M013 · Forces & contact

Elevator Scale & Apparent Weight

When does a scale stop measuring your weight? Whenever the lift accelerates. A scale measures how hard it pushes up on you, not gravity itself. It reads more when the lift accelerates upward, less when it accelerates downward, and zero in free fall, when gravity still acts but nothing pushes back.

Program a lift and compare riding at constant speed with accelerating. Then release the drive and follow the passenger leaving the scale, the impacts on landing and the work done by the moving floor.

Contact state $\text{Ready}$

Selected time $\text{Ready}$

Scale support force $\text{Ready}$

Gravitational force magnitude $\text{Ready}$

Support ratio $\text{Ready}$

Floor height $\text{Ready}$

Passenger foot height $\text{Ready}$

Foot–scale gap $\text{Ready}$

Floor acceleration, upward positive $\text{Ready}$

Passenger velocity, upward positive $\text{Ready}$

Impacts up to clock $\text{Ready}$

Latest impact impulse $\text{Ready}$

Impact dissipation up to clock $\text{Ready}$

Mechanical energy balance residual $\text{Ready}$

Recorded sensor rows $\text{Ready}$

Program a ride and read the scale

Follow the support

Passenger mass

m

75.00\,kg

Recording duration

T

8.00\,s

Initial lift and passenger velocity

v_0

0.00\,\frac{\mathrm m}{\mathrm s}

Acceleration interval 1

a_{f,1}

2.00\,\frac{\mathrm m}{\mathrm s^2}

Acceleration interval 2

a_{f,2}

0.00\,\frac{\mathrm m}{\mathrm s^2}

Acceleration interval 3

a_{f,3}

0.00\,\frac{\mathrm m}{\mathrm s^2}

Acceleration interval 4

a_{f,4}

-2.00\,\frac{\mathrm m}{\mathrm s^2}

Acceleration interval 5

a_{f,5}

0.00\,\frac{\mathrm m}{\mathrm s^2}

Drive: continuous / released

R

0.00\,

Release fraction of run

\tau_r

0.40\,

Bound on force error

\epsilon_N

0.00\,N

Gravity magnitude

g

9.80\,\frac{\mathrm m}{\mathrm s^2}

Sensor sampling rate

f_s

10.00\,Hz

Deterministic error seed

s

17.00\,

Replay fraction

\tau

0.20\,

Drag the five blue acceleration handles or use their sliders. Each command lasts one fifth of the run, and the acceleration jumps instantly from one command to the next. The car is an open test lift driven from outside, and the drive can push down as well as pull up. Release removes the drive and puts the car in ideal free fall. This is not a model of cable elasticity or of a safety system.

Up is positive. Position follows the passenger's feet and the scale surface; the passenger is rigid, with a fixed offset from the feet to the centre of mass. The floor can only push. Once separated, the passenger follows an exact ballistic arc, and the landing is perfectly inelastic, which sets the relative velocity back to zero. There is no ceiling, ground or air resistance, and the body does not deform.

An ideal landing impact has a finite impulse and zero duration, and the event table lists it separately. The force curve shows only the ordinary support force. A sensor sample that falls exactly on an impact is left blank, never filled with a made-up peak. The other samples carry a bounded, deterministic added error; they are not real sensor data.

The work total adds the work the support does continuously and the work the moving floor transfers during impacts, then subtracts the relative kinetic energy dissipated. A zero scale reading does not mean gravity has stopped acting. The prescribed drive can do positive or negative work.

Acquire stores only the sampled force and its timestamps. Replay keeps that record; changing the motion or the sensor clears it. The export includes every raw row, while the table previews at most the first and last 80. Without WebGL the gold clock and keyboard sliders still work. Nothing plays automatically.

The mechanics are ideal. The page states exactly how contact is handled and what the scale measures.

Start with the essentials

Focus question: When does a scale stop measuring your weight?
One-sentence intuition: A floor can push a passenger up, but it cannot pull a passenger down.

Core mathematical model

Support force while in contact

N-mg=ma_p,\qquad N\geq0

The support takes whatever value the motion requires, but only while the passenger touches the floor.

Flight relative to the floor

\begin{aligned}r&=y_p-y_f\geq0\\\ddot r&=-g-a_f\quad(N=0)\end{aligned}

The accelerations are constant, so exact arcs give the moment the gap closes again.

Perfectly inelastic landing

\begin{aligned}J&=m(v_f-v_p^-)\\Q&=\tfrac12m(v_p^--v_f)^2\end{aligned}

The floor's velocity is prescribed from outside, and the impact takes zero time.

Energy balance with a moving floor

\begin{aligned}\Delta(K+U)&=\int N\,\mathrm d y_f\\&\quad+\sum_i J_i v_{f,i}-\sum_i Q_i\end{aligned}

When the floor moves, both the work done during impacts and the energy dissipated in them count.

Common difficulties

Moving down is not the same as accelerating

Typical misconceptionWhenever the elevator goes down, I get lighter.

Better mental modelAt constant speed, up or down, the scale reads your ordinary weight. Only acceleration changes the reading. If the drive pulls the floor down faster than free fall, a gap opens. When you land again, the contact delivers an impulse, not a finite force peak.

Run the experiment

01
Speed or acceleration?
Compare Constant upward speed with Start / cruise / brake.
What to observe: A scale that is moving can still read your ordinary weight.
02
Program the lift
In Leave and return, drag one command below free-fall acceleration.
What to observe: The passenger lifts off the scale instead of feeling a negative support force.
03
Look closely at the landing
Drag the passenger around the return time listed under Acquisition and diagnostics.
What to observe: The velocity jumps because of an impulse, while the positions stay continuous.
04
Record the scale data
Open Acquisition and diagnostics to acquire or export the scale record.
What to observe: The regular force samples and the instantaneous impact impulses are kept separate.

Core mathematical model

Support force while in contact

Flight relative to the floor

Perfectly inelastic landing

Energy balance with a moving floor

Common difficulties

Moving down is not the same as accelerating

Run the experiment

Speed or acceleration?

Program the lift

Look closely at the landing

Record the scale data