Exercício de Dinamica Aplicada (96)

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257 
 
 
PROBLEM 11.178 
Show that sinr hφ θ=  knowing that at the instant shown, step AB of 
the step exerciser is rotating counterclockwise at a constant rate .φ 
 
SOLUTION 
From the diagram 
 2 2 2 2 cosr d h dh φ= + − 
Then 2 2 sinrr dhφ φ=  
Now 
sin sin
r d
φ θ
= 
or 
sin
sin
d
r
φ
θ
= 
Substituting for r in the expression for r 
 
sin
sin
sin
d
r dh
φ φ φ
θ
  = 
 
 
or sin Q.E.D.r hφ θ=   
Alternative solution. 
First note 180 ( )α φ θ= ° − + 
Now r rr rθ θθ= + = +v v v e e 
With B as the origin 
 ( constant 0)Pv d d dφ= =  =