M013 · Forces & contact

Elevator Scale & Apparent Weight

Program a lift, compare constant speed with acceleration, release the drive and follow separation, return impacts and the work of a moving support.

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 ledger residual $\text{Ready}$

Recorded sensor rows $\text{Ready}$

PROGRAM / ACQUIRE / COMPARE

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; acceleration jumps instantaneously. The car is an externally driven open test lift: the drive can push downward as well as pull upward. Release removes that drive and prescribes ideal free fall. This is not a cable-elasticity or safety model.

Up is positive. Position tracks passenger feet and the scale surface; the rigid passenger has a constant centre-of-mass offset. The floor only pushes. Separation follows exact ballistic arcs, then a perfectly inelastic return resets the relative velocity. There is no ceiling, ground, air resistance or compliant body model.

An ideal return impact has a finite impulse and zero duration. The event table reports it separately. The force curve shows only regular support; a sensor sample exactly at an impact is missing, never a made-up peak. Other samples have bounded deterministic additive error; they are not real sensor data.

The work ledger includes continuous support work and work transferred by the moving floor during impacts, minus relative kinetic energy dissipated. A zero support reading does not remove gravitational force. Prescribed drive work can be positive or negative.

Acquire stores only sampled force and timestamps. Replay preserves that record; changing the motion or sensor clears it. Export includes every raw row, while the table previews at most the first and last 80. Gold clock and keyboard sliders remain available without WebGL. No autoplay.

Ideal mechanics, explicit contact and measurement boundaries.

Start with the essentials

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

Core mathematical model

Support is conditional

N-mg=ma_p,\qquad N\geq0

The support equals the required constraint force only while the passenger touches the floor.

Relative flight

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

Exact constant-acceleration arcs locate the next closing contact.

Inelastic return

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

The floor velocity is externally prescribed; impact duration is zero.

Moving-floor energy ledger

\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}

Impact work and dissipation both matter when the floor moves.

Common difficulties

Read the force correctly

Typical misconceptionA downward-moving elevator always makes you lighter.

Better mental modelConstant speed gives ordinary support in either direction. Acceleration changes support. Faster-than-free-fall downward drive creates a gap; returning contact creates 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 moving scale can read the ordinary weight.
02
Program the lift
Drag a command below free-fall acceleration in Leave and return.
What to observe: The load separates instead of receiving a negative support force.
03
Inspect the event
Scrub the gold clock around the listed return time.
What to observe: Velocity changes by an impulse while positions remain continuous.
04
Keep acquisition honest
Acquire the scale record and export it.
What to observe: Regular force samples and instantaneous event impulses are distinct.

Core mathematical model

Support is conditional

Relative flight

Inelastic return

Moving-floor energy ledger

Common difficulties

Read the force correctly

Run the experiment

Speed or acceleration?

Program the lift

Inspect the event

Keep acquisition honest