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How do I calculate the resultant force of a parallelogram?
in Physics by Diamond (81,178 points) | 101 views

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Using an example, assume there are two forces $3N$ acting northwards and $4N$ acting eastwards on a small trailer as shown f the diagram below.

To calculate the resultant for, we we have to establish the diagonal of the quadrilateral formed by the two shapes which will give us the magnitude and direction of the resultant force.

Using Pythagoras' Theorem we can calculate the magnitude of the resultant force:

\[4^2+3^2=r^2\]

which implies that

\[r^2=25\]

hence $r=5$

Now that we have established the magnitude, we can now use trigonometric ratios to calculate the direction relative to the horizontal force.

\[\tan{\theta}=\dfrac{4}{3}\]

which means that

\[\theta = \tan^{-1}{\dfrac{4}{3}}\]

therefore $\theta = 37^{\circ}$

The diagram below shows that the diagonal of the parallelogram is the resultant force of 5 newtons (N) acting at an angle of 37° to the horizontal.

by Diamond (81,178 points)

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