Neglecting the weight of the beam below find the tention in the tie rope and the force component at the Hinge in the terms of What repeat if the uniform weight t is ½W
Answers
Explanation:
ems. Accordingly, we use equilibrium conditions in the component form of (Figure) to (Figure). We introduced a problem-solving strategy in (Figure) to illustrate the physical meaning of the equilibrium conditions. Now we generalize this strategy in a list of steps to follow when solving static equilibrium problems for extended rigid bodies. We proceed in five practical steps.
Problem-Solving Strategy: Static Equilibrium
Identify the object to be analyzed. For some systems in equilibrium, it may be necessary to consider more than one object. Identify all forces acting on the object. Identify the questions you need to answer. Identify the information given in the problem. In realistic problems, some key information may be implicit in the situation rather than provided explicitly.
Set up a free-body diagram for the object. (a) Choose the xy-reference frame for the problem. Draw a free-body diagram for the object, including only the forces that act on it. When suitable, represent the forces in terms of their components in the chosen reference frame. 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. Label all forces—you will need this for correct computations of net forces in the x– and y-directions. 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. A plus sign
(
+
)
means that the working direction is the actual direction. A minus sign
(
−
)
means that the actual direction is opposite to the assumed working direction. (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. 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. 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.
Set up the equations of equilibrium for the object. (a) Use the free-body diagram to write a correct equilibrium condition for force components in the x-direction. (b) Use the free-body diagram to write a correct equilibrium condition for force components in the y-direction. (c) Use the free-body diagram to write a correct equilibrium condition for torques along the axis of rotation. Use to evaluate torque magnitudes and senses.