701_Dynamics 11ed Manual

701_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 Chapter 20 ⎞ ⎞ ⎞ ⎛ 0 ⎞ ⎡⎛ ω'1 ⎞ ⎛ ω1 ⎟ ⎛ ω1 ⎟⎤ ⎛ 0 ⎞ ⎛ ω1 ⎟ ⎡⎛ ω1 ⎟ ⎛ 0 ⎞⎤ ⎜ ⎟ ⎢⎜ ⎟ ⎜ ⎞ ⎜ ⎥ ⎜⎟ ⎜ ⎢⎜ ⎜ ⎟⎥ aC = aB + ⎜ aCB ⎟ + ⎢⎜ 0 ⎟ + ⎜ 0 ⎟ × ⎜ 0 ⎟⎥ × b + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × b ⎥ ... ⎜⎟ ⎜⎟ ⎜ 0 ⎟ ⎢⎜ ω' ⎟ ⎜ 0 ⎟ ⎜ ω ⎟⎥ ⎝ 0 ⎠ ⎜ ω ⎟ ⎢⎜ ω ⎟ ⎝ 0 ⎠⎥ ⎝ ⎠ ⎣⎝ 2 ⎠ ⎝ ⎠ ⎝ 2 ⎠⎦ 2 ⎠ ⎣⎝ 2 ⎠ ⎝ ⎦ ⎛ ω1 ⎞ ⎛ 0 ⎞ ⎜ ⎟⎜ ⎟ + 2⎜ 0 ⎟ × ⎜ vCB ⎟ ⎜ω ⎟ ⎜ 0 ⎟ ⎠ ⎝ 2⎠ ⎝ ⎛ −28.8 ⎞ ⎜ ⎟m aC = −5.45 ⎜ ⎟2 ⎝ 32.3 ⎠ s Problem 20-32 Consider again Example 20.5. The pendulum consists of two rods: AB is pin supported at A and swings only in the y-z plane, whereas a bearing at B allows the attached rod BD to spin about rod AB. At a given instant, the rods have the angular motions shown. Also, a collar C has velocity vC and acceleration aC along the rod. Determine the velocity and acceleration of the collar at this instant. Solve by fixing the x, y, z axes to rod BD in which case the collar appears only to have radial motion. Given: rad s ω'1 = 1.5 rad s ω'2 = −6 ω1 = 4 ω2 = 5 a = 0.5 m vCB = 3 m s rad 2 s rad 2 s b = 0.2 m aCB = 2 m 2 s Solution: ⎛ ω1 ⎟ ⎛ 0 ⎞ ⎜ ⎞⎜⎟ vB = ⎜ 0 ⎟ × 0 ⎜⎟ ⎜ 0 ⎟ ⎝ −a ⎠ ⎝⎠ ⎛ ω'1 ⎞ ⎛ 0 ⎞ ⎛ ω1 ⎟ ⎡⎛ ω1 ⎟ ⎛ 0 ⎞⎤ ⎜ ⎟ ⎜ ⎟ ⎜ ⎞ ⎢⎜ ⎞ ⎜ ⎟⎥ aB = ⎜ 0 ⎟ × 0 + ⎜ 0 ⎟ × ⎢⎜ 0 ⎟ × 0 ⎥ ⎜⎟ ⎜⎟ ⎜ 0 ⎟ ⎝ −a ⎠ ⎜ 0 ⎟ ⎢⎜ 0 ⎟ ⎝ −a ⎠⎥ ⎝⎠ ⎝ ⎠ ⎣⎝ ⎠ ⎦ 699 ...
View Full Document

This note was uploaded on 08/16/2011 for the course EGN 3321 taught by Professor Christianfeldt during the Spring '08 term at University of Central Florida.

Ask a homework question - tutors are online