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I am having difficulty with two questions from a book I am studying about statics. I have seen the answers but it did not help me understand how the answers are derived. I want some advice on how to think about these types of problems and whether there are any tricks which help to solve them.

Question 1 (1st image);

A small probe is gently forced against a circular surface with a vertical force F (the red vector). Determine the n- and t-components of this force as functions of the horizontal position S.

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Question 2 (2nd image);

Determine the x- and y-components of the tension T which is applied to point A of the bar OA. Neglect the effects of the small pulley at B. Assume that R and alpha are known.

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In fact, these are just geometry problems.

The answer to the first question:

$$\begin{align} F_n &= F\dfrac{(r^2 - s^2)^(1/2)}{r} \\ F_t &= F\dfrac{s}{r} \end{align}$$

Figure shows the details of the solution.

Solution of the first question

If you think that way, you can solve the second question.

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