Question:

One end of a rope is fixed to a vertical wall and the other end pulled by a horizontal force of 20 N. The shape of the flexible rope is shown in the figure. Find its mass.

Step-by-step

The puzzling aspect of the problem is that insufficient data have been given in the text. However, the figure can be used as a source of information. Using a protractor you can measure with sufficient accuracy that the tangent to the fixed end of the rope makes an angle of 30◦ with the vertical, as shown in the figure. This means that the tension at the fixed end of the rope is T = 20 N/ sin ${{30}^{\omicron }}$ = 40 N. Similarly, the weight of the rope is equal to the vertical component of the tension there; mg = T cos ${{30}^{\omicron }}$ = 34.6 N, giving the mass of the rope as m = 3.5 kg.
Note. Further information can be obtained from the figure. The centre of gravity of the rope must be vertically above point P because the lines of action of all three forces acting on the rope must meet at a single point.