A force F1with magnitude 10 acts in the direction of θ1= 30◦ and another force F2...

A force F1with magnitude 10 acts in the direction of θ1= 30◦ and another force F2 with magnitude 14 acts in a direction of θ2= 280◦. Find the magnitude and the direction of the resultant force F1+F2.

Expert Solution

The component of F1 along the horizontal direction
F1x = F1 cos = 10 x cos 300 = 8.66 N
The component of F1 along the vertical direction.
F1y = F1 sin = 10 x sin 300 = 5 N
The component of F2 along the horizontal direction.
F2x = F2 cos = 14 x cos 800 = 2.43 N
Where = 360⁰ - 280⁰ = 80⁰
The component of F2 along the vertical direction.
F2y = F2 sin = 14 x sin 800 = 13.79 N
This is directed along the negative y-direction.
The net force along the x-direction.
Fx = F1x + F2x = 8.66 N + 2.43 N= 11.09 N
The net force along the y-direction,
Fy = F1y - F2y = 5 N - 13.79 N =  - 8.79 N
This is also directed along the negative y-direction.
The net force
F = sqrt (Fx2 + Fy2) = 14.15 N
sin = 8.79 N / 11.09 N
= 52.43⁰    measured clockwise from the horizontal.

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genius_generous answered 2 years ago

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