Draw FBDs as required Clearly state, all assumptions made towards solving the pr

Question

Draw FBDs as required Clearly state, all assumptions made towards solving the problem At the given instant of time (t = 0), the collar A is at a divine ro = 0.15m and at rest ( = 0) w.r.t the horizontal rod DC, which is oriented along the x axis. If the horizontal rod BC rotates in the horizontal plane (xz plane) at, a constant rate of = 2rad/s moves inwards (towards B) at a rate of acceleration of 2t mm/s2 (with t m sees), determine Velocity vector A at t = 1. Express your result as a magnitude and direction w.r.t x axis (in the xz plane) The magnitude of the acceleration of the collar A at t = 1s.

Explanation / Answer

a)dVr/dt=2t*10^(-3)m/s^2----------------------- Vr=t^2*10^(-3) m/s------------------------------- dr/dt=Vr=t^2*10^(-3)m/s------ Vr(1)=1^2*10^(-3)=0.001m/s----------- r=0.15-t^3*10^(-3)/3------------ wr=2*0.149666=0.29933m/s r(1)=0.15-1^3*10^(-3)/3=0.14966666m-------------- V=sqrt((Vr)^2 + (wr)^2)=sqrt(0.001^2+0.29933^2)=0.2993316m/s----------- angle with respect to x axis =2*1=2 radian =114.591 degree ------------- b)ar=2*10^(-3)------------------ a_theta=2*2*10^(-3)*2=0.008------------------- a=sqrt((2*10^(-3))^2+0.008^2)------------------- a=0.00824 m/s^2

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