ME240_CA1_W08_Solution - ME 240: Introduction to Dynamics...

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
ME 240: Introduction to Dynamics and Vibrations Mechanical Engineering Department The University of Michigan Winter 2008 Computer Assignment #1 Solution February 8, 2007 Prepared by Joosup Lim ( jooslim@umich.edu ) (i) Free body diagram is shown in Fig.( 1 ). m θ R e ^ n t θ F D mg N Figure 1: Free Body Diagram (ii) Using tangential-normal coordinates, and Newton’s second law, or F = m a , we can write the equations as, ( F - D - mg sin θ ) e t + ( N - mg cos θ ) e n = m ( R ¨ θ e t + R ˙ θ 2 e n ) (1) We can consider tangential components only because there are no friction between the ring and the mass. Hence, s F t = F - D - mg sin θ = mR ¨ θ (2) As given in the handout, the drag force D can be expressed as, D = bv = bv t = bR ˙ θ (3) 1
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
By substituting D and rearranging Eq.( 2 ), we can get the required equation of motion, mR ¨ θ + bR ˙ θ + mg sin θ = F (4) After getting the answer, we can simplify Eq.( 4 ) for numerical simulation, ¨ θ + b m ˙ θ + g R sin θ = F mR (5) (iii) Consider two cases of (a) b = 1 and (b) b = 10 for problem (iii) and (iv). - The time history of the first cycle for each case is presented in Fig.(
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

This note was uploaded on 03/29/2009 for the course MECHENG 240 taught by Professor Perkins during the Spring '09 term at University of Michigan.

Page1 / 6

ME240_CA1_W08_Solution - ME 240: Introduction to Dynamics...

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online