Interactive workbench

Figluma mechanics worksheet

Passenger in an accelerating elevator

A 65 kg passenger stands on a scale in an elevator accelerating upward at 1.8 m s^-2. Find the scale reading.

MechanicsNewton's lawsApparent weightVertical motion

Diagram State

Elevator passenger on a scale with upward normal force, downward weight, and upward acceleration.

  • elevator cab
  • passenger
  • scale
  • normal force
  • weight
  • upward acceleration
  • vertical axis

Givens

SymbolQuantityValueUnit
Passenger masskg
Elevator acceleration upwardm s^-2
Gravitational field strengthm s^-2

Unknowns

SymbolQuantityValueUnit
Scale reading / normal forceN

Coordinate System / Sign Convention

+y is upward, in the direction of the elevator's acceleration.

Assumptions / Constraints Checklist

  • The passenger is at rest relative to the elevator floor, so the passenger shares the elevator's acceleration.
  • The scale reading is the normal force exerted by the scale on the passenger.
  • The elevator acceleration is constant during the instant modeled.
  • Air resistance is negligible.
  • The passenger has the same upward acceleration as the elevator.
  • The normal force points upward and the weight mg points downward.
  • The scale reads force in newtons, not mass in kilograms.
  • With +y upward, the vertical Newton's law equation is N - mg = ma.

Student Solve Checklist

Mark each row only after your setup matches the diagram state; worked equations stay in the teacher key.

  • Choose the upward vertical axis
  • Identify the passenger forces
  • Apply Newton's second law vertically
  • Solve for the scale forceSubstitute values

Student Working Area

Solution / Answer Key

  1. 1. Choose the upward vertical axis

    The elevator accelerates upward, so choosing +y upward makes the acceleration positive.

    Equation-choice checkWhat feature of the diagram, sign convention, or givens makes "Choose the upward vertical axis" the right next equation?Listen for: The elevator accelerates upward, so choosing +y upward makes the acceleration positive.Flag if: Student can only quote "+y = upward" without connecting it to the diagram state or givens.

  2. 2. Identify the passenger forces

    The scale pushes up on the passenger with normal force N. Gravity pulls down with weight mg.

    Equation-choice checkWhat feature of the diagram, sign convention, or givens makes "Identify the passenger forces" the right next equation?Listen for: The scale pushes up on the passenger with normal force N. Gravity pulls down with weight mg.Flag if: Student can only quote "Forces on passenger: N upward, mg downward" without connecting it to the diagram state or givens.

  3. 3. Apply Newton's second law vertically

    Normal force is positive and weight is negative on the chosen axis. The net upward force equals ma.

    Equation-choice checkWhat feature of the diagram, sign convention, or givens makes "Apply Newton's second law vertically" the right next equation?Listen for: Normal force is positive and weight is negative on the chosen axis. The net upward force equals ma.Flag if: Using N = mg and ignoring the upward acceleration.

  4. 4. Solve for the scale force

    Rearranging the vertical equation shows the scale must support weight and provide the extra upward acceleration.

    Equation-choice checkWhat feature of the diagram, sign convention, or givens makes "Solve for the scale force" the right next equation?Listen for: Rearranging the vertical equation shows the scale must support weight and provide the extra upward acceleration.Flag if: Subtracting ma from mg for an upward-accelerating elevator.; Reporting 65 kg as the scale reading instead of converting the force model to newtons.

  5. 5. Substitute values

    The upward acceleration makes the scale reading larger than the passenger's weight. The scale reads about 7.5e2 N.

    Equation-choice checkWhat feature of the diagram, sign convention, or givens makes "Substitute values" the right next equation?Listen for: The upward acceleration makes the scale reading larger than the passenger's weight. The scale reads about 7.5e2 N.Flag if: Student can only quote "N = 65(9.8 + 1.8) = 754 N" without connecting it to the diagram state or givens.

Diagnostic Checklist

Key checkpoint equations

  1. 1. Choose the upward vertical axis
  2. 2. Identify the passenger forces
  3. 3. Apply Newton's second law vertically
  4. 4. Solve for the scale force
  5. 5. Substitute values

Common Wrong Paths

  • Using N = mg and ignoring the upward acceleration.
  • Subtracting ma from mg for an upward-accelerating elevator.
  • Reporting 65 kg as the scale reading instead of converting the force model to newtons.
  • Treating g + a as a speed or acceleration answer instead of multiplying by mass.
  • Putting the normal force downward in the free-body diagram.
  • Using N + mg = ma, which gives weight and normal force the same direction.

Wrong Answer Signals

  • Using N = mg and ignoring the upward acceleration.Usually indicates the "Apply Newton's second law vertically" checkpoint needs review.
  • Subtracting ma from mg for an upward-accelerating elevator.Usually indicates the "Solve for the scale force" checkpoint needs review.
  • Reporting 65 kg as the scale reading instead of converting the force model to newtons.Usually indicates the "Solve for the scale force" checkpoint needs review.
  • Treating g + a as a speed or acceleration answer instead of multiplying by mass.Usually indicates the "Solve for the scale force" checkpoint needs review.
  • Putting the normal force downward in the free-body diagram.Usually indicates the "Solve for the scale force" checkpoint needs review.
  • Using N + mg = ma, which gives weight and normal force the same direction.Usually indicates the "Solve for the scale force" checkpoint needs review.

Tutor Marking Rubric

Tutor score rows use curated Figluma checkpoints as marking cues. They are not automated grading or a symbolic mark scheme.

Tutor Mark Sheet

Manual tutor mark sheet only. Use observed work and leave rows blank when evidence is copied from a reveal.

Total: ___ / 8
Setup
Choose the upward vertical axis
___ / 2
Axes, sign convention, model constraints, and linked-motion/origin choices are stated.If weak, reteach from "Choose the upward vertical axis" before assigning another variant.
Score descriptions
  • 0No usable evidence for this row, or the work contradicts "Choose the upward vertical axis".
  • 1Partly correct, but review this row's checkpoint signal: evidence reaches "Choose the upward vertical axis" but is not yet consistent across the row
  • 2Complete row: Axes, sign convention, model constraints, and linked-motion/origin choices are stated.
Watch signals
  • Use the checkpoint titles when no curated wrong-path signal is listed for this row.
Components
Identify the passenger forces
___ / 2
Resolved components, force directions, normal/friction setup, or velocity split are correct.If weak, reteach from "Identify the passenger forces" before assigning another variant.
Score descriptions
  • 0No usable evidence for this row, or the work contradicts "Identify the passenger forces".
  • 1Partly correct, but review this row's checkpoint signal: evidence reaches "Identify the passenger forces" but is not yet consistent across the row
  • 2Complete row: Resolved components, force directions, normal/friction setup, or velocity split are correct.
Watch signals
  • Use the checkpoint titles when no curated wrong-path signal is listed for this row.
Net-force / governing equation
Apply Newton's second law vertically
___ / 2
The main Newton's law or motion equation uses the right model, signs, and shared variables.If weak, reteach the row from this signal: Using N = mg and ignoring the upward acceleration.
Score descriptions
  • 0No usable evidence for this row, or the work contradicts "Apply Newton's second law vertically".
  • 1Partly correct, but review this row's checkpoint signal: Using N = mg and ignoring the upward acceleration.
  • 2Complete row: The main Newton's law or motion equation uses the right model, signs, and shared variables.
Watch signals
  • Using N = mg and ignoring the upward acceleration.
Result
Solve for the scale force; Substitute values
___ / 2
The final rearrangement, numeric value, units, and direction/speed interpretation are correct.If weak, reteach the row from this signal: Subtracting ma from mg for an upward-accelerating elevator.
Score descriptions
  • 0No usable evidence for this row, or the work contradicts "Solve for the scale force".
  • 1Partly correct, but review this row's checkpoint signal: Subtracting ma from mg for an upward-accelerating elevator.
  • 2Complete row: The final rearrangement, numeric value, units, and direction/speed interpretation are correct.
Watch signals
  • Subtracting ma from mg for an upward-accelerating elevator.
  • Reporting 65 kg as the scale reading instead of converting the force model to newtons.
Total: ___ / 8Add the four row scores after checking actual student evidence. Leave it blank when the work is incomplete or only copied from reveals.Reteach from the first 0 or 1 row before assigning another variant or adding a new problem.

Setup

Axes, sign convention, model constraints, and linked-motion/origin choices are stated.

012
Score guide
  • 0No usable evidence for this row, or the work contradicts "Choose the upward vertical axis".
  • 1Partly correct, but review this row's checkpoint signal: evidence reaches "Choose the upward vertical axis" but is not yet consistent across the row
  • 2Complete row: Axes, sign convention, model constraints, and linked-motion/origin choices are stated.
Checkpoints
  • Choose the upward vertical axis
Watch for
  • Use the checkpoint equations for this row.

Components

Resolved components, force directions, normal/friction setup, or velocity split are correct.

012
Score guide
  • 0No usable evidence for this row, or the work contradicts "Identify the passenger forces".
  • 1Partly correct, but review this row's checkpoint signal: evidence reaches "Identify the passenger forces" but is not yet consistent across the row
  • 2Complete row: Resolved components, force directions, normal/friction setup, or velocity split are correct.
Checkpoints
  • Identify the passenger forces
Watch for
  • Use the checkpoint equations for this row.

Net-force / governing equation

The main Newton's law or motion equation uses the right model, signs, and shared variables.

012
Score guide
  • 0No usable evidence for this row, or the work contradicts "Apply Newton's second law vertically".
  • 1Partly correct, but review this row's checkpoint signal: Using N = mg and ignoring the upward acceleration.
  • 2Complete row: The main Newton's law or motion equation uses the right model, signs, and shared variables.
Checkpoints
  • Apply Newton's second law vertically
Watch for
  • Using N = mg and ignoring the upward acceleration.

Result

The final rearrangement, numeric value, units, and direction/speed interpretation are correct.

012
Score guide
  • 0No usable evidence for this row, or the work contradicts "Solve for the scale force".
  • 1Partly correct, but review this row's checkpoint signal: Subtracting ma from mg for an upward-accelerating elevator.
  • 2Complete row: The final rearrangement, numeric value, units, and direction/speed interpretation are correct.
Checkpoints
  • Solve for the scale force
  • Substitute values
Watch for
  • Subtracting ma from mg for an upward-accelerating elevator.
  • Reporting 65 kg as the scale reading instead of converting the force model to newtons.
  • Treating g + a as a speed or acceleration answer instead of multiplying by mass.
  • Putting the normal force downward in the free-body diagram.
  • Using N + mg = ma, which gives weight and normal force the same direction.