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In this lesson, we will learn how to calculate the moment of a couple of two forces about a point in space.

Q1:

The two forces β πΉ = β 3 β π β 4 β π 1 and β πΉ 2 are acting at the points π΄ ( 6 , β 2 ) and π΅ ( 8 , β 3 ) respectively. Given that they are forming a couple, determine the vector of the couple moment.

Q2:

Given that two forces β πΉ = β β π + 2 β π 1 and β πΉ 2 are acting at two points π΄ ( 2 , 2 ) and π΅ ( β 2 , β 2 ) respectively to form a couple, find the perpendicular distance between the two forces.

Q3:

π΄ π΅ πΆ π· is square having a side length of 3 cm. π» and π belong to π΅ π· , where π β πΆ π» π· = π β π΄ π π΅ = 6 0 β . Given that two equal forces, each of magnitude 5 N, are acting along ο« π π΄ and ο« π» πΆ respectively, find the magnitude of the moment of the couple.

Q4:

π΄ π΅ πΆ π· is a square of side length 8 cm, where two forces of magnitudes 21 N are acting at π΅ and π· respectively, and their lines of action are in the direction of ο« π΄ πΆ and ο« πΆ π΄ respectively. Determine the magnitude of the moment of the couple.

Q5:

What is a couple?

Q6:

π΄ π΅ πΆ π· is a rectangle, in which π΄ π΅ = 5 c m and π΄ π· = 1 0 c m . Two forces of the same magnitude 3 3 β 5 N are acting at π΄ and πΆ in the directions of ο« π΅ π· and ο« π· π΅ respectively. Determine the magnitude of the moment of the couple.

Q7:

π΄ π΅ πΆ π· is a parallelogram, where π΄ π΅ = 1 0 c m , π΅ πΆ = 8 c m , and the perpendicular distance between π΄ π΅ and π· πΆ is 6 cm. Given that two forces of the same magnitude 50 N are acting along ο« π΄ π· and οͺ πΆ π΅ , respectively, determine the magnitude of the moment of the couple.

Q8:

π΄ π΅ πΆ π· π» π is a regular hexagon with sides of length 5 cm. Two forces of the same magnitude 13 N are acting along οͺ πΆ π΅ and ο« π π» , respectively. Determine the magnitude of the moment of the couple.

Q9:

In the figure below, πΉ = 3 1 N and πΉ 1 and πΉ 2 form a couple. Find the algebraic measure of the moment of that couple.

Q10:

The given figure shows two forces each of magnitude 267 newtons acting on two edges of a lamina in the form of a rectangle with dimensions π₯ = 4 2 c m and π¦ = 8 4 c m . Find the moment of the couple if t a n π = 3 4 .

Q11:

Given two forces in a couple, what is the name given to the product of the magnitude of one of the forces and the perpendicular distance between the two forces?

Q12:

π΄ π΅ πΆ π· is a parallelogram, where π΅ πΆ = 1 0 c m and π β π΄ π΅ πΆ = 1 5 0 β . If two forces of the same magnitude 50 N are acting at ο« π΄ π΅ and ο« πΆ π· respectively, determine the magnitude of the moment of the couple, rounding your answer to two decimal places.

Q13:

π΄ π΅ πΆ π· is a rhombus in which its diagonal π΄ πΆ = 7 c m and π β π΄ = 6 0 β . Given that two equal forces, each of magnitude 45 N, are acting along ο« π΄ π· and οͺ πΆ π΅ respectively, find the magnitude of the moment of the couple rounded to two decimal places if necessary.

Q14:

π΄ π΅ πΆ π· is square having a side length of 24 cm, πΈ β π΅ πΆ , and π β π· π΄ , where π΅ πΈ = π· π = 6 c m . Given that two forces, each of magnitude, 34.2 N are acting along ο« π΅ π and ο« π· πΈ respectively, find the magnitude of the moment of the couple.

Q15:

π΄ π΅ πΆ π· π» π is a regular hexagon, having a side length of 5 cm, where a force of magnitude 15 N is acting along ο« πΆ π» , and another force of the same magnitude is acting at π΄ in the direction of ο« π» πΆ . Determine the magnitude of the moment of the couple.

Q16:

π΄ π΅ πΆ π· is a rhombus, where its diagonals π΄ πΆ and π΅ π· are 13 cm and 7 cm respectively, and two forces of the same magnitude 23 N are acting along ο« π΄ π΅ and ο« πΆ π· . Determine the magnitude of the moment of the couple, rounding your answer to two decimal places if necessary.

Q17:

If the norm of the moment of a couple is 750 Nβ m, and the magnitude of one of its two forces is 50 N, determine the length of the moment arm.

Q18:

π΄ π΅ and πΆ π· are two parallel chords in a circle whose radius is 25 cm, and they are at different distances away from the circleβs centre, where π΄ π΅ = 3 0 c m , and πΆ π· = 1 4 c m . Given that two forces of the same magnitude 20 N are acting along ο« π΅ π΄ and ο« πΆ π· , respectively, determine the magnitude of the moment of the couple.

Q19:

π΄ π΅ πΆ π· is an isosceles trapezium, where π΄ π· = π΅ πΆ = 1 3 c m , π΄ π΅ = 1 2 c m , and πΆ π· = 6 c m . Two forces, each of magnitude 50 N, are acting along ο« π΄ π΅ and ο« πΆ π· . Find the magnitude of the moment of the couple rounded to two decimal places, giving your answer in Nβ cm.

Q20:

A light rod π΄ π΅ , which has a length of 22 cm and a mid-point π , is under the action of two forces measured in newtons as shown in the figure. Given that a moment of magnitude 22 Nβ cm is acting on the rod perpendicularly to the vertical plane, determine the moment of the resultant couple acting on the rod.

Q21:

If the two forces β πΉ = β 4 β π + π β π 1 and β πΉ = π β π + 8 β π 2 form a couple, then find the value of π β 8 π .

Q22:

Given that the forces β πΉ 1 , β πΉ 2 , and β πΉ 3 are acting at the points ( β 1 , β 6 ) , ( 3 , 8 ) , and ( 8 , β 8 ) respectively, where the system of forces is equivalent to a couple, β πΉ = 3 β π β 6 β π 1 , and β πΉ = β 9 β π β 4 β π 2 , determine the magnitude of the moment of the couple.

Q23:

Given that β πΉ 1 and β πΉ 2 are two forces which form a couple, where β πΉ = β 8 β π β β π 1 , determine β πΉ 2 .

Q24:

π΄ π΅ πΆ is a right-angled triangle at π΄ , where π΄ π΅ = 1 2 c m and π΄ πΆ = 1 6 c m . The two forces β πΉ 1 and β πΉ 2 , measured in newtons, are acting on the sides of the triangle as shown in the figure below. If the system of forces is equivalent to a couple, determine the magnitudes of β πΉ 1 and β πΉ 2 .

Q25:

The two forces β πΉ = β 6 β π β 3 β π 1 and β πΉ 2 are acting at the points π΄ ( β 3 , 0 ) and π΅ ( β 7 , β 9 ) respectively. Given that they are forming a couple, determine the vector of the couple moment.

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