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Worksheet: Moment of Vector Forces in 2D

Q1:

is a trapezoid in which sides and are parallel, , , and . Forces of magnitude , 2, , 8, and newtons are acting along , , , , and , respectively. If the resultant of the moments of the forces about is zero, and the resultant of the moments of the forces about equals that about , calculate the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

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 9, 12, 3, 1, 11, and 16 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:

is a trapezoid with a right-angle at , where , and . If is drawn perpendicular to the plane of the trapezoid, and a force of magnitude 117 N is acting along , find the moment of the force about .

  • A 526.5 Nā‹…cm
  • B 13 Nā‹…cm
  • C 26 Nā‹…cm
  • D
    1ā€‰053
    Nā‹…cm

Q6:

In the figure, , and . When force acts on wire , the magnitude of the moment about is 1ā€‰959 Nā‹…m. Find the magnitude of force 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 meter, the magnitude of the moment of the force about point š‘‚ , given that the force has a magnitude of 1 7 3 N.

  • A 1 7 6 ā‹… N m
  • B 8 8 6 ā‹… N m
  • C 1 7 8 ā‹… N m
  • D 3 6 7 ā‹… N m

Q9:

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

Q10:

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

Q11:

is a force in the plane of parallelogram . The sum of the moments about , units of moment. The sums of the moments about and are units of moment. Determine the sum of the moments about , .

Q12:

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

  • A
  • B
  • C