If the elevator cable breaks and it falls freely, what would the scale read?

In free fall, both the elevator and the person accelerate downward at a = g. Substituting into N = m(g - g) gives N = 0. The scale would read zero, a state called 'weightlessness.' The person's mass and Earth's gravity are unchanged, but there is no contact force from the scale, making their apparent weight zero.

Is my actual mass changing when the elevator accelerates?

No. Your mass (the amount of matter) is constant. The scale measures force, not mass directly. It is calibrated for Earth's gravity (9.8 m/s²) to display mass. When the elevator accelerates, the force it measures changes, so the converted 'mass' reading changes, but your true mass remains the same.

Does this only happen in elevators?

No, apparent weight changes occur in any accelerating frame. You feel heavier at the bottom of a roller coaster loop (upward acceleration) and lighter at the top. Astronauts experience weightlessness in orbit because they are in continuous free fall around Earth. The elevator is a simple, relatable example of a broader principle.

Why does the scale read my normal weight when the elevator moves at constant speed?

Constant speed means zero acceleration (a=0). From Newton's second law, N - mg = m*0, so N = mg. The forces are balanced, just as when you are stationary on the ground. The reference frame is inertial, so the laws of physics are the same as in a stationary frame.

Elevator Physics

An elevator ride provides a classic demonstration of Newton's second law and the concept of apparent weight. This simulator models a person standing on a bathroom scale inside an accelerating elevator. The scale reading, which corresponds to the normal force exerted by the scale on the person, changes depending on the elevator's motion. When the elevator accelerates upward, the scale reads more than the person's actual weight (mg). During downward acceleration, it reads less. If the elevator moves with constant velocity (including being at rest), the scale reads exactly the person's weight, as the net force is zero. The core physics is governed by Newton's second law: ΣF = ma. Applying this to the vertical direction gives N - mg = ma, where N is the normal force (scale reading), m is mass, g is gravitational acceleration, and a is the elevator's acceleration (positive upward). Solving for the apparent weight yields N = m(g + a). The simulator simplifies reality by assuming a constant gravitational field, a perfectly rigid elevator and scale, and ignoring air resistance or the brief jerk during startup and stopping. By interacting with this model, students directly observe the relationship between acceleration, force, and apparent weight, solidifying their understanding of inertial frames and non-inertial (accelerating) reference frames.

Who it's for: High school and introductory college physics students learning Newton's laws of motion, forces, and free-body diagrams.

Key terms

Apparent weight
Normal force
Newton's second law
Acceleration
Free-body diagram
Inertial frame
Non-inertial frame
Weight

How it works

Standing on a scale in an elevator, you measure the normal force N. In the ground (inertial) frame, N − mg = ma when the elevator accelerates upward with acceleration a, so N = m(g + a). If the cable snaps and the cabin falls freely, a = −g and N = 0 — you feel weightless.

Key equations

N − mg = ma ⇒ N = m(g + a)

Free fall: a = −g → N = 0

Frequently asked questions

If the elevator cable breaks and it falls freely, what would the scale read?: In free fall, both the elevator and the person accelerate downward at a = g. Substituting into N = m(g - g) gives N = 0. The scale would read zero, a state called 'weightlessness.' The person's mass and Earth's gravity are unchanged, but there is no contact force from the scale, making their apparent weight zero.
Is my actual mass changing when the elevator accelerates?: No. Your mass (the amount of matter) is constant. The scale measures force, not mass directly. It is calibrated for Earth's gravity (9.8 m/s²) to display mass. When the elevator accelerates, the force it measures changes, so the converted 'mass' reading changes, but your true mass remains the same.
Does this only happen in elevators?: No, apparent weight changes occur in any accelerating frame. You feel heavier at the bottom of a roller coaster loop (upward acceleration) and lighter at the top. Astronauts experience weightlessness in orbit because they are in continuous free fall around Earth. The elevator is a simple, relatable example of a broader principle.
Why does the scale read my normal weight when the elevator moves at constant speed?: Constant speed means zero acceleration (a=0). From Newton's second law, N - mg = m*0, so N = mg. The forces are balanced, just as when you are stationary on the ground. The reference frame is inertial, so the laws of physics are the same as in a stationary frame.

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