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Worksheet: Moments in 3D

Q1:

The moment of the force about the origin is , where and . Given that the force passes through a point whose -coordinate is 4, find the and coordinates of the point.

  • A ,
  • B ,
  • C ,
  • D ,

Q2:

The moment of the force about the origin is , where and . Given that the force passes through a point whose -coordinate is 13, find the and coordinates of the point.

  • A ,
  • B ,
  • C ,
  • D ,

Q3:

If the force is acting at a point whose position vector, with respect to the origin point, is , and the components of the moment of the force about the -axis and the -axis are 73 and 242 units of moment, respectively, find the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q4:

If a force F i j k = 4 + βˆ’ is acting at a point 𝐴 ( 1 2 , βˆ’ 1 2 , βˆ’ 4 ) , find the magnitude of the component of the moment of F about the 𝑦 -axis.

  • A60 units of moment
  • B16 units of moment
  • C72 units of moment
  • D4 units of moment

Q5:

If a force F i j k = 6 βˆ’ 7 βˆ’ 8 is acting at a point 𝐴 ( 5 , βˆ’ 8 , 1 1 ) , find the magnitude of the component of the moment of F about the 𝑦 -axis.

  • A13 units of moment
  • B141 units of moment
  • C260 units of moment
  • D106 units of moment

Q6:

The forces , , and are acting at a point. If the moment vector of the resultant of these forces about the origin point is , find the intersection point of the line of action of the resultant with the -axis.

  • A
  • B
  • C
  • D

Q7:

If the force is acting at the point and the two components of the moment of about the -axis and the -axis are and 98 respectively, find the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q8:

and , where and are two forces acting at the points and respectively. The sum of moments about the point of origin equals zero. The sum of the moments about the point also equals zero. Determine the values of and .

  • A ,
  • B ,
  • C ,
  • D ,

Q9:

In the figure, 𝐴 𝐡 is a rod fixed to a vertical wall at end 𝐴 . The other end 𝐡 is connected to a wire 𝐡 𝐢 , where 𝐢 is fixed to a different point on the same vertical wall. If the tension in the wire equals 39 N, calculate the moment of the tension about point 𝐴 in newton-meters.

  • A 2 1 6 + 7 2 i k
  • B 5 4 + 2 4 i k
  • C 1 3 + 1 2 i k
  • D 3 2 4 + 4 3 2 i k

Q10:

In the figure shown, a force of magnitude newtons acts at a point , determine the moment vector of the force about the origin in N.m.

  • A
  • B
  • C
  • D

Q11:

Given that a force of magnitude 6 N is acting on 𝐢 as in the figure, determine its moment vector about 𝐴 in newton-centimeters.

  • A 4 8 √ 3 + 7 2 βˆ’ 4 8 i j k
  • B 7 2 βˆ’ 4 8 √ 3 + 4 8 i j k
  • C βˆ’ 4 8 √ 3 βˆ’ 7 2 + 4 8 i j k
  • D βˆ’ 4 8 √ 3 + 7 2 βˆ’ 4 8 i j k

Q12:

In the figure, a force of magnitude 42 newtons is acting along diagonal in a rectangular prism whose dimensions are 18 cm, 18 cm, and 9 cm. Determine the vector moment of the force about in newton-centimeters.

  • A
  • B
  • C
  • D

Q13:

A force having a magnitude of F 1 = 3 1 √ 1 3 n e w t o n s is acting on point 𝐡 in the direction of  𝐴 𝐡 and another force having a magnitude of F 2 = 3 8 √ 6 1 n e w - is acting on point 𝐢 in the direction of  𝐴 𝐢 as shown in the figure. If i , j , and k are a right system of the unit vectors in the direction of π‘₯ , 𝑦 , and 𝑧 , respectively, determine the vector sum of the moments of the forces about point 𝑂 in newton-centimetres.

  • A βˆ’ 5 5 8 + 1 3 6 8 i j Nβ‹…cm
  • B 4 6 8 + 1 0 2 6 + 1 3 6 8 i j k Nβ‹…cm
  • C 1 0 2 6 βˆ’ 5 5 8 + 1 3 6 8 i j k Nβ‹…cm
  • D 4 6 8 + 1 3 6 8 i j Nβ‹…cm

Q14:

If the force is acting at a point whose position vector, with respect to the origin point, is , and the component of the moment of the force about the -axis is moment units, find the length of the perpendicular segment drawn from the origin point to the line of action of .

  • A20 length units
  • B length units
  • C56 length units
  • D length units

Q15:

The forces F 1 = 5 √ 6 7 3 N and F 2 = 1 6 √ 5 6 9 N act along  𝐴 𝐡 and  𝐴 𝐢 , respectively, as shown in the figure. Given that i , j , and k are a right system of unit vectors in the directions of π‘₯ , 𝑦 , and 𝑧 , respectively, find the sum of the moments of the forces about point 𝑂 in newton-metres.

  • A 6 4 0 + 1 6 2 6 i j
  • B 2 7 7 3 + 2 6 4 0 i j
  • C 2 7 7 3 + 1 6 2 6 i j
  • D 6 4 0 + 2 6 4 0 i j