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168_Physics ProblemsTechnical Physics

168_Physics ProblemsTechnical Physics - 170*P6.30 Circular...

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170 Circular Motion and Other Applications of Newton’s Laws *P6.30 (a) The chunk is at radius r = + = 0 137 0 080 0 054 2 . . . m m 4 m. Its speed is v r T = = = 2 2 0 054 2 20 000 60 114 π π . m s m s b g and its acceleration a v r g g c = = = × = × F H G I K J = × 2 2 5 5 4 114 0 054 2 2 38 10 2 38 10 9 8 2 43 10 m s m m s horizontally inward m s m s 2 2 2 b g . . . . . . (b) In the frame of the turning cone, the chunk feels a horizontally outward force of mv r 2 . In this frame its acceleration is up along the cone, at tan . . . = ° 1 13 7 8 3 3 49 2 cm cm 2 a f . Take the y axis perpendicular to the cone: n f mv r 2 49.2° a FIG. P6.30(b) F ma n mv r n y y = + °= = × × °= : sin . . sin . 2 3 5 49 2 0 2 10 2 38 10 49 2 360 kg m s N 2 e je j (c) f n k = = = µ 0 6 360 216 . N N a f F ma mv r f ma a a x x x x x = °−
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