Compare how your weight, mass, and the normal force exerted by the floor change when you are in an elevator that starts from rest and accelerates upward.
F = m A
when at rest.
Force down on floor =weight = m g
Force up from floor on shoes = m g
Force up - Force down = 0 so A = 0
when accelerating upward the force up from floor on shoes must be greater thsn the force down, m g
Fup - m g = m A
so
Fup = m g + m A
When you are in an elevator that starts from rest and accelerates upward, your weight, mass, and the normal force exerted by the floor all experience changes. Let's break down each one:
1. Weight: Weight is the force with which the Earth pulls you toward its center. It is given by the equation W = mg, where W is the weight, m is the mass, and g is the acceleration due to gravity (approximately 9.8 m/s²).
When the elevator accelerates upward, you might feel heavier. This is because the force of acceleration adds to the force of gravity. So, your weight will temporarily increase while the elevator is accelerating.
2. Mass: Mass is the amount of matter in your body. It is a constant property and does not change in different environments. Mass is usually measured in kilograms (kg) and is independent of gravity or any external forces. So, your mass will remain the same regardless of being in an elevator or anywhere else.
3. Normal force: The normal force is the force exerted by a surface to support the weight of an object on it. When you are standing on the floor of an elevator, the normal force is equal and opposite to your weight, which prevents you from sinking through the floor.
As the elevator accelerates upward, the normal force will also change. Initially, when the elevator is at rest, the normal force is equal to your weight. However, when the elevator starts to accelerate upward, the normal force will increase to counterbalance the increase in your weight caused by the acceleration. This ensures that you stay in contact with the floor and do not float.
To summarize, when you are in an elevator that starts from rest and accelerates upward:
- Your weight temporarily increases due to the added force of acceleration.
- Your mass remains constant and does not change.
- The normal force exerted by the floor increases to counterbalance the increase in weight caused by the acceleration.