While sliding a couch across a floor, Andrea and Jennifer exert forces F → A and F → J on the couch. Andrea's force is due north with a magnitude of 130.0 N and Jennifer's force is 32° east of north with a magnitude of 180.0 N. (a) Find the net force in component form. (b) Find the magnitude and direction of the net force. (c) If Andrea and Jennifer's housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force F → DS should they push so that the couch does not move?

Question

Physics

Craig Allison

20 September, 21:31

While sliding a couch across a floor, Andrea and Jennifer exert forces F → A and F → J on the couch. Andrea's force is due north with a magnitude of 130.0 N and Jennifer's force is 32° east of north with a magnitude of 180.0 N. (a) Find the net force in component form. (b) Find the magnitude and direction of the net force. (c) If Andrea and Jennifer's housemates, David and Stephanie, disagree with the move and want to prevent its relocation, with what combined force F → DS should they push so that the couch does not move?

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Reese · Answer 1

Andrea's force is due north with a magnitude of 130.0 N

F → A = (we have considered east as x axis and north as y axis)

Jennifer's force is 32° east of north

in vector form

F → J = 180 cos 58 i + 180 sin58 j

= 95.38 i + 152.64 j

Resultant force

= 130 j + 95.38 i + 152.64 j

b) = 95.38 i + 282.64 j

Magnitude of this vector

R² = 95.38² + 282.64²

R = 298.3 N

Tan θ = 95.38 / 282.64

θ = 18.64 °

c) one must exert an equal and opposite force equal to the resultant

that is 298.3 N to prevent the movement of the