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Unformatted text preview: Problem 1 (10 pts) A child rides a merrygo—round, traveling from location A to location B, in the clockwise direction as shown,
at a. constant speed. Use the direction rosette to answer parts (a) and (b) of this question. i ’ f
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W (a: 5pts) What is the direction of Apt the change in the child’s momentum, between locations A and B? t W
(I Enter your answer here: ¥ (b: 5pts) What is the direction of Fm, the average vector value of the net force acting on the child as
she moves from location A to location B? ﬂ
Enter your answer here: y, ( Pym. (:Lfk, 515?: S1: CiLhrveCJ—L—ﬂxk... vi (S 90.1% (iLfFIZCqLM is? Problem 2 (Spts)
The momentum of a ball is observed to change uniformly with time as given below: I J)  ‘m'
Att=05,_5=(0,0,12)kgm/s (1: o to Eris  Ar 5 <0, 0,. *5? L5 /5 Att=15,p'=(0,0,7)kgm/s .. . __._. . 9 __ __  .u..£f
Att=2s.ﬁ=<0,0,2)kgm/S E! l £0 L. as ' AIL—<0" 0’ '77 L9
Att=35,ﬁ=(0,0,—3)kgm/s [ :.,;l_ E! ("T35 ‘. A55; Z<ol C” :5“>)L5'“/'3 Which of the following statements are true about the net force acting on the ball during the time the ball is observed? Circle a“ that apply. .5 4,,
FM! '— JA = <“xoz‘9>N ® The x component of the net force on the ball is zero. if
B. The z component of the net force on the ball is zero. A ‘ _ CalLid
The 3: component of the net force on the ball is constant. coxcog}! be. Claw5 (
The 3 component of the net force on the ball is constant. 0—2 {‘1' UL E. The 2 component of the net force on the ball is positive. 
® The 2 component of the net force on the ball is negative.
G. The z component of the net force on the ball is changing with time.
H. The ball has no interaction with its surroundings during this time interval. Problem 3 (12 pts) A billiard ball of mass 0.26 kg is moving with a speed of 22.3 m/s in a. direction given by the unit vector
(0.447, O, 0.895). (a: 6pts) What is the vector momentum of the billiard ball? Show all steps in your work. (b: Bpts) What are the angles the momentum vector make with each of the x, y, and z axes? Show all
steps in your work. f: <0.Lflc'F/c/9:%é??> 3<w912mﬁaj Cogﬁi>
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Cosgj: o ®@U;mr'(o):cloc M9 ~7 0??? =5 Eltcmﬂ'CHsj : 26§° Problem 4 (25 pts) Snowﬂakes have sixfold symmetry with arms of approximately identical length. In the example shown
below, a snowﬂake oriented in the x—y plane, has tip A located at (4.33, 2.5, 0) mm with rpect to the
center of the snowﬂake which is at (0, 0,0) mm. 5’ g Snowﬂake lies
in the xy plane (a: 5pts)What is the distance of tip A from the center? Show all steps in your work. I [If] r. : MW <2: gnu (b: 5pts) What is the position vector of tip B relative to the center of the snowﬂake? Show all steps
in your work. P”: 40/ 6‘,o> 'Msw H (c: Spts) What is the position vector of tip D relative to the center of the snowﬂake? Show all steps 6
in your work. "I? : <‘—4~a%/ #26", 0> “M” _" . ._ 3  (d: 5pts) What is the position vector of tip B relative to tip D? Show all steps in your work. ll? " : <,0/ g; 0> ﬂ<JLF33/—2vg/ a)
: <4mgg/ I’L,§‘/ O7M¢L (e: 5pts) What is the unit vector pointing in the direction of the vector you calculated in part (d)? Show
all steps in your work. :: 4331+¥51 : ghéémm‘
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[PW (raw6G Problem 5 (20 pts)
An object of mass 2.5 kg has a. constant net force of (—50,0, 150) N acting on it. At t = 15 s, it has a
momentum of (—30, 20,45) kg  , (a: lOpts) Determine the object’s momentum at an earlier time t = 10 3. You must start from the
momentum principle and show all steps in your work. ... *7 a 3 (PL +‘ PM? At (b: 10pts) If the position of the object was (0, —10, 25) m at t = 10 5, what is the new position of the object at t = 15 5? You must start with a valid form of the position update formula and show
all steps in your work. ——— *9
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J *2, (3832/) Jt32> M/S Problem 6 (15 pts) (a: 5pts) Write down the deﬁnition of the momentum of a. particle that is valid at all speeds. Your answer must be exactly correct to receive credit, including vectors, correct subscripts, etc.
There is no partial credit. .3 9
(Pt:wa . a 012 Tmbﬂ (b: 10pts) In a laboratory experiment, an electron is moving with 3. Speed of 2.7x 108 m/s. What is the
magnitude of the momentum of this particle? Show all steps in your work.  l H Y: L
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.3 :— WWW .: (Quoted—'39 (£40?) 3. :5. 5’6 0:129.— ~W/g Problem 7 (10 pts) A tennis ball is thrown straight up into the air with an initial speed “Hy. It takes the ball 10 s to reach
the maximum height and another 10 s for it to get back to the point from which it was thrown. For this problem, assume that air resistaHCe is negligible.
‘On the diagram below, plot pg, the 3; component of the momentum of the ball, vs. time for the 20 s the ba]l is in the air. P
.V 105 205 ...
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 Spring '08
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