# Worksheet: Moment of Vector Forces in 2D

In this worksheet, we will practice finding the moment of a force or a system of forces about a point.

**Q1: **

is a trapezium 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: **

is an isosceles triangle in which and . Forces of magnitudes 4, 8, and newtons are acting along , , and respectively. Find the magnitude of sum of the forces moments about the midpoint of .

**Q3: **

is a regular hexagon, where forces of magnitudes 14, 8, 18, 3, 5, and 6 newtons are acting along , , , , , and respectively. Determine the magnitude of the additional force that would need to act along so that the algebraic sum of moments about becomes zero.

**Q4: **

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

- A Nā cm,
- B Nā cm,
- C Nā cm,
- D Nā cm,

**Q5: **

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

**Q6: **

In the figure, , and . When force acts on wire , the magnitude of the moment about is 1ā959 Nā m. Find the magnitude of force rounded to two decimal places.

**Q7: **

is a triangle with a right-angle at , where and . A force is acting in the plane of the triangle, where and . Determine the magnitude and the line of action of .

- A , parallel to and passes through the midpoint of
- B , parallel to and passes through the midpoint of
- C , parallel to and passes through the midpoint of
- D , parallel to and passes through the midpoint of
- E , parallel to and passes through the midpoint of

**Q8: **

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

**Q9: **

is a rectangle, where and . A force is acting in the plane of the rectangle, where its moment about equals its moment about , which equals Nā cm, and its moment about is 108 Nā cm. Determine the magnitude and the direction of .

- A , parallel to , passes through the midpoint of
- B , parallel to , passes through the midpoint of
- C , parallel to , passes through the midpoint of
- D , parallel to , passes through the midpoint of

**Q10: **

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 , .

**Q11: **

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

**Q12: **

Given that two parallel forces, each having a magnitude of 26 N, are acting on a lever as shown in the figure, where , , and , find the algebraic measure of the sum of the moments of the two forces about point .

- A 78 Nā cm
- B Nā cm
- C Nā cm
- D Nā cm