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Unformatted text preview: UNIVERSITY OF CALIFORNIA AT BERKELEY
Physics 7A — Section 3 (Stabler) Spring 2001 SECOND MIDTERM EXAMINATION Please do all your work on the front and back pages of this exam. Write your name
on all pages. These problems, like those on the previous exam, are at the same level as the homework.
The only difference is that your answers are to be algebraic, not numerical. You must
attempt all three problems. If you become stuck on one, go on to another and return
to the ﬁrst one later. You should Show all your reasoning, since partial credit will be
allotted. Remember to circle your ﬁnal answer. 36’ ~ ‘3’
DISCUSSION SECTION NUMBER. AND TIME: 36?? ﬂ???" ‘2‘
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1,. are IAKC’E/ll’f Ar Pa». {77 #14247 Problem 1 (20 points) , A dumbbell consists of two small masses M1 and M2 (M1 > M2) attached by a. rigid
rod of length l and negligible mass. The dumbbell'is placed vertically at point P on a frictionless surface and then released. [a] Show in a sketch all the external forces acting on the dumbbell when M1 has fallen
roughly halfway to the surface. ' (b) How far from the initial point P does M3 strike the surface? 1
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the string is at an angle 61 , the mass is released. At the bottom of its swing, it collides '
and sticks to an identical small mass, initially at rest._ The two then continue to swing upward, attaining a. maximum angle 92. 3+“ “3 77 we, kid "a CD’LS‘“ may 40?" (MI! I f
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t. 2. M 141:. g: (2%) ( E1? em” )2 2m} ransom.) Problem 3 (45 points) A uniform stick of mass M and length I is suspended horizontally, with end A on the
edge of a table and end B held up by hand. The end B is suddenly released from rest.
The point of this problem is to determine N , the magnitude of the contact force between the table and stick Just after release. [Mark M I {fa/[+67 015+“! be low L ﬂ ~ 2; ____ __ 0 niform stick about its center of massfisiﬂM 12/12.: Becall that the moment of inertia of a u (a) Let Hem be the linear acceleration of the stick’s center of mass. Find the magnitude
and direction of 13cm just after the release. The magnitude should be written in terms
of g, N. M, and 3, although you may not need all these variables in the ﬁnal expression. a), ﬁnd 05A. the angular acceleration of the stick about (b) Using your answer from (
M, and 5. point A, just after release. Again, express 05A as a function of g, N, (c) Find the magnitude and direction of “E4, the torque on the stick about point A, just after release. [(1) Using your pre ' s anséers, ﬁnd N in terms of M and g. @
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