Lesson 8: Equilibrium of Rigid Bodies

Write your solutions to the following problems and submit them before 6 am on Monday, March 10th.

Submit to the SUBMIT folder on Priscilla or as an attachment to an e-mail message to rfuller@unlinfo.unl.edu or using this Web form.

The solutions to the problems in this lesson are rather formal; that is, all problem solutions follow a regular procedure, which, if done carefully, will almost always produce the desired result. After learning the general procedures and practicing on a few examples, you should find no difficulty in solving any problem in this lesson.

The steps in the formal solution procedure are summarized here:

  1. Draw an imaginary boundary separating the system under consideration from its surroundings.

  2. Draw vectors representing the magnitude, direction, and point of application of all external forces to the system (in other words, construct a free-body diagram).

  3. Choose a convenient reference frame, resolve all of the external forces along these axes, and then apply the first condition of equilibrium.

  4. Choose a convenient axis, evaluate all of the external torques around it, and apply the second condition of equilibrium.The resulting simultaneous equations can then be solved for the desired quantities.

Your Name:

  1. A uniform beam 5.0 m long with mass 10.0 kg is hinged at a wall. The outer end is supported by a guy wire making an angle of 30.0° with the horizontal beam, and an object of mass 20.0 kg is hung on the beam at a point 4.5 m from the wall as shown in the diagram.

    Find the tension in the guy wire and the vertical and horizontal components of the force exerted on the beam hinge by the wall.

  2. A uniform ladder 10.0 m long, with a mass of 20.0 kg, rests against a smooth wall and on a rough floor, with the base of the ladder 6.0 m from the wall. An 80-kg man has climbed the ladder to 8.0 m along the ladder from the bottom. Find the horizontal force that the floor must supply to keep the ladder from slipping.

  3. An object with a weight of 15.0 N is suspended by ropes from two points as shown in the drawing.

    Draw a free-body diagram and solve for the tensions in ropes A and B.

  4. A gate with a uniform mass distribution and weight W is supported by two hinges as shown in the diagram (top left and bottem left of the sign), but to relieve the strain a guy wire is strung to the outer corner of the gate and tightened until there is no horizontal force on the lower hinge.

    Draw a free-body diagram and find the horizontal force on the top hinge in terms of W.

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