Two movers are attempting to push a couch up a ramp. One mover applies a force of 80 N to the right, but the force of friction between the couch and the ramp is providing a force of 110 N in the opposite direction, and the couch slides down the ramp.

To determine the minimum force the second mover needs to apply, we first need to calculate the net force acting on the couch.

The first mover applies a force of 80 N to the right, while the force of friction opposes this motion with a force of 110 N to the left.

The net force (F_net) can be calculated as follows:

\[ F_{\text{net}} = F_{\text{applied}} - F_{\text{friction}} \]

Substituting the known values:

\[ F_{\text{net}} = 80 , \text{N} - 110 , \text{N} = -30 , \text{N} \]

The negative sign indicates that the couch is sliding down the ramp.

To push the couch up the ramp, the net force must be at least zero. Therefore, the total force exerted by both movers must overcome the frictional force of 110 N.

Let \( F_2 \) be the force applied by the second mover. Therefore, the equation for the total force becomes:

\[ F_{\text{total}} = 80 , \text{N} + F_2 \]

To achieve a net force of zero when overcoming friction, we set:

\[ F_{\text{total}} = F_{\text{friction}} \]

\[ 80 , \text{N} + F_2 = 110 , \text{N} \]

Now, solving for \( F_2 \):

\[ F_2 = 110 , \text{N} - 80 , \text{N} = 30 , \text{N} \]

Thus, the minimum force the second mover needs to apply to help push the couch up the ramp is 30 N.