Biophysics Problem 1

What are the horizontal and vertical components of the \(\text {20.0 N}\) force shown in the diagram.

diagram of 20.0 N force


The first and most important step is to construct a diagram of the force vector triangle. We start with the diagram from the book, and then we construct the diagram step by step. Try drawing it yourself on a piece of paper.

Now that you have the completed diagram in front of you, all that is left is to use the formulae for sine and cosine to determine the two components.

diagram indicating horizontal and vertical components

\(\mathrm{\cos = adjacent/hypotenuse \\ \sin = opposite/hypotenuse}\)

For the horizontal component:

 \(\mathrm{Hor. \; comp= \cos(65) \times Hypoteneuse \\           = \cos(65) \times 20.0 \;N \\           = 8.45 \;N .}\)


\(\mathrm{Hor. \;comp = \sin(25) \times Hypoteneuse \\           = \sin(25) \times 20.0 \;N \\           = 8.45\; N}\)

For the vertical component:

\(\mathrm{Vert. \;comp = \cos(25) \times Hypoteneuse \\            = \cos(25) \times 20.0\; N \\            = -18.1\; N}\)


\(\mathrm{Vert. \;comp = \sin(65) \times Hypoteneuse \\            = \sin(65) \times 20.0 \;N \\            = -18.1\; N}\)

If you still can't understand how these results were obtained, then see your prof or T.A.