To determine the minimum force the second mover needs to apply to help push the couch up the ramp, we can start by considering the forces acting on the couch.
Currently, the first mover applies a force of 100 N to the right, and there is a friction force of 140 N acting in the opposite direction (to the left).
Let's calculate the net force acting on the couch with just the first mover:
- Force applied by mover 1: \( +100 , \text{N} \)
- Force of friction: \( -140 , \text{N} \)
The net force acting on the couch is:
\[ \text{Net force} = 100 , \text{N} - 140 , \text{N} = -40 , \text{N} \]
This negative net force indicates that the couch is sliding down the ramp with a force of 40 N acting downwards.
To move the couch up the ramp, the second mover will need to apply enough force to overcome both the existing force of friction (140 N) and the 100 N already applied by the first mover.
In order to achieve a net force that is greater than 0 (to push the couch upwards), we can set up the following equation:
Let \( F \) be the force applied by the second mover. The total force moving the couch upwards would be:
\[ \text{Total upward force} = 100 , \text{N} + F \]
For the couch to slide upwards, this total upward force must be greater than the force of friction (140 N):
\[ 100 , \text{N} + F > 140 , \text{N} \]
To find the minimum force \( F \):
\[ F > 140 , \text{N} - 100 , \text{N} \] \[ F > 40 , \text{N} \]
Therefore, the minimum force the second mover will need to apply is slightly more than 40 N. Among the given options, the closest choice that meets this requirement is:
D. 41 N
Thus, the correct answer is D. 41 N.
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