An eraser weighing `2N` is pressed against the black board with a force of `5N`. The coefficient of friction is `0.4`. How much force parallel to the black board is required to slide the eraser upwards

Options

A. `2N`
B. `2.8N`
C. `4N`
D. `4.8N`

Explanation

To solve the problem of how much force parallel to the blackboard is required to slide the eraser upwards, we can follow these steps:

### Step 1: Identify the forces acting on the eraser
- The weight of the eraser (W) is given as 2 N, acting downwards.
- The force pressing the eraser against the blackboard (N) is given as 5 N, acting perpendicular to the surface of the blackboard.

### Step 2: Calculate the normal force
The normal force (N) is the total force pressing the eraser against the blackboard. In this case, it is given as 5 N.

### Step 3: Calculate the frictional force
The frictional force (f) can be calculated using the formula:
\[ f = \mu \cdot N \]
where:
- \( \mu \) is the coefficient of friction (0.4)
- \( N \) is the normal force (5 N)

Substituting the values:
\[ f = 0.4 \cdot 5 \]
\[ f = 2 \, \text{N} \]

### Step 4: Determine the total force required to slide the eraser upwards
To slide the eraser upwards, the applied force (F) must overcome both the weight of the eraser and the frictional force. Therefore, the total force required is:
\[ F = f + W \]
where:
- \( f \) is the frictional force (2 N)
- \( W \) is the weight of the eraser (2 N)

Substituting the values:
\[ F = 2 \, \text{N} + 2 \, \text{N} \]
\[ F = 4 \, \text{N} \]

### Conclusion
The force required to slide the eraser upwards is **4 N**.

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