Lesson Worksheet: Moment of a Force about a Point in 2D: Vectors Mathematics

In this worksheet, we will practice finding the moment of a planar system of forces acting on a body about a point as a vector.

Q1:

If the force Fij=βˆ’5+π‘š is acting at the point 𝐴(7,3), determine the moment of F about the point 𝐡(7,βˆ’2).

  • A25k
  • B70k
  • Cβˆ’25k
  • Dβˆ’70k

Q2:

Given that force Fij=4βˆ’3 acts through the point 𝐴(3,6), determine the moment M about the origin 𝑂 of the force F. Also, calculate the perpendicular distance 𝐿 between 𝑂 and the line of action of the force.

  • AMk=3, 𝐿=6.6 length units
  • BMk=βˆ’15, 𝐿=3 length units
  • CMk=βˆ’33, 𝐿=6.6 length units
  • DMk=15, 𝐿=3 length units

Q3:

End 𝐴 of 𝐴𝐡 is at (βˆ’6,7) and 𝐴𝐡 has midpoint 𝐷(βˆ’7,1). If the line of action of the force Fij=βˆ’2βˆ’6 bisects 𝐴𝐡, determine the moment of F about point 𝐡.

  • Aβˆ’6k
  • B38k
  • C6k
  • Dβˆ’38k

Q4:

Given that Fij=βˆ’2+2, Fij=βˆ’3βˆ’, and Fij=βˆ’4 are acting at the point 𝐴(2,3), determine the moment M of the resultant of the forces about the point 𝐡(βˆ’2,βˆ’1), and calculate the length of the perpendicular line 𝐿 joining the point 𝐡 to the resultant’s line of action.

  • AMk=4, 𝐿=0.8 length units
  • BMk=βˆ’4, 𝐿=0.8 length units
  • CMk=28, 𝐿=5.6 length units
  • DMk=βˆ’28, 𝐿=5.6 length units

Q5:

The force Fij=3βˆ’4 is acting on the point 𝐴(0,2). Given that 𝐡=(2,3) and 𝐢=(βˆ’2,1), determine the moment of this force about both points 𝐡 and 𝐢.

  • A𝑀=0k, 𝑀=βˆ’11k
  • B𝑀=11k, 𝑀=11k
  • C𝑀=11k, 𝑀=βˆ’11k
  • D𝑀=βˆ’11k, 𝑀=11k
  • E𝑀=βˆ’11k, 𝑀=βˆ’11k

Which of the following would you conclude about the line of action of the force F?

  • AThe line of action of F passes through the point 𝐢.
  • BThe line of action of F bisects 𝐡𝐢.
  • CThe line of action of F is parallel to ⃖⃗𝐡𝐢.
  • DNone of the answers are correct.

Q6:

Given that Fij=2βˆ’, Fij=5+2, and Fij=βˆ’3+2 are acting on the point 𝐴(1,1), determine the moment of the resultant of these forces about the two points 𝐡(2,1) and 𝐢(6,4).

  • AMk=0, Mk=3
  • BMk=βˆ’3, Mk=βˆ’3
  • CMk=0, Mk=0
  • DMk=3, Mk=βˆ’3
  • EMk=βˆ’3, Mk=3

Which of the following would we conclude about the line of action of the resultant force?

  • AThe line of action of the resultant force passes through both points 𝐡 and 𝐢.
  • BThe line of action of the resultant force is parallel to ⃖⃗𝐡𝐢.
  • CThe line of action of the resultant force passes through point 𝐡.
  • DThe line of action of the resultant force bisects 𝐡𝐢.
  • ENone of the answers are correct.

Q7:

The force Fij=3+π‘š is acting at the point 𝐴(βˆ’5,βˆ’4), in parallel to 𝐡𝐷, where the coordinates of the points 𝐡 and 𝐷 are (5,6) and (9,3) respectively. Determine the distance between the point 𝐡 and the line of action of F.

Q8:

Fij=π‘š+ and Fij=π‘›βˆ’5, where F and F are two forces acting at the points 𝐴(3,1) and 𝐡(βˆ’1,βˆ’1) respectively. The sum of moments about the point of origin equals zero. The sum of the moments about the point 𝐢(1,2) also equals zero. Determine the values of π‘š and 𝑛.

  • Aπ‘š=3, 𝑛=βˆ’5
  • Bπ‘š=0.5, 𝑛=βˆ’2.5
  • Cπ‘š=βˆ’2, 𝑛=10
  • Dπ‘š=0.5, 𝑛=7.5

Q9:

If the force Fij=βˆ’3+π‘š is acting on the point 𝐴(5,1), where its moment vector about the point 𝐡(3,4) is k, determine the value of π‘š and the perpendicular distance 𝐿 between 𝐡 and the line of action of the force.

  • Aπ‘š=4, 𝐿=5 length units
  • Bπ‘š=5, 𝐿=√34 length units
  • Cπ‘š=βˆ’5, 𝐿=√3434 length units
  • Dπ‘š=4, 𝐿=15 length units
  • Eπ‘š=5, 𝐿=√3434 length units

Q10:

Fij=+ and Fij=π‘šβˆ’, where F and F are two forces acting on the points 𝐴(2,0) and 𝐡(0,2) respectively. If the sum of moments about the point of origin is 0k, determine the value of π‘š.

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