A small probe P is gently forced against the circular surface with a vertical force F as shown . Determine the n- and t-components of this force as functions of the horizontal positions.

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the normal component of force F_n is F((√(r²-s²)) / r)

the tangential component of force F_t is F(s/r)

Explanation:

Given the data in the image;

from the free body diagram, we write the expression for ∅

sin∅ = s/r

cos∅ = (√(r²-s²)) / r

now expression for normal component of force is;

F_n = Fcos∅

we substitute

F_n = F((√(r²-s²)) / r)

Therefore, the normal component of force F_n is F((√(r²-s²)) / r)

Also for force F_t

F_t = Fsin∅

we substitute

F_t = F(s/r)

Therefore, the tangential component of force F_t is F(s/r)

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