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Lesson: Moment of Vector Forces in 2D

Worksheet • 12 Questions

Q1:

𝐴 𝐡 𝐢 𝐷 is a trapezium in which sides 𝐴 𝐷 and 𝐡 𝐢 are parallel, π‘š ∠ 𝐴 = 9 0 ∘ , 𝐴 𝐡 = 𝐴 𝐷 = 1 8 c m , and 𝐡 𝐢 = 3 6 c m . Forces of magnitude 𝐾 , 2, 𝐹 , 8, and 1 4 √ 2 newtons are acting along  𝐡 𝐴 , οƒͺ 𝐢 𝐡 ,  𝐷 𝐢 ,  𝐷 𝐴 , and  𝐡 𝐷 , respectively. If the resultant of the moments of the forces about 𝐴 is zero, and the resultant of the moments of the forces about 𝐡 equals that about 𝐷 , calculate the values of 𝐹 and 𝐾 .

  • A 𝐹 = 1 2 √ 2 N , 𝐾 = 1 4 N
  • B 𝐹 = 1 2 √ 2 N , 𝐾 = 2 N
  • C 𝐹 = 2 4 N , 𝐾 = 3 8 N
  • D 𝐹 = 2 4 N , 𝐾 = 1 4 N

Q2:

𝐴 𝐡 𝐢 is an isosceles triangle in which π‘š ∠ 𝐡 = 1 2 0 ∘ and 𝐴 𝐢 = 8 √ 3 c m . Forces of magnitudes 4, 8, and 1 8 √ 3 newtons are acting along  𝐴 𝐢 , οƒͺ 𝐢 𝐡 , and  𝐴 𝐡 respectively. Find the magnitude of sum of the forces moments about the midpoint of 𝐡 𝐢 .

Q3:

𝐴 𝐡 𝐢 𝐷 𝐸 𝐹 is a regular hexagon, where forces of magnitudes 9, 12, 3, 1, 11, and 16 newtons are acting along  𝐴 𝐡 , οƒͺ 𝐡 𝐢 ,  𝐢 𝐷 ,  𝐷 𝐸 , οƒͺ 𝐸 𝐹 , and  𝐹 𝐴 respectively. Determine the magnitude of the additional force that would need to act along  𝐹 𝐴 so that the algebraic sum of moments about 𝐸 becomes zero.

Q4:

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

  • A 𝑀 = βˆ’ 2 , 1 9 3  Nβ‹…cm, 𝐹 = βˆ’ 2 5 8 N
  • B 𝑀 = βˆ’ 2 , 1 9 3  Nβ‹…cm, 𝐹 = βˆ’ 1 2 9 N
  • C 𝑀 = βˆ’ 1 0 , 5 5 7  Nβ‹…cm, 𝐹 = βˆ’ 6 2 1 N
  • D 𝑀 = βˆ’ 1 0 , 5 5 7  Nβ‹…cm, 𝐹 = βˆ’ 1 , 2 4 2 N

Q5:

𝐴 𝐡 𝐢 𝐷 is a trapezium with a right-angle at 𝐡 , where 𝐴 𝐷 βˆ₯ 𝐡 𝐢 , and 𝐴 𝐡 = 9 c m . If 𝐷 𝐸 is drawn perpendicular to the plane of the trapezium, and a force of magnitude 117 N is acting along  𝐴 𝐸 , find the moment of the force about 𝐡 .

Q6:

In the figure, 𝐴 𝐡 = 5 m , and 𝐴 𝐢 = 5 m . When force ⃑ 𝐹 acts on wire 𝐡 𝐢 , the magnitude of the moment about 𝐴 is 1 959 Nβ‹…m. Find the magnitude of force ⃑ 𝐹 rounded to two decimal places.

Q7:

𝐴 𝐡 𝐢 is a triangle with a right-angle at 𝐡 , where 𝐴 𝐡 = 1 8 c m and 𝐡 𝐢 = 2 4 c m . A force 𝐹 is acting in the plane of the triangle, where 𝑀 = 𝑀 = 1 8 0 β‹… 𝐴 𝐡 N c m and 𝑀 = βˆ’ 1 8 0 β‹… 𝐢 N c m . Determine the magnitude and the line of action of 𝐹 .

  • A 𝐹 = 1 5 N , parallel to 𝐴 𝐡 and passes through the midpoint of 𝐡 𝐢
  • B 𝐹 = 2 0 N , parallel to 𝐴 𝐡 and passes through the midpoint of 𝐡 𝐢
  • C 𝐹 = 1 5 N , parallel to 𝐡 𝐢 and passes through the midpoint of 𝐴 𝐡
  • D 𝐹 = 1 2 N , parallel to 𝐡 𝐢 and passes through the midpoint of 𝐴 𝐡
  • E 𝐹 = 1 2 N , parallel to 𝐴 𝐡 and passes through the midpoint of 𝐡 𝐢

Q8:

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

Q9:

Given that two parallel forces, each having a magnitude of 26 N, are acting on a lever 𝐴 𝐡 as shown in the figure, where 𝐴 𝐢 = 9 c m , 𝐢 𝐡 = 6 c m , and πœƒ = 4 5 ∘ , find the algebraic measure of the sum of the moments of the two forces about point 𝐴 .

  • A βˆ’ 7 8 Nβ‹…cm
  • B βˆ’ 7 8 √ 3 Nβ‹…cm
  • C 7 8 √ 3 Nβ‹…cm
  • D 78 Nβ‹…cm

Q10:

𝐴 𝐡 𝐢 𝐷 is a rectangle, where 𝐴 𝐡 = 3 6 c m and 𝐡 𝐢 = 4 8 c m . A force 𝐹 is acting in the plane of the rectangle, where its moment about 𝐡 equals its moment about 𝐷 , which equals βˆ’ 1 0 8 Nβ‹…cm, and its moment about 𝐴 is 108 Nβ‹…cm. Determine the magnitude and the direction of 𝐹 .

  • A 𝐹 = 7 . 5 N , parallel to 𝐡 𝐷 , passes through the midpoint of 𝐴 𝐡
  • B 𝐹 = 7 . 5 N , parallel to 𝐴 𝐡 , passes through the midpoint of 𝐡 𝐷
  • C 𝐹 = 3 N , parallel to 𝐴 𝐡 , passes through the midpoint of 𝐡 𝐷
  • D 𝐹 = 3 N , parallel to 𝐡 𝐷 , passes through the midpoint of 𝐴 𝐡

Q11:

⃑ 𝐹 is a force in the plane of parallelogram 𝐴 𝐡 𝐢 𝐷 . The sum of the moments about 𝐴 , 𝑀 = βˆ’ 9 5 𝐴 units of moment. The sums of the moments about 𝐡 and 𝐷 are 𝑀 = 𝑀 = 8 9 𝐡 𝐷 units of moment. Determine the sum of the moments about 𝐢 , 𝑀 𝐢 .

Q12:

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
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