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Unformatted text preview: Plzys 116 Prelim 1 ' Fall 2007 Your Name: SD\ 0‘45 Section Number: ______________ Section Instructor: Problem Points Your Score
1 25
2 30
3 20
4 25
TOTAL 1 00
Instructions: o Please write your name, section number and sectlon instructor at the top.
 There are 4 problems in this exam. The total number of points is 100.
 Make sure that your capy is complete (11 numbered pages) before starting.  The exam is closed book. No graphing calculators are allowed! The last
numberedpage of the exam contains formulae that you may find useful.  You must show your work to receive full credit. Correct answers without justification
will only receive partial credit. " Two blank pages are attached at the end of the exam. They may he used for scratch
paper, but will not be graded unless you clearly refer us to some Clearly Indicated
item there.  You may remove the equation sheet. You do not need to hand it in Witl‘ the rest of the
exam. Phys 116 Prelim 1 Fall 2007 1. [25 points] A block with mass m on a horizontal frictionless table is attached to a central pivot by a
massless rope of length L The block twirls about the pivot with a constant speed v. (a)
a) [2 points]
Draw the force diagram for the block in this initial conﬁguration, which is shown as
viewed from above in Figure (a). Clearly label each force. In the diagram, you do
NOT need to calculate the magnitudes of the forces, nor break them into components. OAR (are, :5 {k8 Jr'eﬁvsCow CA. (Le 10(36— ’l’ke.
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b) [7 points] Find the tension in the rope in terms of m, vand L (as in Figure (a)). use Pakox wor'A‘x w/ Sue: W 5% agave. A
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L. Phys 116 Prelim 1 Fall 2007 The string is cut, and a second block, also with mass m, is installed at the middle of the
rope and both blocks twirl as shown in Figure (b). Again, the outer block has speed v. c) [4 points] .
Draw the force diagram for each block in this new configuration, shown in Figure (b).
Clearly label each force. In the diagram, you do NOT need to calculate the magnitudes of the forces, nor break them into components. 7r“. U. :rou ‘51—
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"PW d) [12 pOints]
Find the tensions in the inner and outer sections of the rope in terms of m, v and L
(as in Figure (a)). u/ M W Care‘— 59—“' “"i "5 L Phys 116 Prelim 1 Fall 2007
2. [30 points] Having watched (too?) many episodes of This Old House, you decide that you could
SUpply your dormitory’s bathroom with a much nicer sink and vanity than Cornell
provides. You buy some sheets of plywood and a new sink and load them into your
friend ’s truck as shown. You’ve secured the plywood, but have simply rested the sink on tap of the plywood, as shown in the figure below.  The plywood rests at an angle 9 with respect to horizontal, the length of the plywood is
L, and the highest end of the plywood is a distance h above the road. The mass of the
sink is M, and the coefficient of friction between the sink and the plywood is it When
leaving Home Depot, in your enthusiasm you rapidly accelerate forward from rest with
acceleration of magnitude a, as indicated. The sink begins to slide up the plywood. Y \ a) '[4 points]
Draw a diagram showing all the forces acting on the sink, clearly labeling each
forces. In the diagram, you do NOT need to calculate the magnitudes of the forces, nor break them into components. Phys 116 Prelim 1 Fall 2007 b) [6 points]
Using the coordinate system shown in the system, write the equations for the
acceleration of the sink in the horizontal (x) and vertical (y) directions in terms of
6, L, h, M, p, a, and constants of nature. You may introduce alternate coordinates if
convenient, but their relationship to x and y must be explicit and clear. Your results should incorporate any constraints in the problem. ) A
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Find the maximum acceleration amax of the truck for which the sink would have
remained at rest at the bottom of the plywood. Express your results in terms of 6, L,
h, M, p, and constants of nature. W M? AWN. ) $~"‘~\"
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Q 5 Phys 116 ' Prelim 1 Fall 2007 d) [1 0 points]
Find the time ttop it takes the sink to reach the top of the plywood. At that time, what \o'
is the sink’s horizontal velocity relative to the (i) the ground and (ii) the truck? You \V
may take 6 = 30° (see formula sheet) and p = 1h/3, but otherwise express your J
results in terms of L, h, M, a, and constants of nature.
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"‘ ’5’?) ' Phys 116 Prelim 1 3. [20 points] The two blocks shown at right are connected by a heavy uniform rope
with mass Mn. An upward force of magnitude F is applied. a) [6 points] Draw three diagrams depicting the forces acting on each of
the three objects, the upper block with mass Mu, the lower
block with mass Md, and the rope. Upper 50% i
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Determine the acceleration of the system. Fall 2007 Z
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o. . Phys 116 Prelim 1 a Fall 2007 c) [10 points] Determine the tensionsat the top and the bottom of the heavy rope. Note: you do
NOT need to determine the tension as a function of height . "’ L
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T '= C "" 3 ":. A, F d) [BONUS 5 points]
Determine the tension at the heavy rope’s midpoint. Note: you still) do NOT need to determine the tension as a function of height. Tr“: A,
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MudM, iMA Prelim 1 Fall 2007 Phys 116 4. [25 points] Snoopy stands on a flat boat so that he is a distance d from shore} He walks a length L on the boat toward shore and then halts. Sn00py’s mass is ms, the mass of the boat
is MB, and one can assume that there is no friction between the boat and the water, or
drag from the air. SHORE r,»
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a) [5 points] \— \~r ~ What is the total buoyant force that the water must exert on the boat? You MUST
justify your result  simPly quoting a correct result will not earn full credit.g t _, .
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What is the total horizontal force and the total vertical force acting on the system of
Snoopy + boat? Phys 116 Prelim 1 Fall 2007 c) [18 points] How far is Snoopy from the shore when he halts (you may ignore the accelerations as he starts and stops). Express your results in terms of d, L, ms, Ma and any
constants of nature; 3 Gib/ML gig/ca; arc to"? ’50 it  a; O g V$ 7. — W V;
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