Lesson Worksheet: Moment of a Couple Mathematics

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

Q1:

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.

Q2:

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

Q3:

In the figure below, š¹=3ļŠ§N and š¹ļŠ§ and š¹ļŠØ form a couple. Find the algebraic measure of the moment of that couple.

Q4:

š“šµ is a horizontal light rod having a length of 60 cm, where two forces, each of magnitude 45 N, are acting vertically at š“ and šµ in two opposite directions. Two other forces, each of magnitude 120 N, are acting in two opposite directions at points š¶ and š· of the rod, where š¶š·=45cm. 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.

Q5:

Given that FļŠ§ and FļŠØ are two forces which form a couple, where FijļŠ§=āˆ’8āˆ’, determine FļŠØ.

  • Aāˆ’āˆ’8ij
  • B8+ij
  • Cij+8
  • Dāˆ’8āˆ’ij

Q6:

Given that two forces FijļŠ§=āˆ’+2 and FļŠØ are acting at two points š“(2,2) and šµ(āˆ’2,āˆ’2) respectively to form a couple, find the perpendicular distance between the two forces.

  • A18āˆš55 length unit
  • B14āˆš55 length unit
  • C4āˆš55 length unit
  • D12āˆš55 length unit

Q7:

Given that the forces in the figure have magnitudes of 56, 105, and 242 newtons, find the algebraic measure of the resultant couple.

Q8:

š“šµš¶š· is a square of side length 8 cm, where two forces of magnitudes 21 N are acting at šµ and š· respectively, and their lines of action are in the direction of ļƒ«š“š¶ and ļƒ«š¶š“ respectively. Determine the magnitude of the moment of the couple.

  • A168āˆš2 Nā‹…cm
  • B336 Nā‹…cm
  • C336āˆš2 Nā‹…cm
  • D168 Nā‹…cm

Q9:

š“šµš¶š· is a rhombus in which its diagonal š“š¶=7cm and š‘šāˆ š“=60āˆ˜. Given that two equal forces, each of magnitude 45 N, are acting along ļƒ«š“š· and ļƒŖš¶šµ respectively, find the magnitude of the moment of the couple rounded to two decimal places if necessary.

Q10:

š“šµš¶š·š»š‘‚ is a regular hexagon with sides of length 5 cm. Two forces of the same magnitude 13 N are acting along ļƒŖš¶šµ and ļƒ«š‘‚š», respectively. Determine the magnitude of the moment of the couple.

  • A130 Nā‹…cm
  • B130āˆš3 Nā‹…cm
  • C65āˆš3 Nā‹…cm
  • D65 Nā‹…cm

This lesson includes 29 additional questions and 259 additional question variations for subscribers.

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