Standing inside an elevator that accelerates upwards causes the passengers to experience their weight as:
Group of answer choices
Reduced by net motion
Decreased
The same as stationary
Increased
None of the Above
The correct answer and explanation is:
The correct answer is: Increased
When an elevator accelerates upward, the passengers inside experience an increased weight. This is because the elevator’s acceleration adds to the force of gravity.
To understand this, it’s important to think about the concept of apparent weight. In a stationary position, the force that the floor exerts on a person is equal to the person’s weight, which is the force of gravity acting on them. When the elevator accelerates upwards, however, the floor must exert an additional force to accelerate the passenger along with the elevator. This extra force adds to the gravitational pull, causing the passenger to feel heavier.
Mathematically, the total force (apparent weight) experienced by the passenger can be described as: Ftotal=m(g+a)F_{\text{total}} = m(g + a)
Where:
- mm is the mass of the person,
- gg is the acceleration due to gravity (approximately 9.8 m/s²),
- aa is the upward acceleration of the elevator.
As the elevator accelerates upwards, the apparent weight increases because the normal force exerted by the floor on the passenger is higher than when the elevator is stationary or moving at a constant speed. This increase in apparent weight can be felt as the person presses harder against the floor of the elevator.
In contrast, if the elevator were accelerating downward, the apparent weight would decrease. If the elevator were in free fall, the passenger would experience weightlessness, as the normal force would be zero.
Therefore, when the elevator accelerates upwards, the passenger feels their weight as increased.