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kirill [66]
3 years ago
11

The three forces shown act on a particle. what is the direction of the resultant of these three forces?

Physics
1 answer:
melisa1 [442]3 years ago
7 0
Missing figure: http://d2vlcm61l7u1fs.cloudfront.net/media/f5d/f5d9d0bc-e05f-4cd8-9277-da7cdda3aebf/phpJK1JgJ.png

Solution:
We need to find the magnitude of the resultant on both x- and y-axis.

x-axis) The resultant on the x-axis is
F_x = 65 N\cdot cos 30^{\circ} - 30 N - 20 N\cdot sin 20^{\circ} = 19.45 N
in the positive direction.

y-axis) The resultant on the y-axis is
F_y = 65 N \cdot sin 30^{\circ} - 20 N \cdot cos 20^{\circ} = 13.70 N
in the positive direction.

Both Fx and Fy are positive, so the resultant is in the first quadrant. We can find the angle and so the direction using
\tan \alpha =  \frac{F_y}{F_x} = \frac{13.70 N}{19.45 N}=0.7
from which we find 
\alpha=35^{\circ}
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