The coefficient of static friction may be

Options

A. less than 1
B. greater than 1
C. equal to 1
D. all

Answer

To determine the possible values of the coefficient of static friction (μs), we can analyze the properties of friction in relation to the forces acting on an object. Here’s a step-by-step solution:

### Step 1: Understanding the Coefficient of Static Friction
The coefficient of static friction (μs) is a dimensionless value that represents the ratio of the maximum static frictional force (Fs) that can act between two surfaces before they start sliding against each other, to the normal force (N) acting on the object.

### Step 2: Establishing the Relationship
The formula for static friction is given by:
\[ F_s = \mu_s \cdot N \]
Where:
- \( F_s \) = static frictional force
- \( \mu_s \) = coefficient of static friction
- \( N \) = normal force

### Step 3: Analyzing the Normal Force
For an object resting on a horizontal surface, the normal force (N) is equal to the weight of the object, which can be expressed as:
\[ N = mg \]
Where:
- \( m \) = mass of the object
- \( g \) = acceleration due to gravity

### Step 4: Considering the Values of μs
1. **Minimum Value**: The coefficient of static friction cannot be negative, as it would imply a negative frictional force, which is not physically possible. Therefore, we conclude:
\[ \mu_s \geq 0 \]

2. **Maximum Value**: The coefficient of static friction can take various values depending on the surfaces in contact. It can be:
- Less than 1 (for many common materials)
- Equal to 1 (for some rough surfaces)
- Greater than 1 (in cases where the surfaces have very high frictional properties)

### Step 5: Conclusion
From the analysis, we can conclude that the coefficient of static friction (μs) can be:
- Greater than or equal to 0
- Less than, equal to, or greater than 1 depending on the materials in contact.

Thus, the possible values for the coefficient of static friction are:
\[ \mu_s \geq 0 \]

### Summary of Possible Values
- μs can be less than 1
- μs can be equal to 1
- μs can be greater than 1