While sliding a couch across a floor, Andrea and Jennifer exert forces FA and F on the couch. Andrea's force is due north with a magnitude of 140.0 N and Jennifer's force is 260 east of north with a magnitude of 220.0 N (a) Find the net force (in N) in component form. net : (b) Find the magnitude (in N) and direction (in degrees counterclockwise from the east axis) of the net force magnitude direction X o counterclockwise from the east axis (c) If Andrea and Jennifer's housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force Fos (in N) should they push so that the couch does not move? (Express your answer in vector form.) Fos

To solve this problem we must make a free body diagram with the forces applied as well as the direction. In the attached images we can see the nomenclature of the direction of the forces and the free body diagram.

a)

Sum of forces in y-axis

Fy = 140 - (220*sin(10))

Fy = 101.8 [N]

Sum of forces in x-axis

Fx = - (220*cos(10))

Fx = - 216.65 [N]

b)

For the above result, for there to be balance we realize that we need one equal to the resulting y-axis but in the opposite direction and another opposite force in direction but equal in magnitude on the x-axis.

Fy = - 101.8 [N]

Fx = 216.65 [N]

c )

Now we need to use the Pythagorean theorem to find the result of these forces.

[tex]F = \sqrt{(101.8)^{2} +(216.65)^{2} } \\F=239.4[N][/tex]

And the direction will be as follows.

α = tan^(-1) (101.8 / 216.65)

α = 25.16° (south to the east)

F = 216.65 i - 101.8 j [N]