492_Dynamics 11ed Manual

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

Info iconThis preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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 ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online