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ME 242 Selected Answers Chapter 3

ME 242 Selected Answers Chapter 3 - 3.1 3.1.2 3.1.4 3.1.6...

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3.1 Cartesian Coordinates 3.1.2 ¨ x = g cos θ sin θ 3.1.4 θ = 44 . 6 3.1.6 ¨ x = 29 . 0 ft/s 2 3.1.8 Δ x = 26 . 7 ft 3.1.10 t = 1 . 64 s 3.1.12 ¨ x = 0 . 407 m/s 2 , ¨ y = 0 . 305 m/s 2 3.1.14 ¨ z = 36 . 4 ft / s 2 3.1.16 ¨ s = - 3 . 33 m / s 2 3.1.18 ¨ x = 7 . 36 m/s 2 3.1.20 N 1 = 50 . 2 lb 3.1.22 a: x 1 static = 0 . 196 m , a m 2 = 0 . 333 m/s 2 b: x 2 static = 0 . 294 m , a m 2 = 0 . 333 m/s 2 3.1.24 a A = gm A sin θ cos θ m B + m A sin 2 θ ı - g sin θ ( m A + m B ) m B + m A sin 2 θ b 1 3.1.26 θ 1 = 34 . 1 , θ 2 = 27 . 8 3.1.28 t * = 5 . 74 × 10 - 2 s 3.1.30 T = 6 μ s m 2 A m C g (1 + μ d ) 3 μ s m A ( m A + m C ) + 4 m A m C 3.1.32 r m = - 0 . 3183 ı m 3.1.34 7.3 car lengths. 3.1.36 ¨ x = - F 0 m = - 5 m/s 2 3.1.38 ¨ x (0) - ¨ y (0) = 6 m/s 2 - 2 m/s 2 = 4 m/s 2 3.1.40 Acceleration of B : - 2 k ( x + δ ) + m B g sin φ - μ d m B g cos φ m B + 4 m A b 1 3.1.42 ¨ x A = - 10 . 2 m/s 2 3.1.44 t = t 1 + t 2 = 1 . 69 s 3.2 Polar Coordinates 3.2.2 a x = g 1 - cos θ 0 sin θ 0 3.2.4 T = - mg sin 30 = - mg 2 3.2.6 t = 0 . 421 s 3.2.8 F θ = 72 r 0 m sinh (6 t ) N 3.2.10 F sp = 0 . 513 e r N 3.2.12 θ = 33 . 2 3.2.14 To 45 : 2.33 s. To N = 0: 2.65 s. 3.2.16 T = 840 . 42 N 3.2.18 T = mg sin θ 3.2.20 v min = 58 . 4 ft/s , v max = 331 ft/s 3.2.22 ¨ θ = g cos θ + 2 v ˙ θ (2 - vt ) 3.3 Path Coordinates 3.3.2 F
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