Final answer:
A mass on a positive slope of a potential energy curve exerts a force in the negative slope direction because the force is the negative of the derivative of potential energy, propelling the mass toward a lower potential energy and stable equilibrium.
Step-by-step explanation:
When dealing with a mass, m, resting on a positive slope of a potential energy curve, which is in the shape of a parabola, it is observed that the mass exerts a force in the direction opposite to that of the positive slope, also known as the negative slope direction. This is because the force on an object is related to the potential energy by the equation F = -dU/dx, where F is the force, U is the potential energy, and dU/dx is the derivative of the potential energy with respect to position, or in other words, the slope of the potential energy curve.
The negative sign indicates that the force is in the opposite direction to the increase in potential energy. A positive slope on the potential energy curve means that the potential energy increases with increasing position. Thus, the force that results is in the negative direction, pushing the mass back toward a position of lower potential energy, which is often associated with a stable equilibrium point.