Question #e4d6c

1 Answer
Nathan L.
Sep 4, 2017

#theta = 120^"o"#

Explanation:

We're asked to find the necessary angle between two force vectors so that the resultant vector has a magnitude equal to that of one of the forces.

Let's make the two force vectors have magnitudes #A# and #B#, and their resultant have magnitude #C#. We can use the law of cosines:

#C^2 = A^2 + B^2 - 2ABcostheta#

Since the two vector magnitudes #A# and #B# are equal, we can just replace #B# with #A#:

#C^2 = 2A^2 - 2A^2costheta#

Now, let's find the angle #theta# between the constituent forces:

#costheta = (2A^2 - C^2)/(2A^2)#

And since the resultant force's magnitude is equal to that of one of the vector magnitudes, #C = A#:

#costheta = (2A^2 - A^2)/(2A^2)#

#costheta = 1/2#

#color(red)(ulbar(|stackrel(" ")(" "theta = 120^"o"" ")|)#

The angle between the two force vectors must be #color(red)(120^"o"#.

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