You step into an elevator, and it accelerates to a downward speed of \(9.2 \mathrm{m} / \mathrm{s}\) in \(2.1 \mathrm{s} .\) How does your apparent weight during this time compare with your actual weight?

Gravitational force is a fundamental natural force that attracts two bodies with mass towards each other. On Earth, this force gives us weight and is responsible for the acceleration objects experience when they fall freely towards the planet's surface. The standard acceleration due to gravity (\(g\)) is approximately \(9.81\text{ m/s}^{2}\) at the Earth's surface.

For any object with mass (\(m\)), its weight (\(w\)) due to the gravitational force can be calculated using the equation: \( w = mg \). It is important to note that weight is a force, measured in Newtons (N), while mass is a property of an object, measured in kilograms (kg). The concept of gravitational force is integral to understanding the notion of apparent weight, particularly when the frame of reference is accelerating, such as in an elevator.

Inertial forces, also known as fictitious or pseudo-forces, arise when the frame of reference is accelerating or decelerating. These forces are not 'real' forces in the sense that they do not originate from any physical interaction. Rather, they are perceived forces that stem from the inertia of a body — its tendency to resist changes in its state of motion.

In the context of the elevator problem, when the elevator accelerates downwards, the inertial force acts upwards. This inertial force affects your apparent weight, making you feel heavier or lighter depending on the direction and magnitude of the elevator's acceleration.

Feeling Lighter or Heavier in an Elevator

Thus, in an accelerating frame of reference like an elevator, these inertial forces can either add to or subtract from the gravitational force, altering the sensation of weight.

The acceleration due to gravity is not just a constant, but also a measure of the strength of gravity's pull on an object. At the Earth's surface, we typically use \(g = 9.81\text{ m/s}^{2}\) for calculations, but this value can change depending on altitude and the geographical location. Acceleration due to gravity dictates how quickly an object will gain speed when falling.

When you encounter a scenario where the acceleration is in the opposite direction to the gravitational pull (such as in the downward-accelerating elevator), the effects of gravity are countered. This means that at an acceleration of \( -9.81\text{ m/s}^{2} \) (opposite to the direction of gravitational pull), you would feel weightless because your body would be in free fall, experiencing no net force – the exact situation illustrated in the elevator problem.