Friction basics — angle of friction The angle which the normal reaction makes with the resultant reaction between two contacting surfaces is called the angle of friction. Do you agree?
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AAgree
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BDisagree
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CAgree only when surfaces are perfectly smooth
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DAgree only for kinetic friction
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EAgree only when there is no impending motion
Answer
Correct Answer: Agree
Explanation
Introduction / Context:The angle of friction is a key geometric way to visualize the frictional interaction between two surfaces. It links the friction coefficient to the orientation of the resultant reaction force.
Given Data / Assumptions:
- Contact between two rigid bodies with dry (Coulomb) friction.
- Normal reaction N and limiting friction F_max = μ N define the resultant reaction R.
- Angle of friction φ is defined at the threshold of sliding (impending motion).
Concept / Approach:At limiting equilibrium, the resultant reaction R is the vector sum of N and F_max. The angle φ between R and N satisfies tan(φ) = F_max / N = μ. Thus, φ is literally the angle that the normal makes with the resultant reaction, consistent with the statement.
Step-by-Step Solution:
Write F_max = μ N at impending motion.Resultant R has components: along the plane = F_max, normal to the plane = N.Thus tan(φ) = (component along plane) / (normal component) = μ.Therefore φ is the angle between R and N (definition of angle of friction).Verification / Alternative check:If μ = 0 (perfectly smooth), φ = 0 and R aligns with N—consistent. Larger μ leads to larger φ, again matching intuition.
Why Other Options Are Wrong:
- Disagree / conditional agreements: The definition does not require smoothness or kinetic sliding; it is defined at the limiting state for static friction.
Common Pitfalls:Confusing angle of friction φ with angle of repose (inclination of an incline at impending slip). They are equal in magnitude but represent different geometric contexts.
Final Answer:Agree