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In this lesson, we will learn how to find and interpret the three components of the moment of a force in the i, j, and k directions.

Q1:

The moment of the force β πΉ about the origin is π π , where β πΉ = β π β 2 β π β β π and π = 2 0 β π + 2 7 β π β 3 4 β π π . Given that the force passes through a point whose π¦ -coordinate is 4, find the π₯ and π§ coordinates of the point.

Q2:

If the force β πΉ = π β π + π β π β β π is acting at a point whose position vector, with respect to the origin point, is β π = 1 4 β π β β π + 1 2 β π , and the components of the moment of the force β πΉ about the π₯ -axis and the π¦ -axis are 73 and 242 units of moment, respectively, find the values of π and π .

Q3:

The forces and act along and , respectively, as shown in the figure. Given that , , and are a right system of unit vectors in the directions of , , and , respectively, find the sum of the moments of the forces about point in newton-meters.

Q4:

In the figure, a force of magnitude 42 newtons is acting along diagonal πΈ π΅ in a cuboid whose dimensions are 18 cm, 18 cm, and 9 cm. Determine the vector moment of the force about π in newton-centimetres.

Q5:

If the force β πΉ , where β πΉ = β 2 β π + πΏ β π β 9 β π , is acting on the point π΄ ( 4 , 5 , β 2 ) , and the moment π π΅ of the force about the point π΅ ( β 4 , β 4 , 3 ) is β 9 1 β π + 8 2 β π + 2 β π , determine the value of πΏ .

Q6:

In the figure, determine the sum of the moment vectors of the forces 86 and 65 newtons about π in newton-centimetres.

Q7:

If a force β πΉ = 4 β π + β π β β π is acting at a point π΄ ( 1 2 , β 1 2 , β 4 ) , find the magnitude of the component of the moment of β πΉ about the π¦ -axis.

Q8:

The forces β πΉ = β β π + 5 β π 1 , β πΉ = β 8 β π + 2 β π 2 , and β πΉ = 8 β π β 2 β π 3 are acting at a point. If the moment vector of the resultant of these forces about the origin point is β 1 0 β π , find the intersection point of the line of action of the resultant with the π¦ -axis.

Q9:

If the force β πΉ = 7 β π + π β π + π β π is acting at the point π΄ ( β 7 , β 5 , 4 ) and the two components of the moment of β πΉ about the π¦ -axis and the π§ -axis are β 7 and 98 respectively, find the values of π and π .

Q10:

β πΉ = π β π + β π 1 and β πΉ = π β π β 5 β π 2 , where β πΉ 1 and β πΉ 2 are two forces acting at the points π΄ ( 3 , 1 ) and π΅ ( β 1 , β 1 ) respectively. The sum of moments about the point of origin equals zero. The sum of the moments about the point πΆ ( 1 , 2 ) also equals zero. Determine the values of π and π .

Q11:

If the force β πΉ = π β π + 3 β π β 3 β π is acting at a point π΄ whose position vector, with respect to the origin point, is β π = β 6 β π β 2 β π + 4 β π , and the component of the moment of the force β πΉ about the π¦ -axis is β 3 0 moment units, find the length of the perpendicular segment drawn from the origin point to the line of action of β πΉ .

Q12:

In the figure shown, a force of magnitude 2 3 β 2 newtons acts at a point π΄ , determine the moment vector of the force about the origin π in Nβ m.

Q13:

A force having a magnitude of newtons is acting on point in the direction of and another force having a magnitude of newtons is acting on point in the direction of as shown in the figure. If , , and are a right system of the one vectors in the direction of , , and , respectively, determine the vector sum of the moments of the forces about point in newton-centimeters.

Q14:

Given that a force of magnitude 6 N is acting on πΆ as in the figure, determine its moment vector about π΄ in newton-centimetres.

Q15:

In the figure, π΄ π΅ is a rod fixed to a vertical wall at end π΄ . The other end π΅ is connected to a wire π΅ πΆ , where πΆ is fixed to a different point on the same vertical wall. If the tension in the wire equals 39 N, calculate the moment of the tension about point π΄ in newton-metres.

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