Apparent Weight in Elevator – HSC Physics
This topic is part of the HSC Physics course under the section Forces, Acceleration and Energy.
HSC Physics Syllabus
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explore the concept of net force and equilibrium in one-dimensional and simple two-dimensional contexts using: (ACSPH050)
– algebraic addition– vector addition– vector addition by resolution into components
- investigate, describe and analyse the acceleration of a single object subjected to a constant net force and relate the motion of the object to Newton’s Second Law of Motion through the use of: (ACSPH062, ACSPH063)
Concept of Apparent Weight in Moving Elevator Explained
In this video, we will discuss the concept of apparent weight in an elevator influenced by its acceleration with practice calculation problems.
True Weight vs Apparent Weight
When you stand on a scale in an elevator, the value displayed is your apparent weight — the force the scale exerts upward on you. This force changes with the motion of the elevator, specifically with its acceleration.
True weight is the gravitational force acting on your body:
$$W = mg$$
Newton’s Laws and Apparent Weight
Newton’s Second Law
Newton’s second law states:
$$F_{\text{net}} = ma$$
In the vertical direction, for a person standing in an elevator:
$$F_N - mg = F_{\text{net}} = ma \quad \Rightarrow \quad F_N = m(g + a)$$
where:
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is the normal force (apparent weight),
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is the acceleration of the elevator (positive if upward, negative if downward).
This expression for normal force is important in determining and comparing the apparent force measured in an elevator when it's moving at constant speed, accelerating upwards or accelerating downwards.
Newton’s Third Law
Newton’s third law states that every action there is an equal and opposite reaction. If you (weight force) push down on the scale, the scale pushes up on you with the same force (normal force). That upward normal force is what gets displayed as your apparent weight, and varies depending on the net force and acceleration of the elevator and objects inside it.
When the elevator is stationary or moving at constant speed (i.e. zero acceleration):
$$F_N = m(g + 0) = mg$$
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Apparent weight equals true weight.
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Net force is zero; the system is in equilibrium.
When the elevator is accelerating upwards, the net force acting on the elevator and the person inside it (standing on a scale) is positive. Since the weight force cannot change, the normal force exerted on the person by the scale must increase to allow for this.
Since the weight displayed by the scale is dependent on the normal force, the apparent weight becomes greater than true weight. A person standing a the scale would feel heavier. This is true in both cases of the elevator moving upwards or downwards (either positive or negative velocity).
$$F_N = m(g + a)$$
where `a > 0`.
When elevator is accelerating in the downward direction (negative), the net force acting on the elevator and objects inside it becomes negative. Again, since the weight force of the person remains unchanged, the normal force exerted by the scale on the person must decrease and become smaller than the weight force.
$$F_N = m(g + a)$$
where `a < 0` causing `F_N` to be reduced such that:
$$F_N < mg$$
In this instance, the apparent weight is less than the true weight. A person standing on the scale would feel lighter.
It is important to understand that the apparent weight depends on the acceleration of the elevator, not its velocity. This means the variation of apparent force depends on whether the acceleration is positive or negative, regardless whether the elevator is moving upwards (positive velocity) or downwards (negative velocity).
Positive acceleration increases the apparent weight, and negative acceleration decreases the apparent weight.