#3D PROBLEMS OF STATIC EQUILIBRIUM PLUS#

We say that a rigid body is in equilibrium when both its linear and angular acceleration are zero relative to an inertial frame of reference. Explain how the conditions for equilibrium allow us to solve statics problems.Draw a free-body diagram for a rigid body acted on by forces.Identify the physical conditions of static equilibrium.

It is balanced when the beam remains level.By the end of this section, you will be able to: The system is in static equilibrium when the beam does not rotate. Here, the free-body diagram for an extended rigid body helps us identify external torques.įigure 12.9 In a torque balance, a horizontal beam is supported at a fulcrum (indicated by S) and masses are attached to both sides of the fulcrum. The reason for this is that in analyzing rotation, we must identify torques acting on the body, and torque depends both on the acting force and on its lever arm. This does not hold true in rotational dynamics, where an extended rigid body cannot be represented by one point alone. In translational dynamics, a body is represented as its CM, where all forces on the body are attached and no torques appear.

Also note that a free-body diagram for an extended rigid body that may undergo rotational motion is different from a free-body diagram for a body that experiences only translational motion (as you saw in the chapters on Newton’s laws of motion). Without the correct setup and a correct diagram, you will not be able to write down correct conditions for equilibrium. Note that setting up a free-body diagram for a rigid-body equilibrium problem is the most important component in the solution process. Also, you may independently check for your numerical answers by shifting the pivot to a different location and solving the problem again, which is what we did in Figure. If they do not, then use the previous steps to track back a mistake to its origin and correct it. Your final answers should have correct numerical values and correct physical units. Evaluate the expressions for the unknown quantities that you obtained in your solution.If the number of unknowns is larger than the number of equations, the problem cannot be solved. Keep in mind that the number of equations must be the same as the number of unknowns. At this point, your work involves algebra only. Simplify and solve the system of equations for equilibrium to obtain unknown quantities.Use Figure to evaluate torque magnitudes and senses. (c) Use the free-body diagram to write a correct equilibrium condition Figure for torques along the axis of rotation. (b) Use the free-body diagram to write a correct equilibrium condition Figure for force components in the y-direction. (a) Use the free-body diagram to write a correct equilibrium condition Figure for force components in the x-direction. Set up the equations of equilibrium for the object.In the selection of the pivot, keep in mind that the pivot can be placed anywhere you wish, but the guiding principle is that the best choice will simplify as much as possible the calculation of the net torque along the rotation axis. On the free-body diagram, indicate the location of the pivot and the lever arms of acting forces-you will need this for correct computations of torques. (b) Choose the location of the rotation axis in other words, choose the pivot point with respect to which you will compute torques of acting forces. A minus sign (-) means that the actual direction is opposite to the assumed working direction.

#3D PROBLEMS OF STATIC EQUILIBRIUM PLUS#

A plus sign (+) means that the working direction is the actual direction. For an unknown force, the direction must be assigned arbitrarily think of it as a ‘working direction’ or ‘suspected direction.’ The correct direction is determined by the sign that you obtain in the final solution. Label all forces-you will need this for correct computations of net forces in the x– and y-directions. As you do this for each force, cross out the original force so that you do not erroneously include the same force twice in equations. When suitable, represent the forces in terms of their components in the chosen reference frame. Draw a free-body diagram for the object, including only the forces that act on it. (a) Choose the xy-reference frame for the problem.

Set up a free-body diagram for the object.

In realistic problems, some key information may be implicit in the situation rather than provided explicitly. Identify the information given in the problem. Identify the questions you need to answer. Identify all forces acting on the object. For some systems in equilibrium, it may be necessary to consider more than one object. Problem-Solving Strategy: Static Equilibrium

3d problems of static equilibrium