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 the sledge, we can follow these steps:

### Step 1: Identify the Given Values
- Horizontal force (F) required to slide the sledge = 490 N
- Weight of the sledge (W) = 600 kgf

### Step 2: Convert Weight from kgf to Newtons
The weight in Newtons can be calculated using the conversion factor where 1 kgf = 9.81 N (approximately 10 N for simplicity in some cases).
\[ W = 600 \, \text{kgf} \times 10 \, \text{N/kgf} = 6000 \, \text{N} \]

### Step 3: Determine the Normal Force (N)
In this case, since the sledge is on a flat surface and there are no vertical forces acting on it other than its weight, the normal force (N) is equal to the weight of the sledge.
\[ N = W = 6000 \, \text{N} \]

### Step 4: Use the Formula for Limiting Friction
The limiting friction (F_friction) can be expressed as:
\[ F_friction = \mu \times N \]
Where:
- \( \mu \) = coefficient of friction
- \( N \) = normal force

Since the horizontal force required to move the sledge is equal to the limiting friction:
\[ 490 \, \text{N} = \mu \times 6000 \, \text{N} \]

### Step 5: Solve for the Coefficient of Friction (μ)
Rearranging the equation to solve for \( \mu \):
\[ \mu = \frac{F_friction}{N} = \frac{490 \, \text{N}}{6000 \, \text{N}} \]
Calculating this gives:
\[ \mu = \frac{490}{6000} \approx 0.08167 \]

### Step 6: Final Result
Thus, the coefficient of friction \( \mu \) is approximately:
\[ \mu \approx 0.0816 \]

### Summary
The coefficient of friction for the sledge is approximately 0.0816.

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