how to understand the frictional force acting in the situation when two blocks are kept in contact with each other?

To grasp the concept of frictional force between two blocks in contact, it's essential to break down the situation into manageable parts. Friction is a force that opposes the relative motion between two surfaces in contact. When two blocks are placed next to each other, the frictional force plays a crucial role in determining how they interact, especially when external forces are applied.

Identifying the Forces at Play

First, let's consider the forces acting on each block. Imagine you have Block A on a surface and Block B resting on top of Block A. The weight of Block B exerts a downward force due to gravity, which is its weight (mass times gravitational acceleration). This weight creates a normal force between Block A and Block B, which is equal to the weight of Block B if Block A is horizontal and there are no other vertical forces acting on it.

Understanding Normal Force

The normal force is crucial because it directly influences the frictional force. The frictional force can be calculated using the formula:

• Frictional Force (F_f) = μ * N

Here, μ represents the coefficient of friction between the two surfaces, and N is the normal force. The coefficient of friction varies depending on the materials in contact; for example, rubber on concrete has a higher coefficient than wood on wood.

Analyzing the Frictional Force

Now, let’s analyze how the frictional force acts when an external force is applied. Suppose you push Block A to the right. If the force is strong enough, Block A will start to move, and Block B will tend to slide off due to inertia. However, the frictional force between Block A and Block B will resist this motion. The maximum static frictional force can be calculated as:

• F_f(max) = μ_s * N

Where μ_s is the coefficient of static friction. If the applied force exceeds this maximum static friction, Block B will start to slide over Block A, transitioning to kinetic friction, which is usually less than static friction.

Example Scenario

Imagine you have a 2 kg block (Block B) resting on a 5 kg block (Block A). If the coefficient of static friction between the blocks is 0.4, the normal force (N) acting on Block B is:

• N = mass of Block B * g = 2 kg * 9.81 m/s² = 19.62 N

Thus, the maximum static frictional force is:

• F_f(max) = μ_s * N = 0.4 * 19.62 N = 7.848 N

If you apply a force greater than 7.848 N to Block A, Block B will begin to slide. If the applied force is less than this value, Block B will remain stationary relative to Block A.

Key Takeaways

Understanding frictional forces in this context involves recognizing the roles of normal force and the coefficients of friction. The interaction between the blocks is governed by these forces, and knowing how to calculate them allows you to predict the behavior of the blocks under various conditions. Whether they remain stationary or one slides over the other depends on the balance of these forces.