Phy 101 Test 3

# Phy 101 Test 3 - l A pendulum consists of four identical...

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Unformatted text preview: l. A pendulum consists of four identical point masses connected by rigid (massless) rods, as shown below. Find the period of such pendulum. . . 7:- 27— /“I :4 1/" I. a" W = Tl/ i1: 40W V5472 2/ 67/ j/Waﬁagz ‘ Z 2L a 277 (/13. I. 552/ A) T247: Z—L—; B)T=47: Egg C)T=27r ﬁg;D)T=27z —L-;®Noneofabove. 3g 2g 3g 3g 2. State the second Kepler’s law of orbital motion: A Planets move in their orbits with constant speeds. ) As a planet moves in its orbit, it sweeps out an equal amount of area in an equal amount of time. C) The speed of a planet’s motion is proportional to the distance between the centers of the planet and the Sun. ‘ D) The period of a planet’s orbital motion is independent from its distance ﬁom the Sun. E) NOne of above. 3. The speed of a wave on a rope is independent of: A) Tension in the rope; The amplitude of the wave; C) Length of the rope; D) Mass of the rope; E) None of above. 4. Find mass m that is required for the perfectly balanced mobile: W 3) mac: 0,4); 5cm 15cm mzaz/y/ 40 cm 20 cm “0‘ A) 0.05 kg; B) 0.10 kg; C) 0.15 kg;@0.20 kg; E) None of above. -2§»’”’GIM +§m1rz=0 W=2 H4 “a. 4’. 5. Two identical planets with masses M and radii R are separated by a distance 2d (center-to-center). A rocket with mass m is at rest midway between the planets. It is at rest at distances (2’ from the centers of the planets. Find the escape velocity of the rocket. v=2"G—34~; B)v=2"%1€; C)v=2"G—:?; D)v=2\/GMd; E)Noneofabove. 6. In a virtual Universe a planet in circular orbit about its Sun (Ms=1020 kg, Rs = 108 m) has a speed V = 102 m/s at altitude h = 108 m from the Sun’s surface. Find the Gravitational Constant G, pertaining to this virtual universe. g% _; mike L :> g ‘ (/9574 4 H} “210-8 leg '7‘ z ’95 ’L A ﬂ 2 A) 5x10”6 m3/szkg; B) 3XlO'7 m3/s2kg;@2x10'8 m3/sgkg; D) 5X10”10 m3/szkg; E) None of above. fl"; \$7.5 Mk , )6 MW A) L/2; B) L/3; (ﬁ-1)L; D) (\B —1)L; E)None ofabove. 2% X?— “ L—X a ( ) 2XL=(L ~02 7. Two stars (with masses M and 2M) are separated by distance L between their centers. If an asteroid becomes trapped at rest between the stars how far from the less massive star will it be? 8. Classify the following waves as transverse/longitudinaI/both: A) Water waves are transverse; light waves are transverse; sound waves in the air are longitudinal; Water waves are both; light waves are transverse; sound waves in the air are longitudinal; C) Water waves are both; light waves are longitudinal; sound waves in the air are longitudinal; D) Water waves are longitudinal; light waves are longitudinal; sound waves in the air are transverse; E) None of above. 9. Calculate the angular momentum of a point object with mass m = 50 kg if it is located at position (2 m, 3 m) and is moving about the origin with velocity v = (5 m/s) x. sztr: Jog—3m, 5% =¢529f3§ﬂ A) 60 kg mZ/s; B) 150 kg mz/s; C) 250 kg mZ/sso kg mZ/s; E) None of above; 10. A child runs towards a rotating merry—go-round and jumps onto it. The ﬁnal angular velocity of the system of the child and the merry-go—round is independent of: A) The direction at which the child approaches the merry-go—round; B) The mass of the child; C) The radial distance ﬁom the axis at which the child lands on the merry-go-round; D The linear velocity of the running child. None of above. 11. Two blocks with masses m1 and m are connected by, a rope with the help of a disk-shaped pulley of mass M and radius R (I = MRZ/Z) on a frictionless plane inclined at angle 6 to horizontal, as shown. When the block m1 is released it slides down the slope with acceleration a. A) Find the acceleratiOn a of the blocks. (15 pt) B) Using the obtained formula, decide on how the acceleration depends on 6, M, R, i.e. if the acceleration increase decide whether will each of these quantities increase, decrease or remain the same. (5 pt) C) If mass m is much larger than both mass m; and mass M of the pulley, determine the limiting value of acceleration a. (5 pt) 12. A ball with massm = 2 kg is attached to a vertical spring with a force constant of k =12O N/m as shown below. At ﬁrst the ball is supported so that the. spring has its equilibrium length. When the ball is slowly released the spring gets stretched and the new equilibrium position of the system is attained. A) Find the adjusted equilibrium position of the system. (lOpt) B) When the block is again moved to the original height and dropped it starts oscillations about the new equilibrium position. Find the period of the oscillation. (Spt) C) Write down expressions for x(t), v(t) and (ICC). (lOpt) y /?I‘WI? : Fs/ya‘qg: 7.20%; A/k2Q7635/v I 2 LL =0377~ 08M 5) 77 m[/ /W - (0,6915 9 C) w~ - fgzs 7— 7,945‘ W? j 24 54X 2015/4.’ J .<.‘ = A] % Fqc/ g'm/?,K?Z-Z€ ...
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