Worksheet: Moment of a Couple

In this worksheet, we will practice calculating the moment of a couple of two forces and the resultant of two or more couples.

Q1:

The two forces Fij=βˆ’3βˆ’4 and F 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 2 k
  • B 1 1 k
  • C 5 k
  • D 1 0 k

Q2:

Given that two forces Fij=βˆ’+2 and F 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 8 √ 5 5 length unit
  • B 1 4 √ 5 5 length unit
  • C 4 √ 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 𝐡𝐷, where π‘šβˆ πΆπ»π·=π‘šβˆ π΄π‘‚π΅=60∘. Given that two equal forces, each of magnitude 5 N, are acting along 𝑂𝐴 and 𝐻𝐢 respectively, find the magnitude of the moment of the couple.

  • A 1 5 √ 3 2 Nβ‹…cm
  • B 1 5 √ 3 Nβ‹…cm
  • C 1 5 √ 2 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 𝐴𝐢 and 𝐢𝐴 respectively. Determine the magnitude of the moment of the couple.

  • A 1 6 8 √ 2 Nβ‹…cm
  • B336 Nβ‹…cm
  • C 3 3 6 √ 2 Nβ‹…cm
  • D168 Nβ‹…cm

Q5:

What is a couple?

  • Aa pair of parallel forces with equal magnitude and the same line of action
  • Ba pair of forces with equal magnitude
  • Ca pair of parallel forces with equal magnitude and opposite direction which do not lie on the same line of action.
  • Da pair of forces with the same magnitude and direction.

Q6:

𝐴 𝐡 𝐢 𝐷 is a rectangle, in which 𝐴𝐡=5cm and 𝐴𝐷=10cm. Two forces of the same magnitude 33√5 N are acting at 𝐴 and 𝐢 in the directions of 𝐡𝐷 and 𝐷𝐡 respectively. Determine the magnitude of the moment of the couple.

Q7:

𝐴 𝐡 𝐢 𝐷 is a parallelogram, where 𝐴𝐡=10cm, 𝐡𝐢=8cm, and the perpendicular distance between 𝐴𝐡 and 𝐷𝐢 is 6 cm. Given that two forces of the same magnitude 50 N are acting along 𝐴𝐷 and οƒͺ𝐢𝐡, 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 οƒͺ𝐢𝐡 and 𝑂𝐻, respectively. Determine the magnitude of the moment of the couple.

  • A130 Nβ‹…cm
  • B 1 3 0 √ 3 Nβ‹…cm
  • C 6 5 √ 3 Nβ‹…cm
  • D65 Nβ‹…cm

Q9:

In the figure below, 𝐹=3N and 𝐹 and 𝐹 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‘₯=42cm and 𝑦=84cm. Find the moment of the couple if tanπœƒ=34.

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?

  • Athe magnitude of the couple
  • Bthe moment of the couple
  • Cthe moment of one force of the two forces of the couple
  • Dthe resultant of the couple

Q12:

𝐴 𝐡 𝐢 𝐷 is a parallelogram, where 𝐡𝐢=10cm and π‘šβˆ π΄π΅πΆ=150∘. If two forces of the same magnitude 50 N are acting at 𝐴𝐡 and 𝐢𝐷 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 𝐴𝐢=7cm and π‘šβˆ π΄=60∘. Given that two equal forces, each of magnitude 45 N, are acting along 𝐴𝐷 and οƒͺ𝐢𝐡 respectively, find the magnitude of the moment of the couple rounded to two decimal places if necessary.

Q14:

𝐴 𝐡 𝐢 𝐷 is a square having a side length of 24 cm, 𝐸∈𝐡𝐢, and π‘‚βˆˆπ·π΄, where 𝐡𝐸=𝐷𝑂=6cm. Given that two forces, each of magnitude 34.2 N are acting along 𝐡𝑂 and 𝐷𝐸, respectively, find the magnitude of the moment of the couple.

  • A369.36 Nβ‹…cm
  • B164.16 Nβ‹…cm
  • C492.48 Nβ‹…cm
  • D123.12 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 𝐢𝐻, and another force of the same magnitude is acting at 𝐴 in the direction of 𝐻𝐢. Determine the magnitude of the moment of the couple.

Q16:

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

  • A283.51 Nβ‹…cm
  • B141.76 Nβ‹…cm
  • C299 Nβ‹…cm
  • D86.29 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 𝐢𝐷 are two parallel chords in a circle whose radius is 25 cm, and they are at different distances away from the circle’s center, where 𝐴𝐡=30cm, and 𝐢𝐷=14cm. Given that two forces of the same magnitude 20 N are acting along 𝐡𝐴 and 𝐢𝐷, respectively, determine the magnitude of the moment of the couple.

Q19:

𝐴 𝐡 𝐢 𝐷 is an isosceles trapezium, where 𝐴𝐷=𝐡𝐢=13cm, 𝐴𝐡=12cm, and 𝐢𝐷=6cm. Two forces, each of magnitude 50 N, are acting along 𝐴𝐡 and 𝐢𝐷. Find the magnitude of the moment of the couple rounded to two decimal places, giving your answer in Nβ‹…cm.

Q20:

A light rod 𝐴𝐡, 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, determine the moment of the resultant couple acting on the rod.

Q21:

If the two forces Fij=βˆ’4+π‘Ž and Fij=𝑏+8 form a couple, then find the value of π‘Žβˆ’8𝑏.

Q22:

Given that the forces F, F, and F 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, Fij=3βˆ’6, and Fij=βˆ’9βˆ’4, determine the magnitude of the moment of the couple.

Q23:

Given that F and F are two forces which form a couple, where Fij=βˆ’8βˆ’, determine F.

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

Q24:

𝐴 𝐡 𝐢 is a right-angled triangle at 𝐴, where 𝐴𝐡=12cm and 𝐴𝐢=16cm. The two forces F and F, 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 and F.

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

Q25:

The two forces Fij=βˆ’6βˆ’3 and F 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 βˆ’ 5 1 k
  • B 4 2 k
  • C βˆ’ 6 6 k
  • D 3 k

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