell count (RBC), the Hematocrit (HCT), and other information.
While each of these is important, the WBC count is especially important as white blood cells are the
cells of the immune system that “are involved in defending the body against both infectious disease and
foreign invaders” (wiki:white blood cells). So, the right data panel has information about the numbers
of component white blood cells in number density (top) and percentage (bottom). The components are
Neutrophils (NEUT), Lymphocytes (LYMPH), Monocytes (MONO), Eosinophils (EO), and Basophils
(BASO).
(a) What is the mass density of hemoglobin (HGB) in g/cm3 in Xena’s body?
(b) How many basophils are in 35 cc’s (cm3 ) of Xena’s blood?
(c) How many eosinophils are in 2 cups of Xena’s blood?
(d) According to Mercy North Iowa ( http://www.mercynorthiowa.com/cbc-normal-ranges ), are any
of the WBC component percentages out of the normal range (Xena is a 35 year old woman). If
so, which ones? (Note: what is considered normal actually varies from hospital to hospital.)
(e) If the blood flow to Xena’s heart is 250 mL/min, how many red blood cells flow to her heart every
second?
(f) Xena’s heart beats, as measured by her pulse, at 60 beats/min. If her heart pumps at 75 mL/beat,
what volume of blood is pumped in one day in liters?
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