Question

Dynamics, please answer all parts.Thank you

9 Given: A mechanical system is shown on the right. You may neglect the masses of the pulleys and cords, and you may assume that the block is initially at rest. Find: a) The kinematic (i.e., dependent motion) equations for the motor-pulley system. This includes the equations for B position, velocity, acceleration, and displacement b) The displacement of block A if the motor pulls down the D cord, which connects motor M and pulley B, by a known distance of Ays. c) The acceleration of block A if a point on the cord M connecting motor M and pulley B accelerates downward at 1 m/s d) Assuming the mass of block A is mA and is known valu draw the free body diagrams (FBD) for the system that is, one FBD for block B, one FBD for pulley B, and one FBD for pulley D). Label Fe as the tension in the cord A connecting motor M and pulley B. e) The acceleration of block A if Fe is the known constant tension in the cord connecting motor M and pulley B. Solution:

Answer 1

length tquations of constraints Datum TUI.1 Is SB SA li: SB + 3B+ Sct sc - la = SA+ SA - Sc Constant ", le are 7. a dse adsc dt -0. + dt 2 VB+ 2 Veto 2VA. Vc 2 & VA Vc co. 2 vot 444=0. VB VA- ie of B moves down then a moves up. QB a A ly for a displacement in case of - O- aDSB + Rose 2 . OSA ose 2 DSA- DSC

16) Given, ASBE DYB (down words) AS B DS A= DYB - - (upwards) displacement of, ASA Blocka m/s (C) AB=1 m/s V a a=- AB 2 aaahh m/s. 0.5 m/s (upwards)

(d) Ti FBD: Pulley e LO fo= TTT = 27, fc Ti ti FBD! Pulley امیر) Tz Tz = DT, To Tz FBD: Pulley just before it block - FA 2 Tz - A fa Block A FBD paa FA - mag ma: A (m. g) from 0 , ③ , ④ 9 Noth bloue B FA : 2fc I'S present to Hace a PBD 2fc- mag: mnian aa afc 9 lup wards ) mA