# 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.

Q1:

In the given figure, if the forces that act on a light rod are equivalent to a couple, find the moment of this couple. Q2:

In the given figure, if the forces that act on a light rod are equivalent to a couple and the moment of this couple is equal to 17 N⋅cm, find and . • A6 N, 6 N
• B6 N, 3 N
• C6 N, 2 N
• D7 N, 2 N
• E7 N, 3 N

Q3:

is a square of side length 90 cm. Forces of magnitudes of 25, 80, 25, and 80 newtons are acting along the square’s 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 N⋅cm Q4:

is a square having a side length of 85 cm. Forces of magnitudes 30, 55, 30, and 55 newtons are acting along the square’s sides, and two equal forces of magnitude newtons, are acting at and in the directions shown in the figure. Find the couple equivalent to the system. Q5:

is a square, where the five forces, measured in newtons, are acting on it as shown in the figure. If the system of forces is equivalent to a couple, determine and . • A,
• B,
• C,
• D,

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 .

Q8:

If is a regular hexagon having a side length of 6 cm, where forces of magnitudes 20 N, 20 N, 13 N, 13 N, and newtons are acting along , , , , and , respectively, and the system is equivalent to a couple, find its moment norm.

• A21 N⋅cm
• B99 N⋅cm
• C N⋅cm
• D N⋅cm

Q9:

is a triangle, where , and three forces of magnitudes 13, 13, and 24 newtons are acting along , , and respectively. If the system of forces is equivalent to a couple, determine the magnitude of its moment.

Q10:

is a rectangle, in which , , and . Forces of magnitudes 225, 275, 265, and 135 newtons act along , , , and respectively. If the system of forces is equivalent to a couple, determine the magnitude of the moment of the forces. This lesson includes 41 additional questions and 396 additional question variations for subscribers.