To determine how much force the second mover needs to apply, we can analyze the forces acting on the couch.
Currently, one mover is applying a force of 80 N forward (up the ramp), while friction is opposing this movement with a force of 110 N backward (down the ramp). The net force acting on the couch can be calculated as follows:
Net force = Force applied by mover 1 - Force of friction Net force = 80 N (up) - 110 N (down) = -30 N
The negative value indicates that there is a net force of 30 N acting down the ramp, meaning the couch is sliding down the ramp.
To move the couch up the ramp, we need the total upward force (from both movers) to exceed the force of friction (110 N). If we denote the force applied by the second mover as \( F_2 \), we can set up the following equation for the total force when both movers push:
Total force = Force applied by mover 1 + Force applied by mover 2 Total force = 80 N + \( F_2 \)
For the couch to move up the ramp, this total force must overcome the frictional force:
80 N + \( F_2 \) > 110 N
To find the minimum force \( F_2 \) required to achieve this, we solve the inequality:
\( F_2 > 110 N - 80 N \) \( F_2 > 30 N \)
Since we are looking for the minimum force the second mover needs to exert, the smallest whole number that satisfies this inequality is:
31 N
Therefore, the answer is 31 N.
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