To determine the minimum force that the second mover needs to apply in order to move the couch up the ramp, we need to consider the forces acting on the couch.
- Force applied by the first mover: 80 N to the right
- Force of friction: 110 N acting to the left (down the ramp)
If the first mover is applying 80 N to the right, and the couch is still sliding down, this means that the net force acting on the couch is still in the direction of the friction (to the left).
Let \( F_2 \) be the force applied by the second mover to the right.
The total force being applied to the right will then be: \[ F_{\text{total}} = F_1 + F_2 = 80 , \text{N} + F_2 \]
The total force acting to the left (friction) is 110 N.
To move the couch up the ramp, the total force to the right must be greater than the force of friction: \[ F_{\text{total}} > 110 , \text{N} \] which means: \[ 80 , \text{N} + F_2 > 110 , \text{N} \]
Subtracting 80 N from both sides gives: \[ F_2 > 30 , \text{N} \]
Therefore, the second mover must apply at least 31 N (to exceed 30 N) to successfully push the couch up the ramp.
So the answer is: 31 N