Force Vectors - Excercise 1

A weight (G) is placed on a ramp.
Given: G, α=30°
Searched: Vector components of G

Solution A: Find the right Angles

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We place the force vector on the tip. By following the new axes (N for normal and T for tangential), we can draw the two components. The 90° angle must be opposite to G. The 60° angle in the lower corner comes from 90°-30°.

Solution B: Apply Trigonometry

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We take the 60° angle and use cos() and sin() to find both the N- and T-components of G:

$\cos \left(\mathrm{(60°)}\right)=\frac{{\mathrm{G}}_{\mathrm{T}}}{\mathrm{G}}$ $\leftrightarrow {\mathrm{G}}_{\mathrm{T}}=\cos \left(\mathrm{(60°)}\right)·\mathrm{G}$ Analogue for the N-compontent.