Question

The coefficient of friction is defined as the ratio of ________.

• A. frictional force to applied force
• B. frictional force to normal force
• C. normal force to frictional force
• D. weight to frictional force
• E. applied force to frictional force

Hint:

$\mu = f / N$.

Answer 1

The Correct Option is B

Step 1: Understanding the Concept
This question asks for the definition of the coefficient of friction (\(\mu\)). The coefficient of friction is a dimensionless scalar value which describes the ratio of the force of friction between two bodies and the force pressing them together.
Step 2: Key Formula or Approach
The force of friction (\(f\)) is experimentally found to be proportional to the normal force (\(N\)) that acts between the surfaces in contact. The constant of proportionality is the coefficient of friction.
This relationship is expressed by the formula:
\[ f = \mu N \] This applies to both static friction (\(f_s \le \mu_s N\)) and kinetic friction (\(f_k = \mu_k N\)).
Step 3: Detailed Explanation
From the formula \(f = \mu N\), we can rearrange it to define the coefficient of friction \(\mu\):
\[ \mu = \frac{f}{N} \] In words, this means the coefficient of friction is the ratio of the frictional force to the normal force.
Let's analyze the options:
(A) frictional force to applied force: Incorrect. The frictional force opposes the applied force (or tendency of motion), but their ratio is not the coefficient of friction.
(B) frictional force to normal force: Correct. This matches our derived definition.
(C) normal force to frictional force: Incorrect. This is the reciprocal of the coefficient of friction (\(1/\mu\)).
(D) weight of the object to frictional force: Incorrect. The normal force is often equal to the weight (on a horizontal surface), but not always (e.g., on an incline or with an external vertical force). The definition is in terms of the normal force, not specifically the weight.
(E) applied force to frictional force: Incorrect.
Step 4: Final Answer
The coefficient of friction is defined as the ratio of the frictional force to the normal force.