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Mechanics

Block on a rough inclineForces / Inclined planes / Friction Crate pulled across a rough floorForces / Horizontal motion / Friction Table block and hanging massConnected particles / Friction / Newton's laws Passenger in an accelerating elevatorNewton's laws / Apparent weight / Vertical motion Projectile launched from a cliffProjectile motion / Kinematics / Vectors

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

State

Givens

$m$ Passenger mass: $65 kg$
$a$ Elevator acceleration upward: $1.8 m s^{- 2}$
$g$ Gravitational field strength: $9.8 m s^{- 2}$

Unknowns

$N$ Scale reading / normal force: $? N$

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

Assumptions

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.

Constraints

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.

Passenger in an accelerating elevator

Active checkpoint: Choose the upward vertical axis

LookSetupChoose the upward vertical axis

ChooseChoose the upward vertical axisThe elevator accelerates upward, so choosing +y upward makes the acceleration positive.

AvoidWrong turnStudent can only quote "+y = upward" without connecting it to the diagram state or givens.

Equation lens

+ y

upward

Choose the upward vertical axisBefore revealing the worked equation, decide what "Choose the upward vertical axis" must establish from the diagram and givens.

Hint before equation

Set the axes, origin, sign convention, or linked-motion choice before writing algebra.

Equation-choice checkWhat feature of the diagram, sign convention, or givens makes "Choose the upward vertical axis" the right next equation?

Step 1 of 5SetupChoose the upward vertical axis

Use the diagram focus, problem state, and scratch workspace first.

Checkpoints

Choose the upward vertical axis
Not yet
Set the axes, origin, sign convention, or linked-motion choice before writing algebra.
Identify the passenger forces
Not yet
Separate driving terms from opposing terms, then assign signs from the positive direction.
Apply Newton's second law vertically
Not yet
Separate driving terms from opposing terms, then assign signs from the positive direction.
Watch: Using N = mg and ignoring the upward acceleration.
Solve for the scale force
Not yet
Substitute after the model equation is settled, then check units and the requested interpretation.
Watch: Subtracting ma from mg for an upward-accelerating elevator.
Substitute values
Not yet
Substitute after the model equation is settled, then check units and the requested interpretation.
Watch: Subtracting ma from mg for an upward-accelerating elevator.

Common traps

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.

Solve Workspace

Solve checklist0 / 4 marked

Checkpoint reveal0 / 5 revealed

Checkpoint progress0 / 5 worked; 0 checked

Equation reasons0 / 5 noted

SetupAxes, sign convention, model constraints, and linked-motion/origin choices are stated.
Choose the upward vertical axis
Use the checkpoint cues before moving on.
ComponentsResolved components, force directions, normal/friction setup, or velocity split are correct.
Identify the passenger forces
Use the checkpoint cues before moving on.
Net-force / governing equationThe main Newton's law or motion equation uses the right model, signs, and shared variables.
Apply Newton's second law vertically
1 common trap tied to this row.
ResultThe final rearrangement, numeric value, units, and direction/speed interpretation are correct.
Solve for the scale forceSubstitute values
5 common traps tied to this row.

Why this equation?

Local note for the active checkpoint. It is copied into the attempt snapshot for validation.

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