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 𝐴𝐡 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 𝐴𝐡 are equivalent to a couple and the moment of this couple is equal to 17 Nβ‹…cm, find F and F.

  • A6 N, 6 N
  • B6 N, 3 N
  • C6 N, 2 N
  • D7 N, 2 N
  • E7 N, 3 N

Q3:

𝐴𝐡𝐢𝐷 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 45√2 newtons, are acting at 𝐴 and 𝐢 as shown in the figure. Calculate the moment of the couple which is equivalent to this system, giving your answer in Nβ‹…cm

Q4:

𝐴𝐡𝐢𝐷 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 25√2 newtons, are acting at 𝐴 and 𝐢 in the directions shown in the figure. Find the couple equivalent to the system.

Q5:

𝐴𝐡𝐢𝐷 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 𝐹 and 𝐹.

  • A𝐹=4N, 𝐹=11N
  • B𝐹=22N, 𝐹=29N
  • C𝐹=22N, 𝐹=11N
  • D𝐹=13N, 𝐹=20N

Q6:

As shown in the figure, 𝐴𝐡𝐢𝐷 is a square of side length 1 m. Two forces, each of magnitude 16 kg-wt, are acting along 𝐴𝐡 and 𝐢𝐷, and another two forces, each of magnitude 𝐹, are acting at 𝐡 and 𝐷, where one of them makes an angle of 15∘ with οƒͺ𝐡𝐢, and the other makes an angle of 15∘ with 𝐷𝐴. If the couple formed by the first two forces is equivalent to that formed by the other two, determine the magnitude of 𝐹 and round to two decimal places.

Q7:

𝐴𝐡𝐢𝐷 is a square having a side length of 50 cm. Forces of magnitudes 30, 60, 160, and 10 newtons are acting at 𝐴𝐡, οƒŸπ΅πΆ, 𝐢𝐷, and 𝐷𝐴, respectively, while two forces of magnitudes 40√2 and 90√2 newtons are acting at 𝐴𝐢 and 𝐷𝐡, respectively. If the system is equivalent to a couple, find its moment considering the positive direction is 𝐷𝐢𝐡𝐴.

Q8:

If 𝐴𝐡𝐢𝐷𝐸𝑂 is a regular hexagon having a side length of 6 cm, where forces of magnitudes 20 N, 20 N, 13 N, 13 N, and 20√3 newtons are acting along 𝐴𝐡, οƒͺ𝐡𝐢, 𝐢𝑂, 𝐸𝐷, and 𝐢𝐴, respectively, and the system is equivalent to a couple, find its moment norm.

  • A21 Nβ‹…cm
  • B99 Nβ‹…cm
  • C99√3 Nβ‹…cm
  • D21√3 Nβ‹…cm

Q9:

𝐴𝐡𝐢 is a triangle, where 𝐡𝐢=48cm, and three forces of magnitudes 13, 13, and 24 newtons are acting along 𝐢𝐴, 𝐴𝐡, and οƒͺ𝐡𝐢 respectively. If the system of forces is equivalent to a couple, determine the magnitude of its moment.

Q10:

𝐴𝐡𝐢𝐷 is a rectangle, in which 𝐴𝐡=45cm, 𝐡𝐢=55cm, and 𝐷𝐸=28cm. Forces of magnitudes 225, 275, 265, and 135 newtons act along 𝐴𝐡, οƒͺ𝐡𝐢, οƒͺ𝐢𝐸, and 𝐸𝐴 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.

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