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In this lesson, we will learn how to find the moment of a force or system of forces about a point.

Q1:

π΄ π΅ πΆ π· is a trapezium in which sides π΄ π· and π΅ πΆ are parallel, π β π΄ = 9 0 β , π΄ π΅ = π΄ π· = 1 8 c m , and π΅ πΆ = 3 6 c m . Forces of magnitude πΎ , 2, πΉ , 8, and 1 4 β 2 newtons are acting along ο« π΅ π΄ , οͺ πΆ π΅ , ο« π· πΆ , ο« π· π΄ , and ο« π΅ π· , respectively. If the resultant of the moments of the forces about π΄ is zero, and the resultant of the moments of the forces about π΅ equals that about π· , calculate the values of πΉ and πΎ .

Q2:

π΄ π΅ πΆ is an isosceles triangle in which π β π΅ = 1 2 0 β and π΄ πΆ = 8 β 3 c m . Forces of magnitudes 4, 8, and 1 8 β 3 newtons are acting along ο« π΄ πΆ , οͺ πΆ π΅ , and ο« π΄ π΅ respectively. Find the magnitude of sum of the forces moments about the midpoint of π΅ πΆ .

Q3:

π΄ π΅ πΆ π· πΈ πΉ is a regular hexagon, where forces of magnitudes 9, 12, 3, 1, 11, and 16 newtons are acting along ο« π΄ π΅ , οͺ π΅ πΆ , ο« πΆ π· , ο« π· πΈ , οͺ πΈ πΉ , and ο« πΉ π΄ respectively. Determine the magnitude of the additional force that would need to act along ο« πΉ π΄ so that the algebraic sum of moments about πΈ becomes zero.

Q4:

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

Q5:

π΄ π΅ πΆ π· is a trapezium with a right-angle at π΅ , where π΄ π· β₯ π΅ πΆ , and π΄ π΅ = 9 c m . If π· πΈ is drawn perpendicular to the plane of the trapezium, and a force of magnitude 117 N is acting along ο« π΄ πΈ , find the moment of the force about π΅ .

Q6:

In the figure, π΄ π΅ = 5 m , and π΄ πΆ = 5 m . When force β πΉ acts on wire π΅ πΆ , the magnitude of the moment about π΄ is 1β959 Nβ m. Find the magnitude of force β πΉ rounded to two decimal places.

Q7:

π΄ π΅ πΆ is a triangle with a right-angle at π΅ , where π΄ π΅ = 1 8 c m and π΅ πΆ = 2 4 c m . A force πΉ is acting in the plane of the triangle, where π = π = 1 8 0 β π΄ π΅ N c m and π = β 1 8 0 β πΆ N c m . Determine the magnitude and the line of action of πΉ .

Q8:

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

Q9:

Given that two parallel forces, each having a magnitude of 26 N, are acting on a lever π΄ π΅ as shown in the figure, where π΄ πΆ = 9 c m , πΆ π΅ = 6 c m , and π = 4 5 β , find the algebraic measure of the sum of the moments of the two forces about point π΄ .

Q10:

π΄ π΅ πΆ π· is a rectangle, where π΄ π΅ = 3 6 c m and π΅ πΆ = 4 8 c m . A force πΉ is acting in the plane of the rectangle, where its moment about π΅ equals its moment about π· , which equals β 1 0 8 Nβ cm, and its moment about π΄ is 108 Nβ cm. Determine the magnitude and the direction of πΉ .

Q11:

β πΉ is a force in the plane of parallelogram π΄ π΅ πΆ π· . The sum of the moments about π΄ , π = β 9 5 π΄ units of moment. The sums of the moments about π΅ and π· are π = π = 8 9 π΅ π· units of moment. Determine the sum of the moments about πΆ , π πΆ .

Q12:

Find the measure of angle , rounded to the nearest minute, so that the moment of the force about has its minimum value.

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