Problem set: Chapter 1
Page 20-23
Multiple choice(6,8,10,12), Problems (4,12,16,32,38,46), and Extra questions
Patrizia Scarcello
211723665
Mr. Storry
SC PHYS 1510 A
Tuesday Sept 20.
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Multiple choice
6) A house is advertised as having 1420 square feet under roof. What is the area of this
house in square meters?
One square foot is equal to 0.09290304 square metres.
1420 X 0.0929= 132 m2
One square meter is equal to 10.7639104167 square feet.
132 m2 X 10.76= 1420
Answer: (b) 132m2
8) Find the polar coordinates corresponding to a point located at (-5.00, 12.00) in
Cartesian coordinates.
r2= (-5)2 + (12)2
r2= 25 + 144
r2= 169
r=
169
r= 13.0
tan( θ ) = -5/12
( θ ) = tan-1 (12/-5)
( θ ) = -67.38o +180o
( θ ) = 113o
Answer: (b)= (13.0, 113o)
10) The price of gasoline at a particular station is 1.5 Euros per litre. An American
student can use 33 Euros to buy gasoline. Knowing that 4 quarts make a gallon and that
one litre is close to one quart. She quickly realized that she can buy how many gallons of
gasoline?
1 US quart = 0.946352946 litres
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4 litres is approximately 1 gallon (when rounded)
1.5 euros X 22 litres =33 euros
22 litres/ 4 = 5.5 gallons
Answer: (b) about 5 gallons
12) A calculator displays a result as 1.365 248 0  107 kg. The estimated uncertainty in
the result is 2  105. How many digits should be included as significant when the result
is written down?
1.37  107 kg
Answer: (c) 2 significant digits
Problems
4)
Physical quantities: Length – [L]; Mass – [M]; Time – [T]; Temperature – [K];
Electric current – [A]
Dimensional formula: Velocity – [L][T -1] unit of m/s.
Acceleration – [L][T-2] unit is m/s2.
The physical quantity on both sides of the equation should be the same. Thus for a
correct equation the same dimensional formula should be shown on both sides of
the physical equation.
(a) ½ mv2= ½ mvo2 +
mgh
The dimesional formula of LHS = [M][LT-1]2 = [M][L2][T-2]
The dimesional formula of RHS = [M][LT-1]2 + {[M][LT-2][L]}2
= [M][LT-1]2 + [M][L3][T-2]
From the end results from the dimensional formula from the Left Hand Side and the
Right Hand Side, we are able to see that this dimensional formula is not the same on both
sides. Thus the equation is dimensionally wrong.
(b) v= vo + at2
The dimesional formula of LHS = [LT-1] = [M0][L1][T-1]
The dimesional formula of RHS = [LT-1] +[LT-2][T]2
The dimensional formula from the LHS and the RHS are not the same. Therefore, this
equation is dimensionally wrong.
(c) ma= v2
The dimesional formula of LHS = [M][LT-2] = [M][L1][T-2]
The dimesional formula of RHS = [LT-1]2
From the LHS and the RHS it is obvious that the dimensional formula on both sides of
the equation are not same. Hence the equation is dimensionally wrong.
12) The radius of a circle is measured to be (10.5 ± 0.2) m calculates the:
(a) Area and
(b) Circumference of the circle and give the uncertainty in each value.
(a)
A = ∙ 10.52
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A= ∙ 110.25
A= 346.4 m2
A= ∙0.22
= 0.13 m2
Therefore, the area of the circle is (346.4 ± 0.13) m2
(b) C=2r
C=2∙ 10.5 ∙
C=66 m
C=2 (0.2) ∙
C= 1.3 m
Therefore, the circumference of the circle is (66 ± 1.3) m
16) A small turtle moves at a speed of 186 furlongs per fortnight. Find the speed of the
turtle in centimetres per second. Note that 1 furlong =220 yards and 1 fortnight=14 days.
1 inch = 2.54 cm
36 in = 36 ∙ 2.54 cm = 91.44 cm
1 yard = 36 in = 91.44 cm
220 yards= 220 ∙ 91.44 cm = 20116.8 cm
1 Furlong= 220 ∙ 91.44 cm = 20116.8 cm
1 fortnight = 14 days
= 14 days * 24 hr/day = 336 hr
= 336 hr * 3600 sec/hr
= 1209600 sec
1 furlong/fortnight = 20116.8 cm / 1209600 sec
186 furlongs/fortnight = (186 * 20116.8 / 1209600) cm/sec
≈ 3.1 cm/sec
Therefore, the turtle moves at a speed of 3.1 centimetres per second
32) Treat a cell in a human body as a sphere of radius 1.0μm (a) determines the volume
of the cell (b) estimate the volume of your body (c) estimate the number of cells in your
body.
micrometer (µm)-- 0.0001 cm
a) V= 4/3 r3
V= 4/3 (0.0001)3
V= 4/3 (1 x 10-12)
V= 4.2 x 10-12 cm 2
b) Volume of a human body ≈ (4.2 x 10-12) (1 x 1014)
≈ 420 cm2
c) An estimate for the number of cells in the human body is: 1 x 1014
(a hundred trillion)
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38) Two points in a rectangular coordinate system have the coordinates (5.0, 3.0) and
(-3.0, 4.0), where the units are centimetres. Determine the distance between these points.
V= (5-(-3)) + (3-4)
V= 8 + (-1)
V= 8 – 1
The x distance between the two points is 8.0 cm and the y distance between then
is 1.0 cm.
D= √x2+y2
= √(8.0cm)2 + (1.0cm)2
= √65 cm2
= 8.1 cm
OR
D= √(x2-x1)2 + (y2-y1)2
= √((-3)- 5)2 + (4-3)2
= √(-8)2 + (1)2
= √(64) + (1)
= √65
= 8.1
Therefore, the distance between these two points is 8.1 cm
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46) In a certain right triangle, the two sides that are perpendicular to each other are 5.00m
and 7.00 m long. What is the length of the third side of the triangle?
a2 + b2 = c2
52 + 72 = c2
25+ 49 = c2
74 = c2
√74 = √c2
8.6= c
Therefore, the length of the third side of the triangle is 8.6 m
Extra questions:
A) How many electrons are there in a water molecule?
B) How many neutrons are there in a deuterium nucleus?
C) What 3 particles combine to make a proton?
D) Is an electron made of quarks?
E) What is the approximate diameter of an atom?
Answer
A) Since water molecules are composed of two atoms of hydrogen and one atom of
oxygen. The hydrogen atoms contain 1 electron each, and the oxygen atom brings
eight electrons. The resulting molecule (H2O) contains ten electrons.
B) The nucleus of the deuterium only contains one neutron and one proton in it.
C) The three particles that combine to make a proton are: 1 down quark (charge of
1/3) and 2 up quarks (charge of 2/3). Therefore, a proton’s charge is +1 (1/3 + 2/3
+ 2/3)
D) No, electrons are not made of quarks, like protons and neutrons, because electrons
are leptons and are not known to be composed of any sub particles.
E) The diameter of an atom ranges approximately from 0.1 to 0.5 nanometer.