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Unformatted text preview: Quiz 3. Monday, February 16th, 2009 PHY 252 SOLUTION Name: l. A U-shaped tube is open to air at atmospheric pressure at both ends, and
contains some mercury. A quantity of water is carefully poured into the
left arm of the tube until the vertical height of the water is H. The
density of water is pW , and the density of mercury is pHg. a. Derive an expression for the gauge pressure at the water—mercury
interface. (2 points) Applﬂ PascaL's ecLua'bt‘on aft A aural. B.
pa + Pwﬂﬂn = P8 + 30333
PA = atmospheric. pressur¢_ ‘. G-auae, pressure at B = Pa‘pa = Pwﬂ (38":18) : loud” 7“ b. Derive an expression for the vertical distance h between the top of the mercury on the
right side of the tube and the top of the water in the left side. (2 points) Applﬂ Pascal); eiua'tion at A anal C.
'93 * 3033A = P“ + 33513:- PA = 9.; = at mospherie pressure , Relative to 3, Pas H ~—- P343 (H-L.) => pan = PM 40,61.
t = (Pa ~10» H +
2. A cable, of density pC and cross-sectional area A, is suspended vertically in the ocean (density p0) to a depth h. Derive an expression for the tension in the cable
as a function of depth z, where 0 S z 5 h . (3 points) z=0 '9 Apt 2) tension = the tuéadh‘t of Um. cable
“that has“; balow '2. _ 2 (mass of cable) K j
117-) - (Mass oi munici- displaces! bank's) 343 ﬂag 2 roams—2):} - Pmﬂclt*1)3
To.) = [rt-'2.) 2 Quiz 3. Monday, February 16'“, 2009 PHY 252 T1 3. A container of water, ﬁlled to a height hl, is sitting on a balance (see figure on left). The
weight of container plus water, recorded by the balance, is W]. A block of aluminum of mass
M is suspended from a wire. When the aluminum is out of the water, the tension recorded on
the wire is T]. (Gravity, of course, is acting downwards.) The block is lowered and completely immersed in the water (see middle figure). The block
does not touch the bottom of the container and is still suspended from the wire. The water
level rises to hz. Assume the container walls are vertical between heights hI and hz, and that
the cross sectional area of the container at these heights is A. The density of water is ,0w , and the density of aluminum, is pA .
a. Give an expression for the new weight recorded on the scale, W2. (1 point) Volume. o-_(- O“; placed. Water = HUM-"4!)
Mass 0:}- all; placed water- : A C 1‘1"“de
Welsh-b oj— displaced water = A (“‘4”) Pmil . _ 2 W. +’ A Chg-kl)Pwﬂ C b. Give an expressio ort e new tensron recore on t e Wire, 2. (1 point) From alcove, reasohin C Decreases clue)
tn human.an Nate; “Fl-W :: cans'tcut't, other-curse the Sudan will Mauel The container is replaced with one that is narrower, which has an even narrower neck
(ﬁgure on right). The same block, when immersed, now raises the water level to height h3. c. Give an expression for the new weight recorded on the scale, W3. (1 point)
Does“ It Matter! wa = w, —. w, + ACkz—k.)pwﬂ
d. Give an expression for the new tension recorded on the wire, T3. (1 point) UnchqndeaL The buodqncﬂ ecluaLs X:an Lueer of the displaced water, The Shape oi— the container is
lH'ElEUdﬂ'b_ ‘13 2: T2 : 71“ACL11“L1)PUJ ...
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- Spring '08
- Mass, applﬂ pascal