Decide whether static friction can maintain rest

1. Orient: Decide whether static friction can maintain rest

Static friction prevents relative sliding between surfaces when the needed tangential force is within a limiting magnitude. The rule is |fₛ|≤μₛN, not fₛ=μₛN in every resting situation. A small push can be balanced by small static friction; no horizontal push may require no friction at all.

2. Explain and derive

For a block initially at rest on a horizontal surface with one positive horizontal applied force F, a rest solution requires friction−F. Check whether F≤μₛN. At the limiting equality, the ideal model still permits rest. Above the bound, rest cannot be maintained and positive sliding begins.

Once sliding begins, this teaching approximation uses kinetic-friction magnitude μₖN opposing the relative sliding direction. It is a different relation with a different coefficient. For the assigned μₛ=0.5 and μₖ=0.3, crossing the threshold changes the force model; the resulting acceleration need not rise smoothly from zero.

The experiment resets the block to rest for each setting. It cannot describe a block that is already moving and then experiences a smaller push; that case requires its velocity state as well. Friction opposes relative slipping or its tendency at the contact, not necessarily the object’s velocity in every frame. Static friction can accelerate a walking person forward.

3. Work an example

With normal force 40 N, maximum static friction is 20 N. An 8 N push is balanced by 8 N static friction, so acceleration is zero. A 22 N push exceeds the bound: kinetic friction is 12 N and initial acceleration is(22−12)/4=2.5 m/s². The specified 4 kg mass stays fixed while the normal load is independently controlled.

4. Predict and investigate

Predict first: If the applied force is well below the static limit, does increasing the normal force change the actual static friction?

At normal force 40 N, compare pushes 8,20 and 22 N. State the regime before calculating friction. Then hold the push at 22 N and increase normal force to 60 N. Explain why increasing the maximum allowed friction need not mean the actual friction reaches that maximum. Use the lesson controls and record the settings with your evidence.

5. Transfer and explain

Try a new practice case

A 4 kg block begins sliding right under a 26 N push. Its normal force is 40 N and μₖ=0.3. Find its initial acceleration.

Your numerical result (m/s²) 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

How would your analysis change if the block were already sliding left? Why is the initially-at-rest assumption necessary for the displayed rule?

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.

Material pair and apparent contact area

The normal force points away from the surface and is perpendicular to it. Friction is tangential. In the supplied dry-friction approximation, coefficients depend on the contacting material pair, and the static coefficient is typically greater than the kinetic coefficient. These are empirical modeling statements, not universal guarantees for every lubricated, adhesive or deforming contact.

At the same normal load and material pair, changing the nominal contact area does not change μN in this approximation. Predict and check: with N=30 N,μs=0.6,μk=0.4, the static limit is 18 N and sliding magnitude is 12 N. Doubling nominal contact area leaves those values unchanged; a 7 N resting push still needs only 7 N static friction. Changing the material pair to μs=0.3,μk=0.2 instead gives a 9 N limit and 6 N sliding magnitude. Keep load, area and material interventions separate, and do not infer the same result when the constitutive assumptions cease to apply.

Framework and source notes

Original teaching prose and numerical cases. College Board AP Physics 1 CED, Unit 2 topic mapping: 2.7. Checked 30 October 2026. This is a content cross-reference, not AP authorization.