Concept: What is the apparent weight for a person (mass m) standing on a scale inside an elevator with acceleration pointing upwards vs a=0?
net force up on person = force up from scale on feet - m g = m a
so
scale reads = m g + m a
if a = 0 of course the scale reads the weight, m g
The apparent weight of a person standing on a scale inside an elevator depends on the acceleration of the elevator. To understand this concept, let's consider two scenarios. In the first scenario, the elevator has an acceleration pointing upwards, while in the second scenario, the elevator's acceleration is zero (a = 0).
Scenario 1: Elevator Accelerating Upwards (a > 0)
When the elevator accelerates upwards, the person inside the elevator experiences an apparent weight that is greater than their actual weight. This is because the person is subject to two forces: their actual weight (due to gravity) and the upward force exerted by the elevator's acceleration. These forces combine to create the apparent weight.
To calculate the apparent weight in this scenario, we can use Newton's second law of motion, which states that the net force acting on an object is equal to the product of its mass and acceleration (F = m * a).
Applying this law:
- The downward force due to gravity is given by F_gravity = m * g, where m is the mass of the person and g is the acceleration due to gravity (~9.8 m/s²).
- The upward force exerted by the elevator is given by F_elevator = m * (g + a), where a is the acceleration of the elevator.
The apparent weight (W_apparent) is the force experienced by the person and can be calculated by subtracting the upward force from the downward force:
W_apparent = F_gravity - F_elevator
= m * g - m * (g + a)
= m * (g - g - a)
= m * (-a)
= -m * a
Therefore, the apparent weight of a person standing on a scale inside an elevator accelerating upwards is equal to their actual weight minus the product of their mass and the acceleration of the elevator (W_apparent = -m * a). The apparent weight is negative because it acts in the opposite direction to the elevator's acceleration.
Scenario 2: Elevator Not Accelerating (a = 0)
When the elevator is not accelerating (a = 0), the person inside the elevator experiences an apparent weight that is equal to their actual weight. In this scenario, the person only experiences their actual weight due to the force of gravity pulling them downwards.
Therefore, the apparent weight of a person standing on a scale inside an elevator with no acceleration is equal to their actual weight (W_apparent = m * g), where m is the mass of the person and g is the acceleration due to gravity.