a block of mass of 2kg is pushed on a rough vertical wall with a force of 40N, coefficient of static friction is 0.5. another horizontal force of 15N , is applied on the block in a direction parallel to the wall . will the block move ? if yes , in which direction? if no,find the frictional force exerted by the wall on the block

To determine whether the block will move and, if so, in which direction, we need to analyze the forces acting on it. We have a block with a mass of 2 kg being pushed against a vertical wall with a force of 40 N. Additionally, there is a horizontal force of 15 N acting parallel to the wall. The coefficient of static friction between the block and the wall is 0.5. Let's break this down step by step.

Identifying the Forces

First, we need to identify the forces acting on the block:

• Applied Force (F_applied): 40 N pushing the block against the wall.
• Horizontal Force (F_horizontal): 15 N acting parallel to the wall.
• Weight (W): The weight of the block, which is calculated as W = mass × gravity = 2 kg × 9.81 m/s² = 19.62 N acting downwards.
• Normal Force (N): The force exerted by the wall on the block, which acts perpendicular to the wall.
• Frictional Force (F_friction): This opposes the motion of the block and acts parallel to the wall.

Calculating the Normal Force

The normal force is equal to the applied force since the block is in equilibrium in the vertical direction. Therefore, we have:

N = F_applied = 40 N

Determining the Maximum Static Friction

The maximum static frictional force can be calculated using the formula:

F_{friction, max} = μ_s × N

Substituting the values:

F_{friction, max} = 0.5 × 40 N = 20 N

Analyzing the Horizontal Forces

Now, let's consider the horizontal forces acting on the block. The horizontal force of 15 N is trying to move the block to the right. The frictional force will act to the left, opposing this motion. Since the maximum static frictional force is 20 N, which is greater than the horizontal force of 15 N, the block will not move.

Finding the Actual Frictional Force

Since the block does not move, the actual frictional force will be equal to the horizontal force applied:

F_friction = F_horizontal = 15 N

Summary of Findings

In conclusion, the block will not move because the maximum static friction (20 N) is greater than the horizontal force (15 N). The frictional force exerted by the wall on the block is 15 N, acting to the left, opposing the applied horizontal force.