Final answer:
The relationship is F=ma, where F is the force, m is the mass, and a is the acceleration; for gravity, it is W=mg, where W is the weight and g is the acceleration due to gravity.
Step-by-step explanation:
The mathematical relationship between the force of gravity acting on an object, its mass, and its acceleration according to Newton's second law of motion is F=ma, where F represents the net external force acting on the object, m represents the mass of the object, and a represents the acceleration of the object. For an object falling towards Earth under the influence of gravity alone, this acceleration is due to gravitational force, which is represented by g, the acceleration due to gravity. Therefore, the weight W of an object, which is the gravitational force acting on it, can be written as W=mg, showing that weight is equivalent to the force of gravity acting on the object.