It is known that a force with a moment of 960 N · m about D is required to straighten the fence post CD. If d = 2.80 m, determine the tension that must be developed in the cable of winch puller AB to create the required moment about Point D. Please give a detailed explanation

Step: 1

Draw the free body diagram of the fence post as follows:

Step: 2

Let be the angle exerted by the cable with the horizontal.

Determine the angle as follows:

Substitute for .

Step: 3

Let the horizontal component of the tension in the cable BC be .

Resolve the tension in the cable as below and obtain the horizontal component

Substitute for .

Step: 4

Resolve the tension in the cable and obtain the vertical component of the tension, in the cable BC.

Substitute for .

Step: 5

Take the moments about D.

Follow the sign conventions as positive for anticlockwise moment and negative for clockwise moment.

Here, is the moment needed for the fence post to straighten.

Substitute for , for and .

Therefore, the tension in the cable BC is .