Static friction adjusts up to a limit
You will be able to: Calculate required static friction and compare it with its maximum.
Why does a gentle push not always move a box?
A 2 kg box has μₛ = 0.5 on a level floor. A 3 N horizontal push produces 3 N of static friction, not 10 N. Ten newtons is the maximum it can supply before slipping.
A useful starting point: Sliding friction and the normal force →
Words and symbols before equations
- Static friction fₛ
- Force that prevents relative sliding when the required value is within its limit.
- Maximum μₛN
- Largest static-friction magnitude in the model.
- Impending slip
- The direction the surfaces would begin moving relative to each other without enough friction.
What this picture assumes
A 2 kg box starts at rest on a fixed level floor, g = 10 m/s². Each setting asks whether rest is possible. Above the limit, the model reports slipping onset and does not calculate subsequent kinetic motion.
Read the picture in three steps
- Locate the labeled sources, system boundary or graph axes. Read the units before comparing values.
- Required friction 6 N left; limit 10 N. Rest is possible; actual static friction equals the required value.
- Check what the picture assumes below. Use the Explore task to predict one change before moving a control.
Connect the picture to the physics
Assume no slip, write the force equation for that state, and calculate the friction required. If |f_required| ≤ μₛN, static contact is possible. Friction adopts that required magnitude and direction, including zero.
If the required force exceeds the limit, the assumed static state fails. For the ensuing slide, use kinetic friction with the appropriate relative-motion direction; μₖ is usually smaller than μₛ for the same surfaces.
On a stationary ramp with no other forces, required static friction is mg sin θ uphill and N = mg cos θ. The condition is tan θ ≤ μₛ. A limiting-angle experiment can estimate μₛ, but repeated trials and uncertainty in the threshold angle are needed. Static friction can also accelerate an object, such as a passenger held to an accelerating vehicle’s floor.
| Property | Static friction | Kinetic friction |
|---|---|---|
| Relative sliding | Absent | Present |
| Magnitude | Adjusts up to μₛN | μₖN in this model |
| Direction | Prevents impending slip | Opposes relative sliding |
A worked example, step by step
A 2 kg box on a level floor has μₛ = 0.5. Compare horizontal pushes of 6 N and 12 N.
- Normal force is 20 N, so the static limit is 10 N.
- For 6 N, the required friction is 6 N opposite the push, below the limit.
- For 12 N, the required friction would be 12 N, above the limit.
- The box cannot remain in that static state; a kinetic-friction model is needed after slipping starts.
fₛ = μₛN holds at the threshold, not for every static situation.
Can static friction be zero?
Compare with an explanation
Yes. With no tendency for relative sliding, zero may be the required value.
Predict. Change one thing. Explain.
Increase the horizontal push slowly. Identify where friction tracks the push and where no-slip becomes impossible. Treat this as a sequence of candidate equilibrium states, not a time simulation.
On narrow screens, swipe or scroll diagrams sideways to read all labels.
Required friction 6 N left; limit 10 N. Rest is possible; actual static friction equals the required value.
A 2 kg box starts at rest on a fixed level floor, g = 10 m/s². Each setting asks whether rest is possible. Above the limit, the model reports slipping onset and does not calculate subsequent kinetic motion.
Explain what you noticed: Which quantity changed? Which stayed fixed? Use the relevant force, system boundary, acceleration or calculus relationship to justify your prediction.
Apply the idea to a fresh problem Practice →Show what you understand.
Two original questions are a starting check, not proof of mastery. Explain your choice before revealing the answer.
Original written challenge
4 points · self-check · not an official AP questionA 3 kg block rests on a 30° incline with μₛ = 0.7. Find the required friction, normal force, maximum friction and whether rest is possible.
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Compare with the answer and four-point rubric
- 1 point: Required uphill friction = 30 sin 30° = 15 N.
- 1 point: N = 30 cos 30° ≈ 25.98 N.
- 1 point: Maximum static friction ≈ 0.7(25.98) = 18.19 N.
- 1 point: Since 15 < 18.19 N, rest is possible; actual friction is 15 N.
Accept equivalent correct methods and explanations. This is a Refresh Kid teaching rubric, not an official AP scoring guideline.
Retrieve it before you reveal it.
RECALL 1Is μₛN always the actual static friction?
No. It is the maximum.
RECALL 2How do you choose static friction direction?
Opposite impending relative slip.
RECALL 3Can static friction act on a moving object?
Yes, if the contacting surfaces do not slip relative to one another.
Revisit these tomorrow and a week later. Try a fresh problem and explain why the method applies.
Static friction adjusts up to a limit
- |fₛ| ≤ μₛN; calculate the required value first.
- For a block resting on a ramp: tan θ ≤ μₛ.
- Static means no relative slipping, not necessarily no motion relative to the ground.
Remember: fₛ = μₛN holds at the threshold, not for every static situation.
Conditions: A 2 kg box starts at rest on a fixed level floor, g = 10 m/s². Each setting asks whether rest is possible. Above the limit, the model reports slipping onset and does not calculate subsequent kinetic motion.
Refresh Kid · AP Physics C: Mechanics Unit 2 (official Unit 2) · Objectives 2.7.B · Review edition
Framework, scope and review status
Mapped to College Board CED, Topic 2.7, objectives 2.7.B. CED effective Fall 2024, current PDF ©2026; checked September 16, 2026 alongside the Fall 2026 clarifications. This is Mechanics Unit 2: Force and Translational Dynamics. The unit covers Topics 2.1–2.10. Calculus is introduced where it is needed for continuous mass and velocity-dependent forces. Shell theorem is applied without requiring a proof; spring combinations are purely series or purely parallel. The lesson breakdown and questions are original Refresh Kid work, not official topic subdivisions.
Implementation and automated checks are separate from independent teacher review and observation of students. Both human review stages remain pending. This is a review edition, not a certified or validated assessment.
Optional further resource: College Board’s released questions and scoring guides. Papers can combine units; this link is an archive, not an assignment of every question to this lesson.
Our learn, explore, practice and recall sequence is informed by the IES learning guide. The exact Refresh Kid implementation has not been evaluated for learning effectiveness.
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