2. Replace the force-couple system shown below with an equivalent force-couple system at point A. Your answer should consist of a single force vector and a single moment vector. y N 3 kN 2m B D 7 kN 5 kN-m E 2m 3 kN 2m
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- Five forces and a couple act on the plate shown in the figure . - Find the resultant ( R ) Of the four forces , and its angle (e). - Locate it with respect to point ( O). - Show where the resultant cuts both the x - and y- axes. 400KN 7m 1o0 KN 6 m lom 800 KN-m V150 KN 18m 7200KN 100 KN L 8 mReplace the three forces shown by an equivalent force-couple system at point A. If the forces are replaced by a single resultant force, determine the distance d below point A to its line of action. 110 N 710 mm 710 mm 710 mm 185 N Answers: Force-couple system at A. The force is positive if to the right, and the couple is positive if counterclockwise. R= i N M= i Single resultant force. d= 100 N N-m mmReplace the given loads with an equivalent force-couple system at O by specifying the resultant R and couple Mo. Next, determine the equation for the line of action of the stand-alone resultant force R. 1.3 m 1.3 m 0.5 0.40 m 5.3 kN m 1.5 m 62 19 kN-m 10.9 kN 6.7 kN 0.40 m Answers: Equivalent force-couple system at O. R = i i+ i j) kN Mo = i kN-m The equation for the line of action of the stand-alone resultant force R: y = i X+ i m
- 4. For the force-couple system as shown, determine the following: Magnitude of the couple moment Mc so that the equivalent system is a single force acting at point P b. a. Point of application of the single equivalent force along line AB if MC is equal to 180 lb-ft counterclockwise. 85 lb 40 ° 100 16 30 lb 15° Mc 35 lb 400 P 1 ft A 85 lb B 1 ft 200 lbWhile cutting a piece of paper, a person exerts the two indicated forces on a paper cutter. Reduce the two forces to an equivalent force-couple system at corner O and then specify the coordinates of the point P in the x- y plane through which the resultant of the two forces passes. The cutting surface is 30" x 30". 5 lb 24 Ib 15" 1" 5" Part 1 There are 2 distinct questions here. We will solve the first question now. Question 1: Replace the two forces shown by an equivalent force-couple system at point O. Find the force part of the force-couple system. Answer: F = i + j+ k) Ibforce at point C as shown. Replace this force by an equivalent force- couple system at point O. Ans. M. = 161 i - 165 j+ 120k N•m 300 mm 20° 250 mm 30° F = 800 N
- 2. Replace the force system acting on the frame by a resultant force (R) and couple moment (MA) at point A. Draw the equivalent force system F=30 kN 2 m 3 m F2=50 kN F= 25 kN 40° 3 m 5 m 30° AReplace the three forces shown by an equivalent force-couple system at point A. If the forces are replaced by a single resultant force, determine the distance d below point A to its line of action. 160 N 470 mm 470 mm 150 N 470 mm 305 N Answers: Force-couple system at A. The force is positive if to the right, and the couple is positive if counterclockwise. R = M = N-m Single resultant force. d = mmReplace the three forces shown by an equivalent force-couple system at point A. If the forces are replaced by a single resultant force, determine the distanced belew point A to its line of action. 100 N 470 mm 470 mm 290 N 470 mm 305 N Answers: Force-couple system at A. The force is positive if to the right, and the couple is positive if counterclockwise. R = i M = N-m Single resultant force. d = i mm
- Current Attempt in Progress Replace the three forces shown by an equivalent force-couple system at point A. If the forces are replaced by a single resultant force, determine the distance d below point A to its line of action. Answers: R= i M = i 290 N 265 N d = Single resultant force. i Force-couple system at A. The force is positive if to the right, and the couple is positive if counterclockwise. 120 N 570 mm 570 mm 570 mm N N-m mmReplace the system of forces acting on the frame as shown by a resultant R at A and a couple acting horizontally through B and C. Force on top 10 kN, bottom left is 40 kN, and bottom right is 50 kN. 1m A 3 m 2 m 4 m OR= 20KN, B = 95KN, C= -95KN OR- -20KN, B = -95kN, C = 95KN OR= 20KN, B = -95KN, C = 95kN OR=-20KN, B = 95KN, C = -95kN mathalino,comQ4b. Force vectors F1 and F2 act on body Pwith the resultant force vector R. The resultant force R= 575 N and the angle between Rand the x-axis is of 320. If F1 = 275 N and the angle between F1 and the x-axis is 560, determine the angle between F2 and the x-axis. *Assume coplanar vector forces and give your answer in degrees to two decimal places. Body, P Answer: y F1 R F2