A horizontal force of 1N is needed to keep a block of mass `0.25kg` sliding on a horizontal surface with a constant speed. Find the coefficient of sliding friction. `(g=10ms^(-2))`

Explanation

To find the coefficient of sliding friction, we can follow these steps:

### Step 1: Identify the given values
- Mass of the block, \( m = 0.25 \, \text{kg} \)
- Horizontal force required to keep the block moving at constant speed, \( F = 1 \, \text{N} \)
- Acceleration due to gravity, \( g = 10 \, \text{m/s}^2 \)

### Step 2: Calculate the normal force (N)
The normal force \( N \) acting on the block is equal to the weight of the block, which can be calculated using the formula:
\[ N = mg \]
Substituting the values:
\[ N = 0.25 \, \text{kg} \times 10 \, \text{m/s}^2 = 2.5 \, \text{N} \]

### Step 3: Use the formula for the coefficient of friction (μ)
The coefficient of sliding friction \( \mu \) is given by the ratio of the frictional force \( F \) to the normal force \( N \):
\[ \mu = \frac{F}{N} \]
Substituting the values we have:
\[ \mu = \frac{1 \, \text{N}}{2.5 \, \text{N}} = 0.4 \]

### Step 4: Conclusion
The coefficient of sliding friction \( \mu \) is \( 0.4 \).

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