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Worksheet: The Moment of a Force about a Point in Space

Q1:

If a force is acting at the point , where the moment of about the origin is , find .

  • A
  • B
  • C
  • D

Q2:

If the force F i j k = βˆ’ 9 βˆ’ 4 βˆ’ is acting at the point 𝐴 ( βˆ’ 3 , 2 , 4 ) , find the moment 𝑀 𝐡 of the force F about the point 𝐡 ( 6 , 7 , 5 ) , then calculate the length of the perpendicular segment 𝐿 from 𝐡 to the line of action of the force.

  • A οƒ  𝑀 = βˆ’ 9 𝐡 i k , 𝐿 = 9 √ 4 3 7
  • B οƒ  𝑀 = 9 + 1 8 + 8 1 𝐡 i j k , 𝐿 = 9 √ 4 3 7
  • C οƒ  𝑀 = 9 + 1 8 + 8 1 𝐡 i j k , 𝐿 = √ 4 1 7
  • D οƒ  𝑀 = βˆ’ 9 𝐡 i k , 𝐿 = √ 4 1 7

Q3:

If the force , where , is acting on the point , and the moment of the force about the point is , determine the value of .

Q4:

If the force , where , is acting on the point , and the moment of the force about the point is , determine the value of .

Q5:

If acts at a point , and the moment of about the origin point is equal to , find the value of .

  • A
  • B31
  • C
  • D

Q6:

If the force , where , is acting on the point , and the moment of the force about the point is , determine the value of .

Q7:

If the force F i j k = βˆ’ βˆ’ 3 is acting at the point 𝐴 ( 8 , 5 , βˆ’ 1 ) , find the moment 𝑀 𝐡 of the force F about the point 𝐡 ( 1 , 4 , 8 ) , then calculate the length of the perpendicular segment 𝐿 from 𝐡 to the line of action of the force.

  • A οƒ  𝑀 = βˆ’ 1 2 + 1 2 βˆ’ 8 𝐡 i j k , 𝐿 = 1 8 √ 3 3 1 1
  • B οƒ  𝑀 = 6 βˆ’ 3 0 βˆ’ 6 𝐡 i j k , 𝐿 = 1 8 √ 3 3 1 1
  • C οƒ  𝑀 = 6 βˆ’ 3 0 βˆ’ 6 𝐡 i j k , 𝐿 = 4 √ 2
  • D οƒ  𝑀 = βˆ’ 1 2 + 1 2 βˆ’ 8 𝐡 i j k , 𝐿 = 4 √ 2

Q8:

In the figure, if the forces F i j k 1 = βˆ’ 7 βˆ’ + 3 and F i j k 2 = βˆ’ 7 + 8 βˆ’ 6 are acting on the point 𝐴 , where 𝐹 1 and 𝐹 2 are measured in newtons, determine the moment vector of the resultant about the point 𝑂 in newton-centimeters.

  • A 2 3 1 βˆ’ 8 5 βˆ’ 9 2 i j k
  • B βˆ’ 9 9 βˆ’ 1 0 2 + 2 2 4 i j k
  • C 2 2 4 βˆ’ 1 0 2 βˆ’ 9 9 i j k
  • D βˆ’ 9 2 βˆ’ 8 5 + 2 3 1 i j k

Q9:

In the figure, determine the sum of the moment vectors of the forces 86 and 65 newtons about 𝑂 in newton-centimeters.

  • A βˆ’ 3 5 1 + 3 1 2 βˆ’ 4 6 8 i j k
  • B βˆ’ 5 1 6 + 6 8 8 i k
  • C βˆ’ 8 6 7 + 6 2 4 + 2 2 0 i j k
  • D βˆ’ 8 6 7 + 3 1 2 + 2 2 0 i j k

Q10:

Find the moment M of the force F about the origin point, given that F i j k = βˆ’ 2 + + , and is acting at a point 𝐴 whose position vector is r i j k = 6 + 6 βˆ’ 3 with respect to the origin point, then determine the length 𝐿 of the perpendicular segment drawn from the origin point to the line of action of the force F .

  • A M i k = 9 + 1 8 , 𝐿 = 3 √ 1 4 2 length units
  • B M i j k = 3 + 1 2 βˆ’ 6 , 𝐿 = 3 √ 1 4 2 length units
  • C M i j k = 3 + 1 2 βˆ’ 6 , 𝐿 = 3 √ 3 0 2 length units
  • D M i k = 9 + 1 8 , 𝐿 = 3 √ 3 0 2 length units