A horizontal force of 490 N is required to slide a sledge weighing 600 kg f over a flat surface. Calculate the coefficient of friction.

Answer

To solve the problem of calculating the coefficient of friction for a sledge weighing 600 kgf that requires a horizontal force of 490 N to slide over a flat surface, we can follow these steps:

### Step 1: Understand the Given Information
- A horizontal force \( F \) of 490 N is required to move the sledge.
- The weight of the sledge \( W \) is 600 kgf.

### Step 2: Convert Weight to Newtons
The weight in kgf (kilogram-force) can be converted to Newtons using the relation:
\[ 1 \text{ kgf} = 9.81 \text{ N} \]
Thus,
\[ W = 600 \text{ kgf} \times 9.81 \text{ N/kgf} = 5886 \text{ N} \]

### Step 3: Identify the Normal Force
In this case, since the sledge is on a flat surface, the normal force \( N \) is equal to the weight of the sledge:
\[ N = W = 5886 \text{ N} \]

### Step 4: Apply the Formula for Limiting Friction
The limiting friction \( F_f \) can be expressed as:
\[ F_f = \mu \cdot N \]
Where \( \mu \) is the coefficient of friction. Since the applied force \( F \) is equal to the limiting friction, we can write:
\[ F = \mu \cdot N \]
Substituting the known values:
\[ 490 \text{ N} = \mu \cdot 5886 \text{ N} \]

### Step 5: Solve for the Coefficient of Friction
Rearranging the equation to solve for \( \mu \):
\[ \mu = \frac{F}{N} = \frac{490 \text{ N}}{5886 \text{ N}} \]

### Step 6: Calculate the Value of \( \mu \)
Now, performing the calculation:
\[ \mu = \frac{490}{5886} \approx 0.0833 \]

### Final Answer
The coefficient of friction \( \mu \) is approximately **0.0833**.

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