#308 As follower AB rolls along the surface

As follower AB rolls along the surface - Mechanical Engineering

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Free Chegg Question

As follower AB rolls along the surface of member C, it exerts a constant force F perpendicular to the surface, (a) Replace F with an equivalent force-couple system at the point D obtained by drawing the perpendicular from the point of contact to the x axis, (b) For a= 1 m and b = 2 m, determine the value of x for which the moment of the equivalent force-couple system at D is maximum.

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Free Chegg Answer

1. 1. Step 1 of 3

      a)

      Find the value of , slope of the tangent to the surface of member C.

      

      Assume be the equivalent force and be the equ0ivalent moment of the force couple system acting at the point D.

      Assume be the angle made by the force, F with the horizontal.

      Since the force is perpendicular to the surface,

      

      

      The equivalent force acting at point D is .

      Therefore, the equivalent force acting at point D is  and it is acting at an angle 

   2. Step 2 of 3

      Find the equivalent moment acting at point D.

      

      Substitute for and  for .

      

      Therefore, the equivalent moment acting at point D is 

   3. Step 3 of 3

      b)

      Write the expression for equivalent moment acting at point D,

      

      Substitute 1 m for a and 2 m for b.

      

      Find the value of x at which the maximum value of couple at point D. Under maximum condition the following condition should satisfy:

      

      

      

      

      Consider only the positive value and neglect the negative value.

      

      Therefore, the value of x is .