Parallel Forces

Problem 236A parallel force system acts on the lever shown in Fig. P-236. Determine the magnitude and position of the resultant. 

 

Solution 236

       downward 

 

       counterclockwise 

       to the right of A 

Thus, R = 110 lb downward at 6 ft to the right of A.           answer

Problem 237Determine the resultant of the four parallel forces acting on the rocker arm of Fig. P-237. 

 

Solution 237

       downward 

       clockwise 

       to the right of O 

Thus, R = 50 lb downward at 4 ft to the right of point O.             answer

Problem 238The beam AB in Fig. P-238 supports a load which varies an intensity of 220 N/m to 890 N/m. Calculate the magnitude and position of the resultant load. 

 

Solution 238

 

 

 

 

Thus, R = 3330 N downward at 3.6 m to the left of A.           answer

Problem 239The 16-ft wing of an airplane is subjected to a lift which varies from zero at the tip to 360 lb per ft at the fuselage according to w = 90x1/2 lb per ft where x is measured from the tip. Compute the resultant and its location from the wing tip. 

Solution 239

 

 

       upward 

 

Thus, R = 3840 lb upward at 9.6 ft from the tip of the wing.           answer

Problem 240The shaded area in Fig P-240 represents a steel plate of uniform thickness. A hole of 4-in. diameter has been cut in the plate. Locate the center of gravity the plate. Hint: The weight of the plate is

equivalent to the weight of the original plate minus the weight of material cut away. Represent the original plate weight of plate by a downward force acting at the center of the 10 × 14 in. rectangle. Represent the weight of the material cut away by an upward force acting at the center of the circle. Locate the position of the resultant of these two forces with respect to the left edge and bottom of the plate. 

 

Solution 240

 

 

 

 

 

Thus, the centroid is located at 6.8 in. to the right of left edge and 4.9 in. above the bottom edge. answer

Problem 241Locate the amount and position of the resultant of the loads acting on the Fink truss in Fig. P-241. 

 

Solution 241

 

 

 

Magnitude of resultant

       downward 

Location of resultant

       to the right of A 

Thus, R = 15 130 N downward at 3.62 m to the right of left support.           answer

Problem 242Find the value of P and F so that the four forces shown in Fig. P-242 produce an upward resultant of 300 lb acting at 4 ft from the left end of the bar. 

 

Solution 242

Sum of vertical forces

 

Moment about point A

           answer 

           answer

Problem 243The resultant of three parallel loads (one is missing in Fig. P-243) is 13.6 kg acting up at 3 m to the right of A. Compute the magnitude and position of the missing load. 

 

Solution 243

Sum of vertical forces

       downward 

 

Moment about point A

 

Thus, F = 31.4 kg downward at 2.48 m to the right of left support.       answer