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# Lesson Worksheet: Equivalent System of Forces to a Couple Mathematics

In this worksheet, we will practice identifying the conditions for a system of coplanar forces to be equivalent to a couple and finding its moment.

**Q3: **

is a square of side length 90 cm. Forces of magnitudes of 25, 80, 25, and 80 newtons are acting along the squareβs sides, and two forces, each of magnitude newtons, are acting at and as shown in the figure. Calculate the moment of the couple which is equivalent to this system, giving your answer in Nβ cm

**Q6: **

As shown in the figure, is a square of side length 1 m. Two forces, each of magnitude 16 kg-wt, are acting along and , and another two forces, each of magnitude , are acting at and , where one of them makes an angle of with , and the other makes an angle of with . If the couple formed by the first two forces is equivalent to that formed by the other two, determine the magnitude of and round to two decimal places.

**Q7: **

is a square having a side length of 50 cm. Forces of magnitudes 30, 60, 160, and 10 newtons are acting at , , , and , respectively, while two forces of magnitudes and newtons are acting at and , respectively. If the system is equivalent to a couple, find its moment considering the positive direction is .