I encountered a problem while solving a question about friction force regarding static bodies

The question is as follows, "A body of weight $W$ is placed on a rough plane inclined to the horizontal at an angle whose tangent is $\frac{7}{24}$. It is tied to a rope and it is pulled by the rope upwards with a force of magnitude $\frac{3}{5}W$ to make the body about to move upwards the plane. If the rope lies in the vertical plane which passed through the line of the greatest slope and the measure of the angle between the rope and the line of the greatest slope is $x$ where $\tan(x) = \frac{3}{4}$. Calculate the coefficient of static friction between the body and the plane, also find the measure of the angle of friction".

The question is straightforward and understandable, and I am not asking for the answer. However what I want to know is:

  • What does the vertical plane mentioned in the question represent?

  • How does the mentioned vertical plane pass through the line of the greatest slope?

  • How does the rope lie in the vertical plane?

  • How to visualize this system in real life if possible?

In a nutshell, I can't really visualize the system while visualization is the key to the question's solution.

Thanks in advance for your help.


1 Answer 1


I try to interpret this weird description. The greatest-sloep line means the vertical line. And the pulling rope forms an angle $x$ with the vetical line: $\tan x = 3 / 4 $. The vertical plane means the vertical line (greatest-slope) and rope both are passing through the body, define the vertical plane.

In a comprehensive way of dscription: The body weight $W$ is pulled with a rope upward with force $3 W / 5$. The rope forms an angle $x$ with the vertical line passing the body, and $\tan x = 3 /4$.

enter image description here

  • $\begingroup$ I would think that the "line of greatest slope" is the one which goes up the incline in your sketch. $\endgroup$
    – R.W. Bird
    Jan 7, 2021 at 15:59
  • $\begingroup$ @R.W.Bird Yes. I think so. $\endgroup$
    – ytlu
    Jan 7, 2021 at 16:02

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