In: Physics
Three forces are applied to an object, as shown in the figure. F1 Baseline has a magnitude of 24.0 newtons (24.0 N) and is directed 30.0° to the left of the +y axis. F2 has a magnitude of 14.9 N and points along the +x axis. What must be the (a) magnitude and (b) direction (specified by the angle theta in the drawing) of the third force F3 such that the vector sum of the three forces is 0 N?
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Three forces are applied to an object, as shown in the
figure.Force F1 has a magnitude of 23.4 newtons (N) and is directed
30.0degrees to the left of the + y axis. Force F2 has a magnitude
of13.1 N and points along the + x axis. A third force F3 is
appliedsuch that the vector sum of the three forces is 0 N. What
are (a)the magnitude and (b) direction of this third force F3?
Specify thedirection as a positive angle relative to the negative x
axis, asshown in the figure.
Sum the y-components of F1 and F2:
Fy =F1cos30 [F2 has no y-components...]
Fy = 20.265 N
Sum the x-components:
Fx = -F1sin30 + F2
Fx = 1.4 N
The third force is cancelling out those components, so:
F3y = - 20.265 N
F3x = -1.4 N
F3 = ?(20.2652 + 1.42)
F3 = 20.31 N
tan? = F3y/F3x = -20.265 /-1.4
? = 86.0 degrees
F3 = 20.31 N @86.0o