Final answer:
To calculate the net force exerted by Andrea and Jennifer, their individual forces need to be resolved into components and added together. The resulting net force's magnitude and direction can then be determined using the Pythagorean theorem and trigonometry. David and Stephanie need to exert an equal and opposite combined force to prevent the couch from moving.
Step-by-step explanation:
To solve for the net force in component form, we first need to break down Andrea's and Jennifer's forces into their x (east-west) and y (north-south) components. Andrea's force is directly north, so her force is 0 N in the x-direction and +130.0 N in the y-direction. Jennifer's force can be broken down using trigonometry: F₁x = F₁ × cos(32°) and F₁y = F₁ × sin(32°).
To find the net force in component form:
- Fnet,x = F₁x + Fᴇx
- Fnet,y = F₁y + Fᴇy
Then calculate the magnitude and direction of the net force:
- Magnitude: √((Fnet,x)^2 + (Fnet,y)^2)
- Direction: tan-1(Fnet,y/Fnet,x)
If David and Stephanie want to prevent the couch from moving, their combined force (FDS) should be equal in magnitude and opposite in direction to the net force applied by Andrea and Jennifer. This is based on Newton's third law — for every action (force) in nature there is an equal and opposite reaction.