Final Answer:
When applying Newton's second law to a man riding an elevator to calculate his acceleration, we must consider the gravitational force (mg) and the normal force (N) exerted by the elevator floor. These forces play a crucial role in determining the net force acting on the person and subsequently their acceleration.
Step-by-step explanation:
In this scenario, Newton's second law (ΣF = ma) is applicable, where ΣF is the net force acting on the person, m is the mass of the person, and a is the acceleration. The force of gravity (mg) acts vertically downward, and the normal force (N) acts perpendicular to the elevator floor. When the elevator accelerates, these forces contribute to the net force experienced by the person.
The gravitational force is given by mg, where m is the mass of the person (in kilograms) and g is the acceleration due to gravity (approximately 9.8 m/s²). The normal force N is equal to mg in the absence of any additional vertical forces.
The net force (ΣF) can be calculated by considering the difference between the gravitational force and the normal force: ΣF = mg - N. If the elevator is accelerating upward, the normal force is smaller than the gravitational force, resulting in a net force in the upward direction. Conversely, if the elevator is accelerating downward, the normal force exceeds the gravitational force, creating a net force in the downward direction.
Understanding these forces and their interplay is essential for accurately determining the acceleration experienced by the person riding the elevator. This application of Newton's second law illustrates the practicality of physics in analyzing real-world scenarios involving forces and motion.