Worksheet: Moment of a Couple

In this worksheet, we will practice calculating the moment of a couple of two forces about a point in space.

Q1:

The two forces ⃑ 𝐹 = βˆ’ 3 ⃑ 𝑖 βˆ’ 4 ⃑ 𝑗 1 and ⃑ 𝐹 2 are acting at the points 𝐴 ( 6 , βˆ’ 2 ) and 𝐡 ( 8 , βˆ’ 3 ) respectively. Given that they are forming a couple, determine the vector of the couple moment.

  • A 1 0 ⃑ π‘˜
  • B 5 ⃑ π‘˜
  • C 2 ⃑ π‘˜
  • D 1 1 ⃑ π‘˜

Q2:

Given that two forces ⃑ 𝐹 = βˆ’ ⃑ 𝑖 + 2 ⃑ 𝑗 1 and ⃑ 𝐹 2 are acting at two points 𝐴 ( 2 , 2 ) and 𝐡 ( βˆ’ 2 , βˆ’ 2 ) respectively to form a couple, find the perpendicular distance between the two forces.

  • A 1 4 √ 5 5 length unit
  • B 4 √ 5 5 length unit
  • C 1 8 √ 5 5 length unit
  • D 1 2 √ 5 5 length unit

Q3:

𝐴 𝐡 𝐢 𝐷 is square having a side length of 3 cm. 𝐻 and 𝑂 belong to 𝐡 𝐷 , where π‘š ∠ 𝐢 𝐻 𝐷 = π‘š ∠ 𝐴 𝑂 𝐡 = 6 0 ∘ . Given that two equal forces, each of magnitude 5 N, are acting along  𝑂 𝐴 and  𝐻 𝐢 respectively, find the magnitude of the moment of the couple.

  • A 1 5 √ 3 2 Nβ‹…cm
  • B 1 5 √ 2 Nβ‹…cm
  • C 1 5 √ 3 Nβ‹…cm
  • D 1 5 √ 2 2 Nβ‹…cm

Q4:

𝐴 𝐡 𝐢 𝐷 is a square of side length 8 cm, where two forces of magnitudes 21 N are acting at 𝐡 and 𝐷 respectively, and their lines of action are in the direction of  𝐴 𝐢 and  𝐢 𝐴 respectively. Determine the magnitude of the moment of the couple.

  • A 3 3 6 √ 2 Nβ‹…cm
  • B 168 Nβ‹…cm
  • C 336 Nβ‹…cm
  • D 1 6 8 √ 2 Nβ‹…cm

Q5:

What is a couple?

  • A a pair of parallel forces with equal magnitude and the same line of action
  • B a pair of forces with equal magnitude
  • C a pair of forces with the same magnitude and direction.
  • Da pair of parallel forces with equal magnitude and opposite direction which do not lie on the same line of action.

Q6:

𝐴 𝐡 𝐢 𝐷 is a rectangle, in which 𝐴 𝐡 = 5 c m and 𝐴 𝐷 = 1 0 c m . Two forces of the same magnitude 3 3 √ 5 N are acting at 𝐴 and 𝐢 in the directions of  𝐡 𝐷 and  𝐷 𝐡 respectively. Determine the magnitude of the moment of the couple.

Q7:

𝐴 𝐡 𝐢 𝐷 is a parallelogram, where 𝐴 𝐡 = 1 0 c m , 𝐡 𝐢 = 8 c m , and the perpendicular distance between 𝐴 𝐡 and 𝐷 𝐢 is 6 cm. Given that two forces of the same magnitude 50 N are acting along  𝐴 𝐷 and οƒͺ 𝐢 𝐡 , respectively, determine the magnitude of the moment of the couple.

Q8:

𝐴 𝐡 𝐢 𝐷 𝐻 𝑂 is a regular hexagon with sides of length 5 cm. Two forces of the same magnitude 13 N are acting along οƒͺ 𝐢 𝐡 and  𝑂 𝐻 , respectively. Determine the magnitude of the moment of the couple.

  • A 65 Nβ‹…cm
  • B 1 3 0 √ 3 Nβ‹…cm
  • C 130 Nβ‹…cm
  • D 6 5 √ 3 Nβ‹…cm

Q9:

In the figure below, 𝐹 = 3 1 N and 𝐹 1 and 𝐹 2 form a couple. Find the algebraic measure of the moment of that couple.

Q10:

The given figure shows two forces each of magnitude 267 newtons acting on two edges of a lamina in the form of a rectangle with dimensions π‘₯ = 4 2 c m and 𝑦 = 8 4 c m . Find the moment of the couple if t a n πœƒ = 3 4 .

Q11:

Given two forces in a couple, what is the name given to the product of the magnitude of one of the forces and the perpendicular distance between the two forces?

  • A the magnitude of the couple
  • B the resultant of the couple
  • C the moment of one force of the two forces of the couple
  • D the moment of the couple

Q12:

𝐴 𝐡 𝐢 𝐷 is a parallelogram, where 𝐡 𝐢 = 1 0 c m and π‘š ∠ 𝐴 𝐡 𝐢 = 1 5 0 ∘ . If two forces of the same magnitude 50 N are acting at  𝐴 𝐡 and  𝐢 𝐷 respectively, determine the magnitude of the moment of the couple, rounding your answer to two decimal places.

Q13:

𝐴 𝐡 𝐢 𝐷 is a rhombus in which its diagonal 𝐴 𝐢 = 7 c m and π‘š ∠ 𝐴 = 6 0 ∘ . Given that two equal forces, each of magnitude 45 N, are acting along  𝐴 𝐷 and οƒͺ 𝐢 𝐡 respectively, find the magnitude of the moment of the couple rounded to two decimal places if necessary.

Q14:

𝐴 𝐡 𝐢 𝐷 is square having a side length of 24 cm, 𝐸 ∈ 𝐡 𝐢 , and 𝑂 ∈ 𝐷 𝐴 , where 𝐡 𝐸 = 𝐷 𝑂 = 6 c m . Given that two forces, each of magnitude, 34.2 N are acting along  𝐡 𝑂 and  𝐷 𝐸 respectively, find the magnitude of the moment of the couple.

  • A 492.48 Nβ‹…cm
  • B 123.12 Nβ‹…cm
  • C 369.36 Nβ‹…cm
  • D 164.16 Nβ‹…cm

Q15:

𝐴 𝐡 𝐢 𝐷 𝐻 𝑂 is a regular hexagon, having a side length of 5 cm, where a force of magnitude 15 N is acting along  𝐢 𝐻 , and another force of the same magnitude is acting at 𝐴 in the direction of  𝐻 𝐢 . Determine the magnitude of the moment of the couple.

Q16:

𝐴 𝐡 𝐢 𝐷 is a rhombus, where its diagonals 𝐴 𝐢 and 𝐡 𝐷 are 13 cm and 7 cm respectively, and two forces of the same magnitude 23 N are acting along  𝐴 𝐡 and  𝐢 𝐷 . Determine the magnitude of the moment of the couple, rounding your answer to two decimal places if necessary.

  • A 299 Nβ‹…cm
  • B 283.51 Nβ‹…cm
  • C 86.29 Nβ‹…cm
  • D 141.76 Nβ‹…cm

Q17:

If the norm of the moment of a couple is 750 Nβ‹…m, and the magnitude of one of its two forces is 50 N, determine the length of the moment arm.

Q18:

𝐴 𝐡 and 𝐢 𝐷 are two parallel chords in a circle whose radius is 25 cm, and they are at different distances away from the circle’s centre, where 𝐴 𝐡 = 3 0 c m , and 𝐢 𝐷 = 1 4 c m . Given that two forces of the same magnitude 20 N are acting along  𝐡 𝐴 and  𝐢 𝐷 , respectively, determine the magnitude of the moment of the couple.

Q19:

𝐴 𝐡 𝐢 𝐷 is an isosceles trapezium, where 𝐴 𝐷 = 𝐡 𝐢 = 1 3 c m , 𝐴 𝐡 = 1 2 c m , and 𝐢 𝐷 = 6 c m . Two forces, each of magnitude 50 N, are acting along  𝐴 𝐡 and  𝐢 𝐷 . Find the magnitude of the moment of the couple rounded to two decimal places, giving your answer in Nβ‹…cm.

Q20:

A light rod 𝐴 𝐡 , which has a length of 22 cm and a mid-point 𝑂 , is under the action of two forces measured in newtons as shown in the figure. Given that a moment of magnitude 22 Nβ‹…cm is acting on the rod perpendicularly to the vertical plane, determine the moment of the resultant couple acting on the rod.

Q21:

If the two forces ⃑ 𝐹 = βˆ’ 4 ⃑ 𝑖 + π‘Ž ⃑ 𝑗 1 and ⃑ 𝐹 = 𝑏 ⃑ 𝑖 + 8 ⃑ 𝑗 2 form a couple, then find the value of π‘Ž βˆ’ 8 𝑏 .

Q22:

Given that the forces ⃑ 𝐹 1 , ⃑ 𝐹 2 , and ⃑ 𝐹 3 are acting at the points ( βˆ’ 1 , βˆ’ 6 ) , ( 3 , 8 ) , and ( 8 , βˆ’ 8 ) respectively, where the system of forces is equivalent to a couple, ⃑ 𝐹 = 3 ⃑ 𝑖 βˆ’ 6 ⃑ 𝑗 1 , and ⃑ 𝐹 = βˆ’ 9 ⃑ 𝑖 βˆ’ 4 ⃑ 𝑗 2 , determine the magnitude of the moment of the couple.

Q23:

Given that ⃑ 𝐹 1 and ⃑ 𝐹 2 are two forces which form a couple, where ⃑ 𝐹 = βˆ’ 8 ⃑ 𝑖 βˆ’ ⃑ 𝑗 1 , determine ⃑ 𝐹 2 .

  • A βˆ’ ⃑ 𝑖 βˆ’ 8 ⃑ 𝑗
  • B βˆ’ 8 ⃑ 𝑖 βˆ’ ⃑ 𝑗
  • C ⃑ 𝑖 + 8 ⃑ 𝑗
  • D 8 ⃑ 𝑖 + ⃑ 𝑗

Q24:

𝐴 𝐡 𝐢 is a right-angled triangle at 𝐴 , where 𝐴 𝐡 = 1 2 c m and 𝐴 𝐢 = 1 6 c m . The two forces ⃑ 𝐹 1 and ⃑ 𝐹 2 , measured in newtons, are acting on the sides of the triangle as shown in the figure below. If the system of forces is equivalent to a couple, determine the magnitudes of ⃑ 𝐹 1 and ⃑ 𝐹 2 .

  • A ⃑ 𝐹 = 3 9 1 N , ⃑ 𝐹 = 3 9 2 N
  • B ⃑ 𝐹 = 6 5 1 N , ⃑ 𝐹 = 5 2 2 N
  • C ⃑ 𝐹 = 1 6 1 N , ⃑ 𝐹 = 2 0 2 N
  • D ⃑ 𝐹 = 5 2 1 N , ⃑ 𝐹 = 6 5 2 N

Q25:

The two forces ⃑ 𝐹 = βˆ’ 6 ⃑ 𝑖 βˆ’ 3 ⃑ 𝑗 1 and ⃑ 𝐹 2 are acting at the points 𝐴 ( βˆ’ 3 , 0 ) and 𝐡 ( βˆ’ 7 , βˆ’ 9 ) respectively. Given that they are forming a couple, determine the vector of the couple moment.

  • A 3 ⃑ π‘˜
  • B βˆ’ 6 6 ⃑ π‘˜
  • C βˆ’ 5 1 ⃑ π‘˜
  • D 4 2 ⃑ π‘˜

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