Answer Vrel=2.11 b1 m/s Arel=22.8 b1 m/s^2 As illustrated, a peg P is constraine

Question

Answer

Vrel=2.11 b1 m/s

Arel=22.8 b1 m/s^2

As illustrated, a peg P is constrained to slide within both a smooth horizontal chute and the slotted link OQ, which is free to rotate about its pivot O with an angular speed and acceleration of and , respectively. At ¿particular instant, the peg is a distance rP/O = 0.9 m from the pivot O, and the link is angled at = 65degree with respect to the horizontal. If the peg's velocity in the chute is a constant tp = 5i m/s, what are vrel and arel? Express your answers in the {b1, b2, b3} basis.

Explanation / Answer

Hope this helps!  When I solved it, I found one more component for the velocity (in the b2 direction).  I encourage you to double check these answers and if something doesn't make sense feel free to ask.

The peg moves to the right so...

Vrel-b1= 5cos(65) = 2.11 m/s b1

Vrel-b2= -5sin(65) = -4.53 m/s b2

arel-b1 = 2r      (This eqn comes from the definition of normal acceleration)

      =Vrel-b2/r      

      =(-4.53m/s)/(0.9m) = -5.03 rad/s

arel-b1 = (-5.03 rad/s)2(0.9m) = 22.8 m/s2

arel-b2 = vtangent'     (The tangential component of acceleration should be the derivative of the tangental velocity.)

      Vtan' = Vrel-b2' = 0 m/s  (The peg moves at a constant 5m/s to the right so the tangental velocity shouldn't change)

arel-b2 = 0 m/s2

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