Question23. While sliding a couch across a floor, Andrea and Jennifer exert forces $\vec{F}_{A}$ and $\vec{F}_{J}$ on the couch. Andrea's force is due north with a magnitude of 130.0 N and Jennifer's force is $32^{\circ}$ 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 $\vec{F}_{D S}$ should they push so that the couch does not move?

Studdy Solution
Calculate the force required by David and Stephanie to prevent the couch from moving.
David and Stephanie need to exert a force $\vec{F}_{DS}$ that is equal in magnitude but opposite in direction to $\vec{F}_{\text{net}}$ .
Thus: $\vec{F}_{DS} = -\vec{F}_{\text{net}}$
This means: $F_{DS_x} = -F_{\text{net}_x}$ $F_{DS_y} = -F_{\text{net}_y}$

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