The potential energy will decrease
Explanation:
The gravitational potential energy of an object is the energy possessed by the object due to its position in the gravitational field, and it is given by the equation
where
m is the mass of the object
g is the acceleration of gravity
h is the height of the object with respect a reference level (usually, ground level)
In this problem, we have a ball that is knocked off a shelf and falls to the floor. As the ball falls to the floor, its altitude decreases. As we see from the equation, the potential energy is directly proportional to the altitude: therefore, as the altitude decreases, the potential energy of the ball will decrease as well.
However, the total mechanical energy of the ball, in absence of air resistance, will remain constant:
E = PE + KE = constant
where KE is the kinetic energy of the ball: this means that during the fall, the potential energy of the ball will be converted into kinetic energy (which is the energy of motion: in fact, the speed of the ball will keep increasing).
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