While sliding a couch across a floor, Andrea and Jennifer exert forces FA and F

Question

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

Explanation / Answer

(A) FA = 140 j

FJ = 220 ( sin26 i + cos26 j)

FJ = 96.44i + 197.7 j

F_net = FJ + FA = 96.44i + 337.7j ....ANs

(B) magnitude = sqrt(96.44^2 + 337.7^2)  

= 351.2 N

direction = tan^-1(337.7/96.44) = 74 deg

(C) Fds = - F_net

= - 96.44i - 337.7 j N

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