ch05 - Chapter 5 Multiparticle Systems 5.1 Force Balance...

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Unformatted text preview: Chapter 5 Multiparticle Systems 5.1 Force Balance and Linear Momentum 131 5.1.1 GOAL: Find center of mass of two particles. GIVEN: Position and mass of particles. DRAW: FORMULATE EQUATIONS: * r G = 1 m 2 X i =1 m i * r i SOLVE: * r G = 1 (5 kg) [(2 kg)(4 * m) + (3 kg)(4 * m)] = 1 . 6 * m + 2 . 4 * m * r G = (2 . 4 * + 1 . 6 * )m 132 5.1.2 GOAL: Find mass center of four particles. GIVEN: Particle mass and position. DRAW: FORMULATE EQUATIONS: * r G = 1 m 4 X i =1 m i * r i / O SOLVE: * r G = 1 (45 slug) [(5 slug)(2 * ft) + (10 slug)[(2 * + 2 * )ft +(20 slug)(2 * ft) + (10 slug)(3 * ft)] * r G = (2 * + 2 3 * )ft 133 5.1.3 GOAL: Find systems center of mass GIVEN: Position and mass of four particles. FORMULATE EQUATIONS: * r G = n i =1 m i * r i m (1) SOLVE: (1) * r G = (2 kg)(0 . 5 * m) + (2 kg)(1 . 2 * m) + (2 kg)(- . 5 * k m) + (2 kg)(- 1 . 2 * + 1 . 5 * k m) 8 kg * r G = . 125 * + 0 . 25 * k m 134 5.1.4 GOAL: Find systems center of mass GIVEN: Position and mass of three particles. DRAW: FORMULATE EQUATIONS: * r G = n i =1 m i * r i m (1) SOLVE: (1) * r G = (5 kg)(- . 2 * m) + (2 kg)(- . 2 * + 0 . 25 * k m) + (6 kg)(0 . 3 * - . 2 * k m) (5 + 2 + 6) kg * r G = (0 . 138 * - . 108 * - . 0538 * k ) m 135 5.1.5 GOAL: Find systems linear momentum. GIVEN: Position, mass and velocity of four particles. DRAW: FORMULATE EQUATIONS: * v G = n i =1 m i * v i m (1) SOLVE: (1) * v G = (2 slug)(5 * ft/s) + (3 slug)(6 * ft/s) + (4 slug)(- 5 * ft/s) + (4 slug)(- 6 * ft/s) (2 + 3 + 4 + 4) slug = (- . 154 * - 1 . 08 * ) slg ft/s * L = m * v G = (- 2 * - 14 * ) slg ft/s 136 5.1.6 GOAL: Find systems linear momentum. GIVEN: Position, mass and velocity of three particles. DRAW: FORMULATE EQUATIONS: * v G = n i =1 m i * v i m (1) SOLVE: (1) * v G = (2 kg)(10 * m/s) + (3 kg)(20 * m/s) + (10 kg)(- 10 * m/s) (2 + 3 + 10) kg =- 1 . 3 * m/s * L = m * v G =- 20 * kg m/s 137 5.1.7 GOAL: Find the total force acting on the floor of a dance platform. GIVEN: Dancers A and B weigh 120 lbs, dancer C weighs 110 lbs and dancer D weighs 150 lbs. * v A = * a A = * v B = * a B = 0 * v C = * v D = 5 * ft/s * a C = * a D =- 6 * ft 2 / s DRAW: SOLVE: Force balances: Restricting ourselves to horizontal motions: m D x D =- F D (1) m C x C =- F C (2) m B x B =- F B (3) m A x A =- F A (4) Using the given accelerations yields F D = 110 lb 32 . 2 ft/s 2 (6 ft/s 2 ) = 20 . 50 lb F C = 150 lb 32 . 2 ft/s 2 (6 ft/s 2 ) = 27 . 95 lb F B = 110 lb 32 . 2 ft/s 2 (0) = 0 lb F A = 110 lb 32 . 2 ft/s 2 (0) = 0 lb Total force acting on the floor: F T OT AL = F A + F B + F C + F D = 20 . 50 lb + 27 . 95 lb = 48 . 45 lb 138 5.1.8 GOAL: Determine the velocity of a four car pileup....
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This note was uploaded on 09/19/2009 for the course ME 242 taught by Professor Kam during the Spring '06 term at Nevada.

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ch05 - Chapter 5 Multiparticle Systems 5.1 Force Balance...

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