2/77 Calculate the magnitude of the tension T and the angle θ for which the eye bolt will be under a resultant downward force of 15 kN.
2/78 Determine the resultant R of the four forces acting on the gusset plate. Also find the magnitude of R
and the angle θx which the resultant makes with the x-axis.
2/79 Determine the equivalent force–couple system at the origin O for each of the three cases of forces being applied to the edge of a circular disk. If the resultant can be so expressed, replace this force–couple system with a stand-alone force.
2/80 Determine the height h above the base B at which the resultant of the three forces acts.
2/81 Where does the resultant of the two forces act?
2/82 Under nonuniform and slippery road conditions, the two forces shown are exerted on the two rear-drive wheels of the pickup truck, which has a limited-slip rear differential. Determine the y-intercept of the resultant of this force system.
2/83 If the resultant of the two forces and couple M passes through point O, determine M.
2/84 Determine the magnitude of the force F applied to the handle which will make the resultant of the three forces pass through O.
2/85 Determine and locate the resultant R of the two forces and one couple acting on the I-beam.
2/86 A commercial airliner with four jet engines, each producing 90 kN of forward thrust, is in a steady,
level cruise when engine number 3 suddenly fails. Determine and locate the resultant of the three remaining engine thrust vectors. Treat this as a two-dimensional problem.
2/87 Replace the three forces acting on the bent pipe by a single equivalent force R. Specify the distance x from point O to the point on the x-axis through which the line of action of R passes.
2/88 The directions of the two thrust vectors of an experimental aircraft can be independently changed from the conventional forward direction within limits. For the thrust configuration shown, determine the equivalent force–couple system at point O. Then replace this force–couple system by a single force and specify the point on the x-axis through which the line of action of this resultant passes. These results are vital to assessing design performance.
2/89 Determine the resultant R of the three forces acting on the simple truss. Specify the points on the x- and y-axes through which R must pass.
2/90 The gear and attached V-belt pulley are turning counterclockwise and are subjected to the tooth load of 1600 N and the 800-N and 450-N tensions in the V-belt. Represent the action of these three forces by a resultant force R at O and a couple of magnitude M. Is the unit slowing down or speeding up?
2/91 The design specifications for the attachment at A for this beam depend on the magnitude and location of the applied loads. Represent the resultant of the three forces and couple by a single force R at A and a couple M. Specify the magnitude of R.
2/92 In the equilibrium position shown, the resultant of the three forces acting on the bell crank passes
through the bearing O. Determine the vertical force P. Does the result depend on θ?
2/93 Two integral pulleys are subjected to the belt tensions shown. If the resultant R of these forces passes through the center O, determine T and the magnitude of R and the counterclockwise angle it makes with the x-axis.
2/94 While sliding a desk toward the doorway, three students exert the forces shown in the overhead view. Determine the equivalent force–couple system at point A. Then determine the equation of the line of action of the resultant force.
2/95 Under nonuniform and slippery road conditions, the four forces shown are exerted on the four drive wheels of the all-wheel-drive vehicle. Determine the resultant of this system and the x- and y-intercepts of its line of action. Note that the front and rear tracks are equal (i.e., AB = CD)
2/96 The rolling rear wheel of a front-wheel-drive automobile which is accelerating to the right is subjected to the five forces and one moment shown. The forces Ax =240 N and Ay =2000 N are forces transmitted from the axle to the wheel, F 160 N is the friction force exerted by the road surface on the tire, N = 2400 N is the normal reaction force exerted by the road surface, and W 400 N is the weight of the wheel/tire unit. The couple M = 3N.m is the bearing friction moment. Determine and locate the resultant of the system.
2/97 A rear-wheel-drive car is stuck in the snow between other parked cars as shown. In an attempt to free the car, three students exert forces on the car at points A, B, and C while the driver’s actions result in a forward thrust of 200 N acting parallel to the plane of rotation of each rear wheel. Treating the problem as two-dimensional, determine the equivalent force–couple system at the car center of mass G and locate the position x of the point on the car centerline through which the resultant passes. Neglect all forces not shown.
2/98 An exhaust system for a pickup truck is shown in the figure. The weights Wh, Wm, and Wt of the head-pipe, muffler, and tailpipe are 10, 100, and 50 N, respectively, and act at the indicated points. If the exhaust-pipe hanger at point A is adjusted so that its tension FA is 50 N, determine the required forces in the hangers at points B, C, and D so that the force–couple system at point O is zero. Why is a zero force–couple system at O desirable?
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