A force of 147N is required to just slide a sledgeweighing 500N over a surface of ice. Calculate the coefficient the coefficient of friction between the surface of contact of the sledge and the ice.

Options

A. A) 0.472
B. B) 0.294
C. C) 0.354
D. D) 0.262

Answer

To calculate the coefficient of friction between the sledge and the ice, we can follow these steps:

### Step 1: Understand the problem
We have a sledge weighing 500 N, and it requires a force of 147 N to just start sliding it over the ice. We need to find the coefficient of friction (μ) between the sledge and the ice.

### Step 2: Identify the forces involved
The force required to slide the sledge (F) is equal to the maximum static friction force (F_friction) when the sledge is just about to move. The maximum static friction can be expressed as:
\[ F_{friction} = \mu \times F_N \]
where:
- \( \mu \) = coefficient of friction
- \( F_N \) = normal force (which, in this case, is equal to the weight of the sledge)

### Step 3: Write down the known values
- Weight of the sledge (W) = 500 N
- Force required to slide the sledge (F) = 147 N

### Step 4: Relate the normal force to the weight
Since the sledge is on a horizontal surface, the normal force (F_N) is equal to the weight of the sledge:
\[ F_N = W = 500 \, N \]

### Step 5: Set up the equation for friction
From the relationship established in Step 2, we can write:
\[ F = \mu \times F_N \]
Substituting the known values:
\[ 147 \, N = \mu \times 500 \, N \]

### Step 6: Solve for the coefficient of friction (μ)
Rearranging the equation to solve for μ gives:
\[ \mu = \frac{F}{F_N} = \frac{147 \, N}{500 \, N} \]

### Step 7: Calculate μ
Now, we can perform the calculation:
\[ \mu = \frac{147}{500} = 0.294 \]

### Final Answer
The coefficient of friction (μ) between the sledge and the ice is **0.294**.

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