Two Dimensional Moment and Couple

Sample Problem 2/11

Sample Problem 2/12

Sample Problem 2/13

Sample Problem 2/14

Sample Problem 2/15

2/117 Determine the moment of force F about point O.

2/118 Determine the moment of force F about point A.

2/119 Determine the moment about O of the force of magnitude F for the case (a) when the force F is

applied at A and for the case (b) when F is applied at B.

2/120 In opening a door which is equipped with a heavy duty return mechanism, a person exerts a force P of magnitude 32 N as shown. Force P and the normal n to the face of the door lie in a vertical plane.

Compute the moment of P about the z-axis.

2/121 The two forces acting on the handles of the pipe wrenches constitute a couple M. Express the couple as a vector.

2/122 The bent bar has a mass ρ per unit of length. Determine the moment of the weight of the bar about point O.

2/123 A helicopter is shown here with certain three-dimensional geometry given. During a ground test,

a 400-N aerodynamic force is applied to the tail rotor at P as shown. Determine the moment of this force about point O of the airframe.

2/124 The 24-N force is applied at point A of the crank assembly. Determine the moment of this force about point O.

2/125 The right-angle pipe OAB of Prob. 2/108 is shown again here. Replace the 750-N tensile force which the cable exerts on point B by a force–couple system at point O.

2/126 Determine the moment associated with the pair of 400-N forces applied to the T-shaped structure.

2/127 If the magnitude of the moment of F about line CD is 50N.m , determine the magnitude of F.

2/128 A mechanic applies the horizontal 100-N force perpendicular to the wrench as indicated in the figure. Determine the moment of this force about the bolt center O. The wrench centerline lies in the x-y plane.

2/129 Two 4-N thrusters on the nonrotating satellite are simultaneously fired as shown. Compute the moment associated with this couple and state about which satellite axes rotations will begin to occur.

2/130 Compute the moment MO of the 1.2-kN force about the axis O-O.

2/131 A space shuttle orbiter is subjected to thrusts from five of the engines of its reaction control system. Four of the thrusts are shown in the figure; the fifth is an 850-N upward thrust at the right rear, symmetric to the 850-N thrust shown on the left rear. Compute the moment of these forces about point G and show that the forces have the same moment about all points.

2/132 In picking up a load from position B, a cable tension T of magnitude 24kN is developed. Calculate the moment which T produces about the base O of the construction crane.

2/133 The specialty wrench shown is used for difficult-to-access bolts which have a low torque specification. Determine the moment about O of the 40-N force applied at point A of the wrench handle. Discuss any shortcomings of this wrench.

2/134 In order to decrease the undesirable moment about the x-axis, a mechanic uses his left hand to support the wrench handle at point B. What upward force F must he exert in order that there be no moment about the x-axis? What then is the net moment about O?

2/135 Determine the moment of the 400-N force about point A by (a) using the vector cross-product relation and (b) resolving the force into its components and finding their respective moments.

2/136 The specialty wrench shown in the figure is designed for access to the hold-down bolt on certain automobile distributors. For the configuration shown where the wrench lies in a vertical plane and a horizontal 200-N force is applied at A perpendicular to the handle, calculate the moment MO applied to the bolt at O. For what value of the distance d would the z-component of MO be zero?

2/137 The moment M applied to the pulley wheel causes a tension T 80 N in the cable which is secured to the wheel at D and to the ground at E. Determine the moment about O of this 80-N force as applied
at C.

2/138 An 320-N force is applied to the end of the wrench as the sprocket wheel is attached to an engine
crankshaft. The force is perpendicular to the plane containing points O, A, and B. Determine the moment of this force about point O.

2/139 Using the principles to be developed in Chapter 3 on equilibrium, one can determine that the tension in cable AB is 143.4 N. Determine the moment about the x-axis of this tension force acting on
point A. Compare your result with the moment of the weight W of the 15-kg uniform plate about the x-axis. What is the moment of the tension force acting at A about line OB?

2/140 The rigid pole and cross-arm assembly of Prob. 2/105 is shown again here. Determine the vector
expression for the moment of the 1.2-kN tension (a) about point O and (b) about the pole z-axis. Find
each moment in two different ways.

2/141 A 5-N vertical force is applied to the knob of the window-opener mechanism when the crank BC is horizontal. Determine the moment of the force about point A and about line AB.

2/142 Determine the vector expression for the moment Mo of the 600-N force about point O. The design specification for the bolt at O would require this result.