Friction and limiting equilibrium
Objective. Use F≤μR and interpret impending motion.
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Learn: the key idea
Friction opposes relative motion or impending motion between surfaces, with maximum friction given by F≤μR, where μ is the coefficient of friction and R is the normal reaction. Limiting equilibrium occurs when friction reaches its maximum possible value μR just before motion begins, so F=μR exactly at that point. For example, a block on the verge of sliding on a surface with μ=0.4 and R=20N has maximum friction F=0.4×20=8N. Below this limiting value, friction adjusts to exactly balance other forces and prevent motion.
Worked example
A block in limiting equilibrium has normal reaction 25N and coefficient of friction 0.3. Find the maximum frictional force acting, given F≤μR.
- 1In limiting equilibrium, friction equals its maximum value
- 2Maximum friction is given by F=μR
- 3F=0.3×25
- 4F=7.5N
Answer: 7.5N
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Start practisingCommon mistake. Students assume friction always equals μR, even when an object is in equilibrium and not on the point of moving. Always use F≤μR and only set F=μR when the object is in limiting equilibrium or actually moving.
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