Worksheet: Moment of a Couple

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

Q1:

The two forces āƒ‘ š¹ = āˆ’ 3 āƒ‘ š‘– āˆ’ 4 āƒ‘ š‘— 1 and āƒ‘ š¹ 2 are acting at the points š“ ( 6 , āˆ’ 2 ) and šµ ( 8 , āˆ’ 3 ) respectively. Given that they are forming a couple, determine the vector of the couple moment.

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

Q2:

Given that two forces āƒ‘ š¹ = āˆ’ āƒ‘ š‘– + 2 āƒ‘ š‘— 1 and āƒ‘ š¹ 2 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.

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

Q3:

š“ šµ š¶ š· is square having a side length of 3 cm. š» and š‘‚ belong to šµ š· , where š‘š āˆ  š¶ š» š· = š‘š āˆ  š“ š‘‚ šµ = 6 0 āˆ˜ . Given that two equal forces, each of magnitude 5 N, are acting along ļƒ« š‘‚ š“ and ļƒ« š» š¶ respectively, find the magnitude of the moment of the couple.

  • A 1 5 āˆš 3 2 Nā‹…cm
  • B 1 5 āˆš 2 Nā‹…cm
  • C 1 5 āˆš 3 Nā‹…cm
  • D 1 5 āˆš 2 2 Nā‹…cm

Q4:

š“ šµ š¶ 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.

  • A 3 3 6 āˆš 2 Nā‹…cm
  • B 168 Nā‹…cm
  • C 336 Nā‹…cm
  • D 1 6 8 āˆš 2 Nā‹…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:

š“ šµ š¶ š· is a rectangle, in which š“ šµ = 5 c m and š“ š· = 1 0 c m . Two forces of the same magnitude 3 3 āˆš 5 N are acting at š“ and š¶ in the directions of ļƒ« šµ š· and ļƒ« š· šµ respectively. Determine the magnitude of the moment of the couple.

Q7:

š“ šµ š¶ š· is a parallelogram, where š“ šµ = 1 0 c m , šµ š¶ = 8 c m , and the perpendicular distance between š“ šµ and š· š¶ is 6 cm. Given that two forces of the same magnitude 50 N are acting along ļƒ« š“ š· and ļƒŖ š¶ šµ , respectively, determine the magnitude of the moment of the couple.

Q8:

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

  • A 65 Nā‹…cm
  • B 1 3 0 āˆš 3 Nā‹…cm
  • C 130 Nā‹…cm
  • D 6 5 āˆš 3 Nā‹…cm

Q9:

In the figure below, š¹ = 3 1 N and š¹ 1 and š¹ 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 š‘„ = 4 2 c m and š‘¦ = 8 4 c m . Find the moment of the couple if t a n š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:

š“ šµ š¶ š· is a parallelogram, where šµ š¶ = 1 0 c m and š‘š āˆ  š“ šµ š¶ = 1 5 0 āˆ˜ . If two forces of the same magnitude 50 N are acting at ļƒ« š“ šµ and ļƒ« š¶ š· respectively, determine the magnitude of the moment of the couple, rounding your answer to two decimal places.

Q13:

š“ šµ š¶ š· is a rhombus in which its diagonal š“ š¶ = 7 c m and š‘š āˆ  š“ = 6 0 āˆ˜ . Given that two equal forces, each of magnitude 45 N, are acting along ļƒ« š“ š· and ļƒŖ š¶ šµ respectively, find the magnitude of the moment of the couple rounded to two decimal places if necessary.

Q14:

š“ šµ š¶ š· is square having a side length of 24 cm, šø āˆˆ šµ š¶ , and š‘‚ āˆˆ š· š“ , where šµ šø = š· š‘‚ = 6 c m . Given that two forces, each of magnitude, 34.2 N are acting along ļƒ« šµ š‘‚ and ļƒ« š· šø respectively, find the magnitude of the moment of the couple.

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

Q15:

š“ šµ š¶ š· š» š‘‚ is a regular hexagon, having a side length of 5 cm, where a force of magnitude 15 N is acting along ļƒ« š¶ š» , and another force of the same magnitude is acting at š“ in the direction of ļƒ« š» š¶ . Determine the magnitude of the moment of the couple.

Q16:

š“ šµ š¶ š· is a rhombus, where its diagonals š“ š¶ and šµ š· are 13 cm and 7 cm respectively, and two forces of the same magnitude 23 N are acting along ļƒ« š“ šµ and ļƒ« š¶ š· . Determine the magnitude of the moment of the couple, rounding your answer to two decimal places if necessary.

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

Q17:

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.

Q18:

š“ šµ and š¶ š· are two parallel chords in a circle whose radius is 25 cm, and they are at different distances away from the circleā€™s centre, where š“ šµ = 3 0 c m , and š¶ š· = 1 4 c m . Given that two forces of the same magnitude 20 N are acting along ļƒ« šµ š“ and ļƒ« š¶ š· , respectively, determine the magnitude of the moment of the couple.

Q19:

š“ šµ š¶ š· is an isosceles trapezium, where š“ š· = šµ š¶ = 1 3 c m , š“ šµ = 1 2 c m , and š¶ š· = 6 c m . Two forces, each of magnitude 50 N, are acting along ļƒ« š“ šµ and ļƒ« š¶ š· . Find the magnitude of the moment of the couple rounded to two decimal places, giving your answer in Nā‹…cm.

Q20:

A light rod š“ šµ , which has a length of 22 cm and a mid-point š‘‚ , is under the action of two forces measured in newtons as shown in the figure. Given that a moment of magnitude 22 Nā‹…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 āƒ‘ š¹ = āˆ’ 4 āƒ‘ š‘– + š‘Ž āƒ‘ š‘— 1 and āƒ‘ š¹ = š‘ āƒ‘ š‘– + 8 āƒ‘ š‘— 2 form a couple, then find the value of š‘Ž āˆ’ 8 š‘ .

Q22:

Given that the forces āƒ‘ š¹ 1 , āƒ‘ š¹ 2 , and āƒ‘ š¹ 3 are acting at the points ( āˆ’ 1 , āˆ’ 6 ) , ( 3 , 8 ) , and ( 8 , āˆ’ 8 ) respectively, where the system of forces is equivalent to a couple, āƒ‘ š¹ = 3 āƒ‘ š‘– āˆ’ 6 āƒ‘ š‘— 1 , and āƒ‘ š¹ = āˆ’ 9 āƒ‘ š‘– āˆ’ 4 āƒ‘ š‘— 2 , determine the magnitude of the moment of the couple.

Q23:

Given that āƒ‘ š¹ 1 and āƒ‘ š¹ 2 are two forces which form a couple, where āƒ‘ š¹ = āˆ’ 8 āƒ‘ š‘– āˆ’ āƒ‘ š‘— 1 , determine āƒ‘ š¹ 2 .

  • A āˆ’ āƒ‘ š‘– āˆ’ 8 āƒ‘ š‘—
  • B āˆ’ 8 āƒ‘ š‘– āˆ’ āƒ‘ š‘—
  • C āƒ‘ š‘– + 8 āƒ‘ š‘—
  • D 8 āƒ‘ š‘– + āƒ‘ š‘—

Q24:

š“ šµ š¶ is a right-angled triangle at š“ , where š“ šµ = 1 2 c m and š“ š¶ = 1 6 c m . The two forces āƒ‘ š¹ 1 and āƒ‘ š¹ 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 āƒ‘ š¹ 1 and āƒ‘ š¹ 2 .

  • A āƒ‘ š¹ = 3 9 1 N , āƒ‘ š¹ = 3 9 2 N
  • B āƒ‘ š¹ = 6 5 1 N , āƒ‘ š¹ = 5 2 2 N
  • C āƒ‘ š¹ = 1 6 1 N , āƒ‘ š¹ = 2 0 2 N
  • D āƒ‘ š¹ = 5 2 1 N , āƒ‘ š¹ = 6 5 2 N

Q25:

The two forces āƒ‘ š¹ = āˆ’ 6 āƒ‘ š‘– āˆ’ 3 āƒ‘ š‘— 1 and āƒ‘ š¹ 2 are acting at the points š“ ( āˆ’ 3 , 0 ) and šµ ( āˆ’ 7 , āˆ’ 9 ) respectively. Given that they are forming a couple, determine the vector of the couple moment.

  • A 3 āƒ‘ š‘˜
  • B āˆ’ 6 6 āƒ‘ š‘˜
  • C āˆ’ 5 1 āƒ‘ š‘˜
  • D 4 2 āƒ‘ š‘˜

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