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Midterm3_Fall08_key

# Midterm3_Fall08_key - 1 Two particles of masses m1= 2 kg...

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Unformatted text preview: 1. Two particles of masses m1= 2 kg and mg: 0.4 kg slide in opposite directions over a frictionless surface with initial constant velocities v1 = 2 m/s and V2 = 4 rn/s, respectively. The particles collide at point 0 and bounce as it is indicated in the ﬁgure below. a) Determine the velocities of the two particles after the collision. (18points) b) Is the collision elastic or inelastic? Explain your answer. (7points) " r, 2585 V COHMWl-‘m 99 em MDW‘Qulrﬁm y 4/ it! 2H gr? = Iﬁsvtp 03‘? V743- O "2 Vigg- 0.06? Veg ”—3 Vii 3: 0,0651 U1_f 234 = l.'7‘S\/,& +0.37% 2) 2H:Wg('o,ogquﬂ+o.3?vzf "9 V240 2 9?] mlS’ Vt : aoeCIIV-ilmrs) :10. BEE-WIS I b) KB; 2 flz‘mlfvlcq + Elim'LVzc‘L: "51.9.3, X mil/.JQ' + Jimr; Vzgq : C3306": +£1.41: : 4.59 :3— 7i CEO i @i’ K‘e “Jr CmgeAUﬂoo ‘ 2.Two blocks, m1 = 0.1 kg and m2 = 6 kg are connected by a massless string through a pulley of mass M. The rotational inertia of the pulley is ICOM = V2 MR2, with M = 0.3 kg and a radius R: 0.2 m. Block m2 lies on a 20° incline plane and is pulled upward by applying a force of 90 N. The incline is frictionless. a) Write down, using symbols, the equations of motion of the masses and the pulley. (8 points) b) Obtain the acceleration of the masses. (8points) 0) Calculate the forces of tension in the two sides of the pulley. (9 points) ’Cexi z: TT\+TT% : RT; hRT "‘5 4'3; M¢Q:*K ﬁl~ﬁn§ m H?) + (a) i =5 W (3) K o .3 ﬁning-t. i:—??-‘2.~W3\$in20 +p2‘17; :1 (mi+mrz'+—£M\Os rm. +PFW Sit-120°: q ‘ ‘. ‘LF.W+J§,M"— *9 1‘1 = “-03%? mm 0) T\ 2 m. (ta-H1} :: (33 T; :T‘, + iMQ Bees N E H u '1 (b) a= l 1.02: “Vs-Z 3. (a) A thin rod is pivoted about its center. A 8-N force is applied 3 m from the pivot and a 4-N force is applied 7 m from the pivot, as shown. Calculate the magnitude of the total torque about the pivot. (12.5 points) “E. F‘SN I '2: TwF. .. Sin (205+. V‘z E 93v; 3—710: = (ans (3 m ten 2&0qu m on “sf 4% (b) Calculate the moment of inertia of the system below with respect to the rotational axis shown. The system is made of a thin rod of mass M = 0.2 kg and length L = 2 m and three balls, each of them of mass m = 2 kg. You can neglect the spherical shape of the balls and assume that they are particles. (12.5 points) :2; ‘ 2/3 L E “BL ié—mes m. "‘1' 1/3 L m\$ 4. A uniform thin rod of length 2.5 m and mass 1.5 kg can rotate in a horizontal plane about a vertical axis through its center. The rod was initially at rest when a 10 g bullet traveling in the horizontal plane of the rod is ﬁred into the rod. The bullet lodges in the rod at a distance of 0.5 m from its left end. As can be seen in the picture below, the direction of the bullets velocity makes an angle of 60° with the rod. If the velocity of the bullet was 250 m/s before the impact with the rod, determine: (a) What is the angular velocity of the rod/bullet assembly after the collision? TIP: Think about the conservation of the angular momentum. (25 points) (j ...
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