Worksheet: Moment of Vector Forces in 2D

In this worksheet, we will practice finding the moment of a force or a system of forces about a point.

Q1:

š“ šµ š¶ š· is a trapezium in which sides š“ š· and šµ š¶ are parallel, š‘š āˆ  š“ = 9 0 āˆ˜ , š“ šµ = š“ š· = 1 8 c m , and šµ š¶ = 3 6 c m . Forces of magnitude š¾ , 2, š¹ , 8, and 1 4 āˆš 2 newtons are acting along ļƒ« šµ š“ , ļƒŖ š¶ šµ , ļƒ« š· š¶ , ļƒ« š· š“ , and ļƒ« šµ š· , respectively. If the resultant of the moments of the forces about š“ is zero, and the resultant of the moments of the forces about šµ equals that about š· , calculate the values of š¹ and š¾ .

  • A š¹ = 2 4 N , š¾ = 1 4 N
  • B š¹ = 1 2 āˆš 2 N , š¾ = 2 N
  • C š¹ = 2 4 N , š¾ = 3 8 N
  • D š¹ = 1 2 āˆš 2 N , š¾ = 1 4 N

Q2:

š“ šµ š¶ is an isosceles triangle in which š‘š āˆ  šµ = 1 2 0 āˆ˜ and š“ š¶ = 8 āˆš 3 c m . Forces of magnitudes 4, 8, and 1 8 āˆš 3 newtons are acting along ļƒ« š“ š¶ , ļƒŖ š¶ šµ , and ļƒ« š“ šµ respectively. Find the magnitude of sum of the forces moments about the midpoint of šµ š¶ .

Q3:

š“ šµ š¶ š· šø š¹ is a regular hexagon, where forces of magnitudes 14, 8, 18, 3, 5, and 6 newtons are acting along ļƒ« š“ šµ , ļƒŖ šµ š¶ , ļƒ« š¶ š· , ļƒ« š· šø , ļƒŖ šø š¹ , and ļƒ« š¹ š“ respectively. Determine the magnitude of the additional force that would need to act along ļƒ« š¹ š“ so that the algebraic sum of moments about šø becomes zero.

Q4:

Five known forces, measured in newtons, are acting on the square š“ šµ š¶ š· , with side length 17 cm. A sixth force š¹ will be applied at the midpoint of š¶ š· , and perpendicular to it, as shown in the figure. Firstly, determine the algebraic sum of the moments of the forces (excluding š¹ ) about š¶ . Secondly, determine the value of š¹ that would make the algebraic sum of the moments about š¶ equal to zero.

  • A š‘€ = āˆ’ 1 0 , 5 5 7 ļŒ¢ Nā‹…cm, š¹ = āˆ’ 1 , 2 4 2 N
  • B š‘€ = āˆ’ 2 , 1 9 3 ļŒ¢ Nā‹…cm, š¹ = āˆ’ 1 2 9 N
  • C š‘€ = āˆ’ 1 0 , 5 5 7 ļŒ¢ Nā‹…cm, š¹ = āˆ’ 6 2 1 N
  • D š‘€ = āˆ’ 2 , 1 9 3 ļŒ¢ Nā‹…cm, š¹ = āˆ’ 2 5 8 N

Q5:

š“ šµ š¶ š· is a trapezium with a right-angle at šµ , where š“ š· āˆ„ šµ š¶ , and š“ šµ = 9 c m . If š· šø is drawn perpendicular to the plane of the trapezium, and a force of magnitude 117 N is acting along ļƒ« š“ šø , find the moment of the force about šµ .

Q6:

In the figure, š“ šµ = 5 m , and š“ š¶ = 5 m . When force āƒ‘ š¹ acts on wire šµ š¶ , the magnitude of the moment about š“ is 1ā€‰959 Nā‹…m. Find the magnitude of force āƒ‘ š¹ rounded to two decimal places.

Q7:

š“ šµ š¶ is a triangle with a right-angle at šµ , where š“ šµ = 1 8 c m and šµ š¶ = 2 4 c m . A force š¹ is acting in the plane of the triangle, where š‘€ = š‘€ = 1 8 0 ā‹… š“ šµ N c m and š‘€ = āˆ’ 1 8 0 ā‹… š¶ N c m . Determine the magnitude and the line of action of š¹ .

  • A š¹ = 1 2 N , parallel to š“ šµ and passes through the midpoint of šµ š¶
  • B š¹ = 1 5 N , parallel to šµ š¶ and passes through the midpoint of š“ šµ
  • C š¹ = 1 2 N , parallel to šµ š¶ and passes through the midpoint of š“ šµ
  • D š¹ = 1 5 N , parallel to š“ šµ and passes through the midpoint of šµ š¶
  • E š¹ = 2 0 N , parallel to š“ šµ and passes through the midpoint of šµ š¶

Q8:

Determine, to the nearest newton metre, the magnitude of the moment of the force about point š‘‚ , given that the force has a magnitude of 173 N.

Q9:

š“ šµ š¶ š· is a rectangle, where š“ šµ = 3 6 c m and šµ š¶ = 4 8 c m . A force š¹ is acting in the plane of the rectangle, where its moment about šµ equals its moment about š· , which equals āˆ’ 1 0 8 Nā‹…cm, and its moment about š“ is 108 Nā‹…cm. Determine the magnitude and the direction of š¹ .

  • A š¹ = 3 N , parallel to šµ š· , passes through the midpoint of š“ šµ
  • B š¹ = 7 . 5 N , parallel to š“ šµ , passes through the midpoint of šµ š·
  • C š¹ = 3 N , parallel to š“ šµ , passes through the midpoint of šµ š·
  • D š¹ = 7 . 5 N , parallel to šµ š· , passes through the midpoint of š“ šµ

Q10:

āƒ‘ š¹ is a force in the plane of parallelogram š“ šµ š¶ š· . The sum of the moments about š“ , š‘€ = āˆ’ 9 5 š“ units of moment. The sums of the moments about šµ and š· are š‘€ = š‘€ = 8 9 šµ š· units of moment. Determine the sum of the moments about š¶ , š‘€ š¶ .

Q11:

Find the measure of angle , rounded to the nearest minute, so that the moment of the force about has its minimum value.

  • A
  • B
  • C
  • D

Q12:

Given that two parallel forces, each having a magnitude of 26 N, are acting on a lever š“ šµ as shown in the figure, where š“ š¶ = 9 c m , š¶ šµ = 6 c m , and šœƒ = 4 5 āˆ˜ , find the algebraic measure of the sum of the moments of the two forces about point š“ .

  • A 78 Nā‹…cm
  • B āˆ’ 7 8 āˆš 3 Nā‹…cm
  • C 7 8 āˆš 3 Nā‹…cm
  • D āˆ’ 7 8 Nā‹…cm

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