When an elevator is moving up with an acceleration equal to gravity (g), the apparent weight of a body inside the elevator can be different from its actual weight. The apparent weight refers to the force experienced by the body due to its interaction with the elevator.
To determine the apparent weight, we need to consider the forces acting on the body inside the elevator. There are two main forces involved: the gravitational force (weight) and the normal force.
- Gravitational Force (Weight): The weight of the body is the force exerted on it due to gravity. It is given by the formula:
Weight = mass × acceleration due to gravity (g)
- Normal Force: The normal force is the force exerted by a surface to support the weight of an object resting on it. In this case, the normal force is the force exerted by the elevator floor on the body.
When the elevator is moving up with an acceleration equal to gravity, the normal force will be greater than the weight of the body to provide the necessary upward acceleration.
Therefore, the apparent weight of the body in the elevator will be the sum of the weight and the additional force due to the acceleration:
Apparent weight = Weight + Force due to acceleration
Apparent weight = Weight + mass × acceleration
Apparent weight = mass × g + mass × g
Apparent weight = 2 × mass × g
In summary, when an elevator is moving up with an acceleration equal to gravity, the apparent weight of a body inside the elevator is twice its actual weight (2 × weight).