Physics 2C Summer Session II
Quiz #1
Multiple Choice. Choose the answer that best completes the
statement or answers the question.
1. A 1000m wide dam holds back a lake that is 32m deep and 20km
long. What force does the water exert on the dam (include atmospheric pressure,
Patm = 1:013 105 P a)?
A) 3:25 109 N B) 6:50 1010 N C) 5:02 109 N D) 8:26 109 N E)
1:65 1011 N .
R
The force on the dam is given by F = P dA: Since P = P0 + gz and
dA = W dz; the total force is
Z 32
Z 32
F = W
(Patm + gz) dz = 1000
1:013 105 + 9:8 103 z dz
0
F
=
8:26
0
9
10 N ! D
You could also …nd the force via
F
= hP i A =
F
=
1:013
gd
Wd
2
9:8 103 32
105 +
2
Patm +
32000 = 8:26
109 N
2. A partially full beer bottle with an interior diameter of 36mm and
an exterior diameter of 48mm is ‡oating upright in water. A drinker takes a
swallow and replaces the bottle after which it ‡oats 21mm higher than before.
How much beer was swallowed? (Assume that the density of beer is identical
to that of water.)
A) 85cm3
B) 21cm3
C) 55cm3
D) 152cm3
The change in displacement by the beer bottle is
V =
E) 38cm3
2
4
(4:8) 2:1 = 38cm3 ! E
3. Assuming g = 9:8m=s2 ; what is the mass contained inside a column
of air with a cross-sectional area of 3m2 extending from the sea level to the top
of the atmosphere (P1atm = 1:013 105 P a)?
A) 31; 000kg
B) 31kg
C) 3:04
105 kg D) 304kg
1
E) N eed more data.
The total weight of the air column is
F = Patm A = 1:013
105
3 = 3:04
105 N:
Hence the mass is
m = F=g = 3:04
105 =9:8 = 31; 000kg ! A
4. A tank of height of h = 10m is full of water, see …gure 1. At what
height, y, should a small hole be cut in the tank so that initially the water
reaches its maximum horizontal distance from the base of the tank?
Figure 1: Problem 4
A) 2m
B) 4m
C) 5m
D) 6m
E) 8m
From Bernoulli’
s
equation
the
horizontal
velocity
of the water as it exits the
p
tank
is
v
=
2g
(h
y):
The
time
for
the
water
to
fall
through
p
p a height
py is t =
2y=g:
Hence
the
horizontal
distance
traveled
is
x
=
vt
=
2g
(h
y)
2y=g =
p
2 y (h y): To maximize x we take the derivative of this expression and set it
equal to zero to …nd
dx
dp
=2
y (h
dy
dy
h 2y
y) = p
= 0 ! ymax = h=2 = 5m ! C
y (h y)
5. At what Fahrenheit temperature is Fahrenheit exactly 100 higher
than Celsius?
A) 165 F B) 185 F C) 265 F D) 165 F E) 85 F
The relation between Fahrenheit and Celsius is TC = 5 (TF
condition TF = TC + 100 we …nd
TF
100 =
5
(TF
9
32) =9: For the
32) ! TF = 185: ! B
6. A 1kg piece of Al-Ag alloy weighs 8:654N when submerged in water.
Given the densities wat = 1g=cm3 ; Al = 2:7g=cm3 , Ag = 10:5g=cm3 ; the
2
percentage of Al (by volume) in the alloy is (keep 4 signi…cant …gures during
your calculation)
A) 25%
B) 30%
C) 35%
D) 40%
E) 45%
A free body diagram of the alloy in water results in
F + FB
= mg = F +
mg
=
F
=
wat gV = mg = gV
mg F
gV
= wat
= wat
wat gV !
mg
gV
mg
9:8
1g=cm3 = 8:55g=cm3
wat =
mg F
9:8 8:654
Hence the percentage of Al is found from
=
)
Al + (1
8:55 = 2:7 + 10:5 (1
= :25 ! A
Ag
)
7. A constant volume thermometer is …lled with Ar gas whose pressure
is 500P a at the triple point of water (:01 C)?. What will be the pressure at a
temperature of 125 C?
A) 729P a
B) 343P a
C) 866P a
D) 1092P a
E) 666P a
For a constant volume thermometer the pressure satis…es
P = Ptp
273 + 125
T
= 500
= 729P a ! A
Ttp
273
8. A hot rock with a mass of m = 500g and a temperature of T = 330 C
is dropped into a bowl containing 3:5kg of water at a temperature of T = 22 C:
Determine the speci…c heat of the rock given that the speci…c heat of water is
c = 4184J=kgK and the …nal equilibrium temperature of the water (and rock)
is T = 31 C.
A) 17:5J=kgK
B) 777J=kgK
C) 882J=kgK
799J=kgK
The equilibrium temperature is found from mr cr (Tr
Hence the speci…c heat of the rock is
cr =
mw (T Tw )
3:5 (31
cw =
mr (Tr T )
:5 (330
D) 1952J=kgK
T ) = mw cw (T
E)
Tw ) :
22)
4184 = 881:6J=kgK ! C
31)
9. A circular lake is 9m deep. Solar energy is incident on the lake
at an average rate of 240W=m2 : If the lake absorbs all of this energy without
3
exchanging any heat with its surroundings, approximately how many days will
it take to heat the lake from 10 C to 20 C? (Use the speci…c heat of water that
was given in problem 8.)
A) 19
B) 22
C) 26
D) 18
E) need more data
The total heat absorbed by the lake is Q = H t: Hence
t
=
t
=
1000
mc T
R2 h c T
=
=
2
H
I
R
1:569 106
= 18:2days ! D
3600 24
9
4184
240
10
= 1:569
106 sec
10. One end of a 4cm diameter iron rod (thermal conductivity k = 80:4W= (m K))
is immersed in ice water. The other end is immersed in boiling water. The rod
is well insulated so that there is no heat loss out the sides. What is length of
the rod if the heat ‡ow, H, along the rod is H = 28W ?
A) 1:44m B) 65cm C) 88cm D) 44cm E) 36cm
The expression for the thermal conductivity is H = kA T = x: Hence the
length of the rod is found from
2
x=
80:4 (:02) 100
kA T
=
= :36 ! E
H
28
4