Laws of Motion · Lesson 8 of 14
Static Friction and the Onset of Slipping
“Treat static friction as a self-adjusting contact force and test whether a no-slip motion is possible.”
• Distinguish normal and tangential components of contact force. • Determine static friction from the required motion before checking its limit. • Find no-slip acceleration limits for a box in a vehicle. • Explain why friction can point along the motion of a body.
Friction concerns relative motion at a contact
Two contacting surfaces can exert both a perpendicular force and a tangential force. The perpendicular component is normal reaction; the tangential component is friction. Static friction applies when the contacting surfaces do not slide relative to each other. Its direction opposes the relative slipping that would occur without it, not necessarily the body’s velocity relative to the ground.
A box carried by an accelerating train moves forward with the train. The floor’s static friction on the box also points forward, supplying its acceleration. Without that friction, the floor would slide forward underneath it. A walking foot similarly receives forward traction from the ground when it pushes backward. These examples show why “friction always opposes motion” is too imprecise.
The inequality comes before the limiting equality
If a horizontal 3 N pull acts on an otherwise unforced resting block with a 10 N static-friction limit, the friction is 3 N opposite the pull, not 10 N. As the pull grows, static friction can grow to match it. At impending slip, its magnitude reaches μ_sN. Beyond that, the assumed no-slip state fails and a sliding-friction model is needed. In a setup with no tangential demand, static friction can be zero.
Problem
A 2 kg box rests on a level floor with μ_s = 0.40. Take g = 10 m/s². Find static friction for horizontal pulls of 3 N and 7 N, and test a 9 N pull.
- 1.Normal force is 20 N because the box has no vertical acceleration and the pull is horizontal. The static limit is 0.40 × 20 = 8 N.
- 2.At 3 N pull, friction is 3 N opposite the pull; at 7 N, it is 7 N opposite.
- 3.A 9 N pull would require 9 N of static friction, above the available 8 N. The block cannot remain at rest. Its sliding acceleration needs μ_k, which has not been provided.
How to find the direction without guessing
Temporarily imagine the tangential friction removed while retaining the other forces and constraints. Ask which way the surfaces would begin to slide relative to one another. Friction opposes that tendency. Then write equations with a chosen signed direction. If the solution gives a negative friction value, the force acts opposite your provisional arrow. Finally check that its magnitude lies within μ_sN.
The no-slip acceleration limit
Problem
For μ_s = 0.15 and g = 10 m/s², find the largest train acceleration that keeps a box fixed relative to its floor.
- 1.The required friction is ma; maximum available friction is 0.15mg.
- 2.No slip requires a ≤ 0.15 × 10 = 1.5 m/s².
- 3.The box mass cancels because both inertial demand and available friction are proportional to mass in this model. Above the limit, the box slips backward relative to the train even if it still moves forward relative to the ground.
Normal force can change the available friction
If a pull has an upward component, the floor needs less normal force to support the body, reducing the friction limit. A downward component increases N and can increase available friction. This is why the contact geometry belongs in the calculation before μ_sN is evaluated. The usual approximate dry-friction model predicts weak dependence on apparent contact area; it is an empirical approximation, not a universal microscopic law.
Useful friction and limiting models
Friction can prevent slipping, transmit traction and keep an object in a circular turn. Its coefficient depends on the surfaces and conditions, including contamination and wear. “Smooth” in an ideal problem usually means tangential friction is neglected. “Rough” means friction can be present, but does not establish that it is at its maximum. Do not replace an unknown static friction by μ_sN until impending slip is justified.
Quiz
A resting block needs 4 N of friction to balance a pull, and μ_sN = 10 N. What is the static-friction magnitude?
Key Takeaways
• Static friction prevents relative slipping and can accelerate a body. • Its actual value adjusts up to the limit μ_sN. • Determine the required force first, then check the inequality. • The normal force depends on geometry and acceleration. • A rough contact does not automatically mean limiting friction.