Answer
See the detailed answer below.
Work Step by Step
In this problem, we analyze the force between two nucleons by examining the slope of the potential energy graph.
The force between two nucleons is determined by the negative of the slope of the potential energy graph,
$$ F = -\dfrac{dU}{dr} $$
This means that where the slope of the potential energy curve is steepest, the force is strongest.
$\bullet$ The force is zero at $ r = 1.0 \, \text{fm} $, where the potential energy $ U $ reaches its maximum negative value. At this point, the nucleons are in a stable equilibrium because there is no net force pushing them closer or pulling them apart.
$\bullet$ The maximum force occurs at $ r = 1.5 \, \text{fm} $, where the slope of the potential energy curve reaches its maximum value. This force is about $ -8900 \, \text{N} $, as we found it in the previous problem, indicating a strong attractive force pulling the nucleons together.
$\bullet$ For distances less than $ 1.0 \, \text{fm} $, the slope of the potential energy curve is negative, meaning that the force is positive. This represents a repulsive force pushing the nucleons apart, as they are too close.
$\bullet$ For distances greater than $ 1.0 \, \text{fm} $, the slope is positive, so the force becomes negative, which corresponds to an attractive force, pulling the nucleons toward each other.
