Problem The direction of the 75-lb forces may vary, but the angle between the forces is always 50 o. Determine the value of  for which the resultant of the forces acting at A is directed horizontally to the left. 240 lb 30 o  50 o 75 lb A

Solving Problems on Your Own 1. Determine the resultant R of two or more forces. 2. Draw a parallelogram with the applied forces as two adjacent sides and the resultant as the included diagonal. 3. Set the resultant, or sum of the forces, directed horizontally. The direction of the 75-lb forces may vary, but the angle between the forces is always 50 o. Determine the value of  for which the resultant of the forces acting at A is directed horizontally to the left. 240 lb 30 o  50 o 75 lb A Problem 2.129

Problem Solution Determine the resultant R of two or more forces. We first Replace the two 75-lb forces by their resultant R 1, using the triangle rule.  50 o 25 o R1R1 R 1 = 2(75 lb) cos25 o = lb R 1 = lb  +25 o 240 lb 30 o  50 o 75 lb A

Draw a parallelogram with the applied forces as two adjacent sides and the resultant as the included diagonal. Set the resultant, or sum of the forces, directed horizontally. Problem Solution 30 o  +25 o R2R2 R 1 = lb 240 lb Consider the resultant R 2 of R 1 and the 240-lb force and recall that R 2 must be horizontal and directed to the left. Law of sines: sin(  +25 o ) 240 lb = sin(30 o ) lb sin(  +25 o ) = (240 lb) sin(30 o ) lb =  + 25 o = o  = 37.0 o