# Worksheet: Equivalent of a System of Coplanar Forces to a Couple

Q1:

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 ,

Q2:

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.

Q3:

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.

• A 480 N⋅cm
• B 120 N⋅cm
• C 960 N⋅cm
• D 240 N⋅cm

Q4:

In a triangle , and . Forces of magnitudes 2, 2, and newtons are acting at , , and , respectively. If the system is equivalent to a couple, find the magnitude of its moment considering the positive direction is .

• A 22 N⋅cm
• B 44 N⋅cm
• C N⋅cm
• D N⋅cm

Q5:

is a triangle, where , , and , and forces of magnitudes 64 N, 24 N, and 56 N are acting along , , and respectively. If the system of forces is equivalent to a couple, determine the magnitude of its moment.

• A 96 N⋅cm
• B 48 N⋅cm
• C N⋅cm
• D N⋅cm

Q6:

is a square of side length 60 cm, where and , such that . Forces of magnitudes 75, 5, 40, 40, and g-wt are acting at , , , , and , respectively. If the system is equivalent to a couple, find its moment considering the positive direction is .

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:

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.

Q9:

is a rectangle in which , and is midpoint of . Forces of magnitudes 7 N, 2 N, 6 N, 18 N, N, and N are acting along , , , , , and respectively. If this system of forces is equivalent to a couple, find the norm of its moment.

• A 24 N⋅cm
• B 60 N⋅cm
• C 72 N⋅cm
• D 84 N⋅cm

Q10:

In a trapezium , , , , and . Given that forces of magnitudes 54, 70, 78, and 74 newtons are acting along , , , and respectively. If the system of forces is equivalent to a couple, find the magnitude of the moment of the forces.

Q11:

is a regular pentagon whose side length is 16 cm. Five forces, each of magnitude 11 N, are acting at , , , , and , respectively. If the system is equivalent to a couple, find the magnitude of its moment, considering the positive direction is , rounded to two decimal places, if needed.

Q12:

is a pentagon in which , , , and . Forces of magnitudes 72 N, 57 N, 78 N, 57 N, and 30 N are acting along , , , , and respectively. If this system is equivalent to a couple, find its moment norm.

• A 4 404 N⋅cm
• B 1 842 N⋅cm
• C 2 202 N⋅cm
• D 3 684 N⋅cm

Q13:

is a regular hexagon of side length 8 cm, and forces of magnitudes 2, 13, and 11 newtons are acting at , , and respectively. If the system is equivalent to a couple, determine the magnitude of the moment of the forces.

• A 36 N⋅cm
• B N⋅cm
• C 52 N⋅cm
• D N⋅cm

Q14:

is a regular hexagon whose side length is 7 cm. Forces of magnitudes of 9, 8, 10, 9, 8, and 10 newtons are acting along , , , , , and respectively. Find the magnitude of the moment of the couple that is equivalent to the system.

• A 98 N⋅cm
• B N⋅cm
• C 378 N⋅cm
• D N⋅cm

Q15:

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.

• A 21 N⋅cm
• B N⋅cm
• C 99 N⋅cm
• D N⋅cm