492_Dynamics 11ed Manual

# 492_Dynamics 11ed Manual - Engineering Mechanics Dynamics...

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Unformatted text preview: Engineering Mechanics - Dynamics aman Chapter 16 ⎛ 0 ⎞ ⎡⎛ 0 ⎞ ⎛ 0 ⎞⎤ ⎛ 0 ⎞ ⎛ 0 ⎞ = ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × ⎜ −d ⎟⎥ + 2⎜ 0 ⎟ × ⎜ −v ⎟ ⎜ ⎟ ⎢⎜ ⎟ ⎜ ⎟⎥ ⎜ ⎟ ⎜ ⎟ ⎝ ω ⎠ ⎣⎝ ω ⎠ ⎝ 0 ⎠⎦ ⎝ ω ⎠ ⎝ 0 ⎠ aman ⎛ 5.00 ⎞ ft = ⎜ 3.75 ⎟ ⎜ ⎟2 ⎝ 0.00 ⎠ s aman = 6.25 ft 2 s *Problem 16-136 While the swing bridge is closing with constant rotation ω, a man runs along the roadway such that he is running outward from the center at speed v with acceleration a, both measured relative to the roadway. Determine his velocity and acceleration at this instant. Given: ω = 0.5 v=5 rad s ft s a=2 ft 2 s d = 10 ft Solution: vman ⎛ 0 ⎞ ⎛0⎞ ⎛ 0 ⎞ = ⎜ −v ⎟ + ⎜ 0 ⎟ × ⎜ −d ⎟ ⎜⎟⎜⎟⎜ ⎟ ⎝ 0 ⎠ ⎝ω⎠ ⎝ 0 ⎠ aman ⎛ 0 ⎞ ⎛ 0 ⎞ ⎡⎛ 0 ⎞ ⎛ 0 ⎞⎤ ⎛ 0 ⎞ ⎛ 0 ⎞ = ⎜ −a ⎟ + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × ⎜ −d ⎟⎥ + 2⎜ 0 ⎟ × ⎜ −v ⎟ ⎜ ⎟ ⎜ ⎟ ⎢⎜ ⎟ ⎜ ⎟⎥ ⎜ ⎟ ⎜ ⎟ ⎝ 0 ⎠ ⎝ ω ⎠ ⎣⎝ ω ⎠ ⎝ 0 ⎠⎦ ⎝ ω ⎠ ⎝ 0 ⎠ vman aman ⎛ 5.00 ⎞ ft = ⎜ −5.00 ⎟ ⎜ ⎟s ⎝ 0.00 ⎠ ⎛ 5.00 ⎞ ft = ⎜ 0.50 ⎟ ⎜ ⎟2 ⎝ 0.00 ⎠ s vman = 7.07 ft aman = 5.02 ft s 2 s Problem 16-137 A girl stands at A on a platform which is rotating with constant angular velocity ω. If she walks at constant speed v measured relative to the platform, determine her acceleration (a) when she reaches point D in going along the path ADC, and (b) when she reaches point B if she follows the path ABC. 490 ...
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