A block of mass m is pressed against a vertical wall with a horizontal force F=mg.another force F'=mg/2 is acting upon the block. If the coefficient of friction between the block and wall is l/2,the friction between them is

To determine the frictional force acting on the block pressed against the wall, we need to analyze the forces at play. We have a block of mass \( m \) pressed against a vertical wall with a horizontal force \( F = mg \) and another force \( F' = \frac{mg}{2} \) acting on it. The coefficient of friction between the block and the wall is \( \mu = \frac{1}{2} \). Let's break this down step by step.

Identifying the Forces

First, let’s identify the forces acting on the block:

• Weight (W): The weight of the block acts downward and is given by \( W = mg \).
• Horizontal Force (F): The force pressing the block against the wall is \( F = mg \).
• Additional Force (F'): There is also an additional force acting on the block, \( F' = \frac{mg}{2} \), which we need to consider.

Calculating the Normal Force

The normal force \( N \) exerted by the wall on the block is equal to the horizontal force \( F \). Thus, we have:

N = F = mg

Determining the Maximum Frictional Force

The maximum frictional force \( f_{\text{max}} \) that can act on the block is determined by the coefficient of friction and the normal force:

f_{\text{max}} = \mu N = \frac{1}{2} \cdot mg = \frac{mg}{2}

Net Forces Acting on the Block

Next, we need to consider the net forces acting on the block. The block experiences a downward gravitational force \( mg \) and an upward frictional force \( f \). The additional force \( F' = \frac{mg}{2} \) acts in the horizontal direction, but since we are primarily concerned with the vertical forces for friction, we focus on the weight and the frictional force.

Setting Up the Equation

For the block to remain stationary, the frictional force must balance the weight of the block. Therefore, we set up the equation:

f = mg

Finding the Frictional Force

Since the maximum frictional force \( f_{\text{max}} = \frac{mg}{2} \) is less than the weight of the block \( mg \), the block cannot rely on friction alone to counteract its weight. Instead, we need to find the actual frictional force that acts on the block. The frictional force will be equal to the maximum frictional force, which is:

f = f_{\text{max}} = \frac{mg}{2}

Conclusion

In this scenario, the frictional force acting on the block is \( \frac{mg}{2} \). This means that while the block is pressed against the wall, the frictional force is sufficient to counteract the additional forces acting on it, but it is not enough to support the entire weight of the block, which is why it remains in equilibrium under these conditions.