Q17E - University Physics with Modern Physics

Question

Question: A 9.00-m-long uniform beam is hinged to a vertical wall and held horizontally by a 5.00-m-long cable attached to the wall 4.00 m above the hinge (Fig. E11.17). The metal of this cable has a test strength of 1.00 kN, which means that it will break if the tension in it exceeds that amount. (a) Draw a free-body diagram of the beam. (b) What is the heaviest beam that the cable can support in this configuration? (c) Find the horizontal and vertical components of the force the hinge exerts on the beam. Is the vertical component upward or downward?

Step-by-Step Solution

Answer

(a) The diagram is drawn below.

Step 1: Given Data

The length of a beam is 9 m

The length of a cable is 5 m

The strength of a cable is 1 kN

Step 2: Concept

The drawing of all the forces acting on the system is known as free body diagram.

Step 3(a): Draw a free-body diagram

The free body diagram is,

The free body diagram of a system shows the applied force, movement and resulting reactions in given conditions

From the figure, T is the tension acting on the cable, w is the weight placed on the beam.

Therefore the various forces acting on the hinged beam are obtained.