Unformatted text preview: Physics TA Midterm #2.. A. Zettl, Spring 213133. Both sides of one sheet notes (sus" a l l") olt. All
problems worth 20 points. BOX your final answers! ﬂ 1. A thin hollow spherical shell of mass M and radius R is fixed in space. centered on the origin. Two
small holes are drilled through the shell where it is pierced by the aaais. A small mass m moves along the s—
aitis from x=xu to szrsu; it can pass right through the holes in the shall. :1} Determine the gravitational potential energy Uta} of the system, where x is the {variable} position of to.
Consider all values of x from —a.;. to +Ko Also, plot Ufa] vs. it. b] Determine the gravitational force Fts} on rn1 for all values of x from sic. to Ho. Also, [110* Fixl' VS» H
Deﬁne F as negative if it points in the *K direction and positive if it points in the +x direction. E A” r; "as; are on. 2. a solid rubber ball of mass M and radius it starts from rest at height H and rolls without slipping down
a wood ramp inclined at angle El front the horizontal. The ramp and part of the ﬂat wood floor at the bonom
have a “mirror image" ice ﬂoor and similarly inclined ice ramp. The ice surfaces are absolutely frictionless. a} To what maximum height ll will the hall go up the ice ramp? h} After returning from the ice ramp, will the ball go up the wood ramp to its original height H? lustif y
your conclusion with an informative yet concise physical argument [you need not use equations here}. 3. A flywheel from a piece of machinery is in the shape of a solid disc with IS holes in it. The ﬂywheel with
holes has radius R=El.5ﬂrn, thickness flﬂlm, and lots] mass M=iﬁkg. Each hole has a radius ﬂﬂﬁrn and is
centered 3.25m from the ﬂywheel axis {see drawing]. Determine the moment of inertia I for the ﬂywheel rotated about its axis.
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4. A dumhell. consisting of two "point" masses [each of mass M) connected by a rigid massless rod of
length l... rotates freely at angular velocity as about a centered normal axis on a frictionless pivot. lust as the
dumbell comes into position, two spiders [each of mass m) drop simultaneously a very short distance vertically
from their spider web perches onto the masses and grab hold. The dumbell {with spiders} continues to rotate.
but with a {perh aps different) angular velocity Inf.
a} Determine (of.
h} Determine the kinetic energy of the system {dumbell + spiders} before and after the spiders grab hold. You
may assume that the spiders are essentially at rest just as they grab hold (but do not assume they have zero
kinetic energy nﬁer they grab hold). ls the ﬁnal kinetic energy larger or smaller than the initial kinetic energy?
c) The spiders. in a new coordinated effort. now simultaneously crawl radially inward along the rod.
Determine a: for the rotating system as a function of radial position r for the spiders. Note that r ranges from
to to a. [email protected] ‘9 . mg (L o’—
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5. A wire drn long with total mass 6kg is bent into a flat. single—loop configuration, with horizontal "ends" sticking our from the top of the loop, as shown below. The centered loop has radius (Him. The left end of the
wire is attached to a frictionless hinge [at the origin of our s—y coordinate system} and the right end is supported by a massless string inclined at angle a=3ll° from the horizontal. clamor to ..c. . a} Find the {x and y] coordinates of the center of mass of the bent wire. ‘3 (if; f3 ‘  a
b} Find the tension T in the string. 3; if _ . _ T39
[Hint Exploit symmetries] ' ' " ...
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 Spring '08
 Lanzara
 Physics

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