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Lesson: Equivalence of Two Couples

Sample Question Videos

Worksheet • 8 Questions • 1 Video

Q1:

𝐴 𝐡 is a horizontal light rod having a length of 60 cm, where two forces, each of magnitude 45 N, are acting vertically at 𝐴 and 𝐡 in two opposite directions. Two other forces, each of magnitude 120 N, are acting in two opposite directions at points 𝐢 and 𝐷 of the rod, where 𝐢 𝐷 = 4 5 c m . If they form a couple equivalent to the couple formed by the first two forces, find the measure of the angle of inclination that the second two forces make with the rod.

Q2:

In a rectangle 𝐴 𝐡 𝐢 𝐷 , 𝐴 𝐡 = 1 8 c m and 𝐡 𝐢 = 2 4 c m . Two forces, each of magnitude 360 N, are acting along  𝐴 𝐡 and  𝐢 𝐷 . Two other forces, each of magnitude 𝐹 , are parallel to βƒ–     βƒ— 𝐡 𝐷 and acting on the points 𝐴 and 𝐢 . If the two couples are equivalent, find the value of 𝐹 .

Q3:

𝐴 𝐡 𝐢 𝐷 is a parallelogram in which π‘š ∠ 𝐴 = 6 0 ∘ , 𝐴 𝐡 = 8 c m , and the diagonal 𝐡 𝐷 is perpendicular to 𝐴 𝐡 . If two forces, each of magnitude 7 N, are acting along  𝐡 𝐴 and  𝐷 𝐢 , find the magnitude of each of the two forces F and βˆ’ F that act at 𝐴 and 𝐢 perpendicularly to the diagonal 𝐴 𝐢 so that they form a couple equivalent to the couple by the two forces mentioned earlier.

  • A F = √ 2 1 N , βˆ’ = √ 2 1 F N
  • B F = 8 N , βˆ’ = 8 F N
  • C F = 1 4 √ 3 3 N , βˆ’ = 1 4 √ 3 3 F N
  • D F = 7 √ 3 N , βˆ’ = 7 √ 3 F N

Q4:

𝐴 𝐡 𝐢 𝐷 is a rectangle, where 𝐴 𝐡 = 8 c m and π‘š ∠ 𝐴 𝐷 𝐡 = 1 5 ∘ . Two forces of the same magnitude 8 newtons are acting along  𝐴 𝐡 and  𝐢 𝐷 , and another two forces of the same magnitude 𝐹 form a couple that is acting at 𝐡 and 𝐷 , where one of them makes an angle of 3 0 ∘ with βƒ–     βƒ— 𝐡 𝐢 . Determine the magnitude of 𝐹 so that the couple formed by the last two forces is equivalent to that formed by the first two forces.

  • A 4 √ 6 newtons
  • B 8 √ 6 newtons
  • C 8 √ 3 newtons
  • D 4 √ 3 newtons

Q5:

As shown in the figure, 𝐴 𝐡 𝐢 𝐷 is a square of side length 1 m. Two forces, each of magnitude 16 kg-wt, are acting along  𝐴 𝐡 and  𝐢 𝐷 , and another two forces, each of magnitude 𝐹 , are acting at 𝐡 and 𝐷 , where one of them makes an angle of 1 5 ∘ with οƒͺ 𝐡 𝐢 , and the other makes an angle of 1 5 ∘ with  𝐷 𝐴 . 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.

Q6:

𝐴 𝐡 is a rod having a length of 6 m and negligible weight. Two equal forces, perpendicular to the rod and each with a magnitude of 70 N , are acting at its points of trisection in opposite directions. Given that these two forces are replaced by two other forces, each with a magnitude of 170 N , that are acting at the ends of the rod, such that they form a couple that is equivalent to the first, determine the angle of inclination of these two forces with the rod rounding the result to the nearest minutes.

  • A 7 5 3 β€² ∘
  • B 7 8 7 β€² ∘
  • C 1 1 5 3 β€² ∘
  • D 8 2 7 β€² ∘
  • E 2 4 1 9 β€² ∘

Q7:

𝐴 𝐡 𝐢 𝐷 is a rectangle, where 𝐴 𝐡 = 3 2 c m , and π‘š ∠ 𝐴 𝐷 𝐡 = 3 0 ∘ . Two forces, each with a magnitude of 16 newtons act along  𝐴 𝐡 and  𝐢 𝐷 , forming a couple. If, instead of these forces, two other forces, each with magnitude 𝐹 newtons, were to act outside the rectangle on 𝐡 and 𝐷 such that they made angles of 1 5 ∘ with 𝐡 𝐢 and 𝐷 𝐴 , respectively and formed an equivalent couple to the first two forces, find the value of 𝐹 .

  • A 8 √ 6
  • B 8 √ 3
  • C8
  • D 8 √ 2

Q8:

In a rectangle 𝐴 𝐡 𝐢 𝐷 , 𝐴 𝐡 = 7 2 c m and 𝐡 𝐢 = 9 6 c m . Two forces, each of magnitude 930 N, are acting along  𝐴 𝐡 and  𝐢 𝐷 . Two other forces, each of magnitude 𝐹 , are parallel to βƒ–     βƒ— 𝐡 𝐷 and acting on the points 𝐴 and 𝐢 . If the two couples are equivalent, find the value of 𝐹 .

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