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In this lesson, we will learn how to identify the conditions for a system of coplanar forces to be equivalent to a couple and find its moment.

Q1:

π΄ π΅ πΆ π· 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 πΉ 1 and πΉ 2 .

Q2:

π΄ π΅ πΆ π· is a square having a side length of 85 cm. Forces of magnitudes 30, 55, 30, and 55 newtons are acting along the squareβs sides, and two equal forces of magnitude 2 5 β 2 newtons, are acting at π΄ and πΆ in the directions shown in the figure. Find the couple equivalent to the system.

Q3:

π΄ π΅ πΆ π· is a square having a side length of 50 cm. Forces of magnitudes 30, 60, 160, and 10 newtons are acting at ο π΄ π΅ , ο π΅ πΆ , ο πΆ π· , and ο π· π΄ , respectively, while two forces of magnitudes 4 0 β 2 and 9 0 β 2 newtons are acting at ο π΄ πΆ and ο π· π΅ , respectively. If the system is equivalent to a couple, find its moment considering the positive direction is π· πΆ π΅ π΄ .

Q4:

π΄ π΅ πΆ is a triangle, where π΅ πΆ = 4 8 c m , and three forces of magnitudes 13, 13, and 24 newtons are acting along ο« πΆ π΄ , ο« π΄ π΅ , and οͺ π΅ πΆ respectively. If the system of forces is equivalent to a couple, determine the magnitude of its moment.

Q5:

In a triangle π΄ π΅ πΆ , π΄ π΅ = π΅ πΆ = 2 2 c m and π β π΅ = 1 2 0 β . Forces of magnitudes 2, 2, and 2 β 3 newtons are acting at ο« π΄ π΅ , οͺ π΅ πΆ , and ο« πΆ π΄ , respectively. If the system is equivalent to a couple, find the magnitude of its moment considering the positive direction is π΄ π΅ πΆ .

Q6:

π΄ π΅ πΆ is a triangle, where π΄ π΅ = 8 c m , π΅ πΆ = 3 c m , and π β π΅ = 6 0 β , and forces of magnitudes 64 N, 24 N, and 56 N are acting along ο« π΄ π΅ , οͺ π΅ πΆ , and ο« πΆ π΄ respectively. If the system of forces is equivalent to a couple, determine the magnitude of its moment.

Q7:

π΄ π΅ πΆ π· is a square of side length 60 cm, where πΈ β οͺ πΆ π΅ and πΉ β ο« πΆ π· , such that πΆ πΈ = πΆ πΉ = 1 8 0 c m . Forces of magnitudes 75, 5, 40, 40, and 3 5 β 2 g-wt are acting at ο« π΄ π΅ , οͺ π΅ πΆ , ο« πΆ π· , ο« π· π΄ , and οͺ πΈ πΉ , respectively. If the system is equivalent to a couple, find its moment considering the positive direction is π· πΆ π΅ π΄ .

Q8:

π΄ π΅ πΆ π· is a rectangle, in which π΄ π΅ = 4 5 c m , π΅ πΆ = 5 5 c m , and π· πΈ = 2 8 c m . Forces of magnitudes 225, 275, 265, and 135 newtons act along ο« π΄ π΅ , οͺ π΅ πΆ , οͺ πΆ πΈ , and ο« πΈ π΄ , respectively. If the system of forces is equivalent to a couple, Determine the magnitude of the moment of the forces.

Q9:

π΄ π΅ πΆ π· is a rectangle in which π΄ π΅ = 1 2 c m , π΅ πΆ = 6 c m and π is midpoint of π΄ π΅ . Forces of magnitudes 7 N, 2 N, 6 N, 18 N, 3 β 5 N, and 1 0 β 2 N are acting along οͺ πΆ π΅ , ο« π΄ π΅ , ο« π· π΄ , ο« πΆ π· , ο« π΄ πΆ , and ο« π πΆ respectively. If this system of forces is equivalent to a couple, find the norm of its moment.

Q10:

In a trapezium π΄ π΅ πΆ π· , π β π΄ = π β π΅ = 9 0 β , π΄ π· = 2 7 c m , π΄ π΅ = 3 5 c m , and π΅ πΆ = 3 9 c m . Given that forces of magnitudes 54, 70, 78, and 74 newtons are acting along ο« π· π΄ , ο« π΄ π΅ , οͺ π΅ πΆ , and ο« πΆ π· 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:

πΈ π΄ π΅ πΆ π· is a pentagon in which π β πΈ = π β π΅ = π β πΆ = 9 0 β , πΈ π΄ = 2 4 c m , π΄ π΅ = πΆ π· = 1 9 c m , and π΅ πΆ = 2 6 c m . Forces of magnitudes 72 N, 57 N, 78 N, 57 N, and 30 N are acting along ο« πΈ π΄ , ο« π΄ π΅ , οͺ π΅ πΆ , ο« πΆ π· , and ο« π· πΈ respectively. If this system is equivalent to a couple, find its moment norm.

Q13:

π΄ π΅ πΆ π· πΈ π is a regular hexagon of side length 8 cm, and forces of magnitudes 2, 13, and 11 newtons are acting at ο« π΄ π΅ , ο« πΆ π , and ο« πΈ π· respectively. If the system is equivalent to a couple, determine the magnitude of the moment of the forces.

Q14:

π΄ π΅ πΆ π· π» π 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 ο« π΅ π΄ , ο« π΄ π , ο« π» π , ο« π» π· , ο« π· πΆ , and οͺ π΅ πΆ respectively. Find the magnitude of the moment of the couple that is equivalent to the system.

Q15:

If π΄ π΅ πΆ π· πΈ π is a regular hexagon having a side length of 6 cm, where forces of magnitudes 20 N, 20 N, 13 N, 13 N, and 2 0 β 3 newtons are acting along ο« π΄ π΅ , οͺ π΅ πΆ , ο« πΆ π , ο« πΈ π· , and ο« πΆ π΄ , respectively, and the system is equivalent to a couple, find its moment norm.

Q16:

π΄ π΅ πΆ π· is a trapezium, where π β π΄ = π β π΅ = 9 0 β , π΄ π΅ = 2 4 c m , π΄ π· = 1 1 c m and π΅ πΆ = 1 8 c m . πΈ and π are the midpoints of π΄ π΅ and π΅ πΆ respectively. Forces of magnitude 77 N, 175 N, 220 N, and 10 N are acting along ο« π΄ π· , ο« π· πΆ , ο« πΆ π΄ , and ο« πΈ π , respectively. If the system of forces is equivalent to a couple, determine the magnitude of the moment of the forces.

Q17:

π΄ π΅ πΆ π· is a quadrilateral in which π΄ π΅ = π΄ π· = 8 c m , π΅ πΆ = πΆ π· = 1 3 c m , and π β π΅ π΄ π· = 1 2 0 β . Forces act on the directed line segments ο« π΄ π΅ , οͺ π΅ πΆ , ο« πΆ π· , and ο« π· π΄ . If the system is reduced to a couple having a moment of 4 2 β 3 Nβ cm in the direction of π΄ π΅ πΆ π· , find the magnitude of πΉ ο§ and πΉ ο¨ .

Q18:

π΄ π΅ πΆ π· is a trapezium in which π΄ π· β₯ π΅ πΆ , π΄ π΅ is perpendicular to them, πΈ is the projection of π· on π΅ πΆ , π΅ πΆ = 1 6 c m , π΄ π΅ = 1 2 c m , and π΄ π· = 1 1 c m . Forces of magnitudes 5 1 1 4 1 3 4 1 0 1 0 , , , , a n d newtons are acting along ο« πΆ π΄ , ο« π΄ π· , ο« π· πΆ , ο« πΈ π· , and ο« π΄ π΅ respectively. If the system is equivalent to a couple, find the magnitude of the couple moment.

Q19:

π΄ π΅ πΆ π· is an isosceles trapezium in which π΄ π· β₯ π΅ πΆ , π΄ π· = 1 5 c m , π΄ π΅ = π· πΆ = 1 7 c m , and π΅ πΆ = 3 1 c m . Forces having magnitudes of 51, 79, 51, and 31 newtons are acting in the directions of ο« π΄ π΅ , οͺ π΅ πΆ , ο« πΆ π· , and ο« π· π΄ , respectively. If the system is equivalent to a couple, find the magnitude of its moment considering the positive direction is π· πΆ π΅ π΄ .

Q20:

π΄ π΅ πΆ π· is a rectangle, where π΄ π΅ = π₯ cm, π΅ πΆ = 2 π₯ cm, and πΈ and π are the midpoints of π΄ π· and π΅ πΆ , respectively. Forces of magnitudes 8 N, 8 N, 3 1 β 2 N, and 2 3 β 2 N are acting along ο« πΈ π΄ , ο« π΄ π΅ , οͺ π΅ πΈ , and ο« π· π , respectively. Given that this system of forces is equivalent to a couple, determine the magnitude of its moment in terms of π₯ , giving your answer in N β cm.

Q21:

The sides of an equilateral triangle π΄ π΅ πΆ , taken the same way round, completely represent three forces with a drawing scale of 4 cm to 8 N. If the length of a side of the triangle is 24 cm, find the magnitude of the resulting couple, giving an exact answer in Nβ cm.

Q22:

π΄ π΅ is a rod having a length of 105 cm and negligible weight. Forces of magnitudes 214 N, 67 N, 115 N, and 176 N are acting on the rod as shown in the figure. Given that πΆ and π· are the points of trisection of π΄ π΅ , determine the algebraic sum of the moments of these forces about the point π΄ .

Q23:

Three forces ο« π΄ π΅ , οͺ π΅ πΆ and ο« πΆ π΄ are represented by the sides of a right-angled triangle π΄ π΅ πΆ where π΅ is a right-angle. 1 cm on the triangle represents 40 N of force, and π΄ π΅ = 1 9 c m and π΅ πΆ = 4 0 c m . Find the magnitude of the resulting couple.

Q24:

π΄ π΅ πΆ π· is a quadrilateral, where π΄ π΅ = 1 8 c m , π΅ πΆ = 2 4 c m , πΆ π· = π· π΄ = 1 7 c m , and π β π΄ π΅ πΆ = 9 0 β . Given that four forces, measured in newtons, are acting on the quadrilateral as shown in the given figure, determine the magnitude of the moment of the equivalent couple.

Q25:

Three forces of magnitudes 15, 10, and 15 newtons are acting along ο« π΄ π΅ , οͺ π΅ πΆ , and ο« πΆ π΄ respectively. Given that π΄ π΅ = π΄ πΆ = 3 6 c m and π΅ πΆ = 2 4 c m , determine the magnitude of the resultant couple rounded to the nearest hundredth.

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