Infer mass from a force–acceleration relationship

1. Orient: Infer mass from a force–acceleration relationship

Newton’s second law relates the net force on a fixed-mass object to its acceleration: Fnet=ma. The word net matters. A pulling-force reading alone is not net force when friction or another horizontal interaction also acts. Before fitting mass, specify which forces the sensor includes and which must be subtracted.

2. Explain and derive

Plot force vertically against acceleration horizontally. For a correctly zeroed sensor measuring net force, the slope is mass and the intercept is zero. The slope units N/(m/s²) reduce to kg. Plotting acceleration against force instead would give reciprocal mass; swapping axes without changing the interpretation is a common error.

A constant sensor zero offset c produces readings Fread=ma+c. Differences remove c: (Fread,2−Fread,1)/(a₂−a₁)=m. Dividing an individual uncorrected reading by acceleration gives m+c/a, which varies across the dataset. A nonzero intercept is useful evidence to investigate, not a reason to force the fitted line through the origin.

The synthetic experiment varies the assigned mass and sensor offset. Actual evidence would require independent calibration, repeated trials, aligned force and acceleration measurements and a check for drag or changing mass. A linear graph does not by itself distinguish an offset from every possible unmodeled constant force; the physical measurement plan must resolve that ambiguity.

3. Work an example

For assigned mass 3 kg and offset 2 N, readings at accelerations 0,1,2,3 m/s² are 2,5,8,11 N. Using the endpoints gives mass=(11−2)/(3−0)=3 kg. A one-point estimate at 1 m/s² would give 5 kg; at 3 m/s² it would give 11/3 kg. Their inconsistency reveals the missing intercept.

4. Predict and investigate

Predict first: Will adding a constant 2 N sensor offset change the fitted slope or only the intercept?

Hold mass fixed while varying offset; compare slopes using two well-separated data points. Then hold offset fixed and change mass. Explain which graph feature changes in each intervention. Write a calibration test that could distinguish a sensor offset from an actual constant opposing force. Use the lesson controls and record the settings with your evidence.

5. Transfer and explain

Try a new practice case

Net-force sensor readings are 7 N at 1 m/s² and 19 N at 4 m/s², with a constant unknown zero offset. Infer mass.

Your numerical result (kg) Check number

Reveal worked check (practice, not mastery)

This extra practice is not saved and does not award mastery. Record your first answer, explanation and whether you revealed help in the lesson notebook. Use the lesson’s saved question separately.

6. Reflect and retain evidence

Why would an acceleration-scale error bias the inferred mass even if the force-sensor intercept were corrected?

Retain your first answer, force diagram, equations, units, assumptions and a changed-case prediction. Public worked checks are practice, not independent mastery evidence. Supplied synthetic outputs do not certify actual laboratory skill.

Framework and source notes

Original teaching prose and numerical cases. College Board AP Physics 1 CED, Unit 2 topic mapping: 2.5; science practices 1, 2, 3. Checked 30 October 2026. This is a content cross-reference, not AP authorization.