To determine how much force the second mover needs to apply, we first need to analyze the forces acting on the couch.
The first mover applies a force of 75 N to the right (up the ramp), while friction opposes this motion with a force of 110 N (down the ramp).
The net force acting on the couch can be calculated as follows:
\[ \text{Net force} = \text{Force applied by first mover} - \text{Force of friction} \]
Substituting the values:
\[ \text{Net force} = 75 , \text{N} - 110 , \text{N} = -35 , \text{N} \]
The negative sign indicates that the net force is directed down the ramp. To move the couch up the ramp, the total force applied (combined force of both movers) must overcome the frictional force.
To counteract the friction and achieve a net force of at least 0 N (to just start moving up the ramp), the total force applied by both movers must be equal to the frictional force of 110 N.
Let \( F_2 \) be the force applied by the second mover. Then we have:
\[ 75 , \text{N} + F_2 = 110 , \text{N} \]
Now, solving for \( F_2 \):
\[ F_2 = 110 , \text{N} - 75 , \text{N} \] \[ F_2 = 35 , \text{N} \]
Therefore, the second mover needs to apply a minimum force of 35 N to help push the couch up the ramp.
The correct answer is 35 N.