(a) Explanation The magnitude of the force F acting on the origin of the coordinate system is 250 lb . The angles the x , y and z components of force make with the origin of the coordinate system are θ x = 65 ° and θ y = 40 ° . Write the expression for the sum of the squares of the cosines of all the angles of the components of the force with respect to the origin of the coordinate system. cos 2 θ x + cos 2 θ y + cos 2 θ z = 1 (I) Here, θ x is the angle between x component of force and the origin of the coordinate system, θ y is the angle between y component of force and the origin of the coordinate system, and θ z is the angle between z component of force and the origin of the coordinate system. Write the equation for the x component of force. F x = F cos θ x (II) Here, F x is the x component of force, F is the magnitude of force, and θ x is the angle the x component of force makes with the origin of the coordinate system. Write the equation for the y component of force. F y = F cos θ y . (III) Here, F y is the y component of force and θ y is the angle the y component of force makes with the origin of the coordinate system. Write the equation for the z component of force. F z = F cos θ z (IV) Here, F z is the z component of force and θ z is the angle the z component of force makes with the origin of the coordinate system. Conclusion: Substitute 65 ° for θ x and 40 ° for θ y in the equation (I) and rearrange it to find θ z . cos 2 65 ° + cos 2 40 ° + cos 2 θ z = 1 cos θ z = ± 0 (b) To determine The angle θ z made by the z component of force with the origin of the coordinate system.

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Chapter 2.4, Problem 2.81P

(a)

To determine

The components of the force of magnitude 250 lb acting at the origin of a coordinate system.

(b)

To determine

The angle θz made by the z component of force with the origin of the coordinate system.

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Chapter 2.4, Problem 2.80P

Chapter 2.4, Problem 2.82P

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The components of the force of magnitude 250 lb acting at the origin of a coordinate system.

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The components of the force of magnitude 250 lb acting at the origin of a coordinate system.

The angle θz made by the z component of force with the origin of the coordinate system.

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Chapter 2 Solutions