To determine how much force the second mover needs to apply in order to push the couch up the ramp, we first analyze the forces acting on the couch.
- Force applied by the first mover: \( F_1 = 80 , \text{N} \) (to the right/up the ramp).
- Force of friction: \( F_{\text{friction}} = 110 , \text{N} \) (to the left/down the ramp).
Since the couch is sliding down the ramp, the total force acting on the couch in the direction of the ramp needs to be positive for it to move up.
Let \( F_2 \) be the force applied by the second mover. The net force \( F_{\text{net}} \) acting on the couch can be expressed as:
\[ F_{\text{net}} = F_1 + F_2 - F_{\text{friction}} \]
For the couch to move upward, we need \( F_{\text{net}} > 0 \). Setting up the inequality:
\[ 80 + F_2 - 110 > 0 \]
This simplifies to:
\[ F_2 - 30 > 0 \]
\[ F_2 > 30 \]
Therefore, the second mover must apply at least 31 N to ensure that the total force is positive.
Thus, the minimum force that the second mover needs to apply to help push the couch up the ramp is 31 N.
The correct answer is 31 N.