# 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 N⋅cm,
• B N⋅cm,
• C N⋅cm,
• D N⋅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 1 959 N⋅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 N⋅cm, and its moment about is 108 N⋅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 N⋅cm
• B N⋅cm
• C N⋅cm
• D N⋅cm

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