To determine the minimum force that the second mover needs to apply to help push the couch up the ramp, we need to consider the forces acting on the couch.
Currently, one mover is applying a force of 80 N to the right (up the ramp), and the force of friction opposing this motion is 110 N down the ramp.
The net force acting on the couch can be calculated as follows:
Net force = Applied force - Friction force Net force = 80 N (up) - 110 N (down) Net force = 80 N - 110 N = -30 N
This means that the couch is experiencing a net force of 30 N downward (it is sliding down the ramp). Therefore, to overcome this downward force of 30 N and to push the couch up the ramp, the second mover will need to apply a force that is at least equal to this net force.
Thus, the second mover will need to apply at least 30 N in addition to the existing 80 N to achieve a net upward force.
If the second mover applies 30 N, the total applied force would be:
Total applied force = 80 N (first mover) + 30 N (second mover) = 110 N
This would balance out the friction force, allowing the couch to stay still. Therefore, the second mover will need to apply at least:
30 N
to help push the couch up the ramp. Hence, the answer is 30 N.