21.  The drawing shows a uniform horizontal beam attached to a vertical wall by a frictionless hinge and supported from below at an angle q = 39° by a brace that is attached to a pin. The beam has a weight of 340 N. Three additional forces keep the beam in equilibrium. The brace applies a force  to the right end of the beam that is directed upward at the angle q with respect to the horizontal. The hinge applies a force to the left end of the beam that has a horizontal component  and a vertical component . Find the magnitudes of these three forces.

 

w0428

The beam is at rest and so the sum of the torques must equal zero.  But we can choose about which point we calculate the torques.  Choose where the beam touches the wall then the lever arm for both the horizontal and vertical component of the hinge force will be zero, so they provide no torques about that point.  So the sum of the torques becomes:

 

 

 

 

 

 

 

 

To find the horizontal and vertical hinge forces we can use the sum of the forces in the x and y directions.

 

 

 

 

 

 

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This page last updated on January 11, 2020