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Unformatted text preview: 1. Write a very short answer to the following questions.
(a) Under what conditions is angular momentum conserved. L
ﬂ. : M 5: TC 44cm. 15 o: adrenal 49’19‘1 i 34‘3"“: Momm‘l'u’v‘s u H cwuﬁv’ccx. (1)) Brieﬂy describe why Newton’s third law only applies to central forces. CanLra‘ for cc 5 OJ“!— pafcts 'I' ka+ moi” clan S
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\HN Alﬁe 1;. Kick 4‘, ecu/L VII2f . 2. A paxticle of mass m is subject to the following force:
F 2 11(933 m 4.112 + 3:13))":
Where A is a constant. (:1) Determine the points when the particle is in equilibrium.
(b) Which of these points is stable and which are unstable. (0) Is the motion bounded or unbounded? a) £1”; thanum bcgur‘s 1.4.:be F10 5" X3" “WtE'Tbtb C“) K(X"3(V”3ﬁ 3. A ball of mass m1 is dropped from a tall tower. The force due to air resistance on the bail is
__ F = k1m1v2, where k1 is a constant. (a) What is the terminal velocity of the ball.
(b) What is the velocity of the ball as a function of time? (c) If a second ball of mass m2 and k2 is dropped at the same time as the ﬁrst, what is the
separation between the balls after a time t? kw
T‘rm‘ﬁfkl ULtod'L) ”VJ"4“. MIN1 Z—F 1" 5 é '3? Fv“ ”‘3 4. A small block of mass m is placed in a spherical bowl of radius R. (a) If the block is allowed to slide without friction, show that when the block is moved a small distance away from the bottom of the how], it will exhibit simple harmonic motion.
Label all forces and appropriate angles on the diagram below. (b) Determine the angular frequency of the motion. c Now assume that there is a frictional force, F : be, where b is a constant and v is the
f velocity of the block. Determine the value of R for which the block will stop moving the
moment it reaches the bottom of the bowl. The block’s initial velocity is zero. 5‘4 ‘Qr 5,wa IﬂirManl‘Q. M's: 3"} DE' + mfxeo c) Fclc‘llm =3; 5.: M =7 me + 526 + ”~39” .L x 4 Z >E+ 0%" :0
=9 2m '5: W {3‘ m P
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 Spring '08
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