Force and Acceleration of Box A and B

This numerical on Newton's Laws of Motion is designed specifically for students of Class 11, Class 12, and AP Physics. This problem explores the effects of a constant horizontal force applied to two blocks, A and B. This scenario offers a practical application of Newton's Laws of Motion, shedding light on the interactions of forces within a system.

Problem Statement

A constant horizontal force (Fₐ) is applied to block A, which pushes against block B with a 20.0 N force directed to the right. When the same force (Fₐ) is applied to block B, block A exerts a 10.0 N force on block B, directed to the left. The blocks have a combined mass of 12.0 kg. The questions to solve are:

• (a) What is the acceleration of the system in the first scenario?
• (b) What is the magnitude of the force (Fₐ) applied?

Approach to the Solution

To solve this problem, we'll use Newton's Second Law of Motion, which states that the force acting on an object equals its mass multiplied by its acceleration (F = m * a). We'll break down the problem into two parts for each scenario described.

Part A: Calculating Acceleration

In the first scenario, we're given that block A pushes block B with a 20.0 N force to the right. This force is the result of block A being pushed by the applied force (Fₐ), not Fₐ acting directly on block B. Given the total mass of the system (12.0 kg) and that block B is twice as heavy as block A, we can deduce the masses: block B (mB) is 8.0 kg and block A (mA) is 4.0 kg.

Using Newton's Second Law for block B, where the only force acting is the 20.0 N from block A, we get:

20.0 N = mB * a

Substituting mB's value:

20.0 N = 8.0 kg * a

Solving for 'a':

a = 20.0 N / 8.0 kg = 2.5 m/s²

Since both blocks move together, their acceleration is the same: 2.5 m/s².

Part B: Determining the Force (Fₐ)

In the second scenario, knowing the acceleration remains 2.5 m/s² (as the total mass and applied force haven't changed) helps us calculate Fₐ. The formula Fₐ = (mA + mB) * a gives us:

Fₐ = (4 kg + 8 kg) * 2.5 m/s² = 30 N

Thus, the magnitude of the force Fₐ applied to achieve this acceleration is 30 N.

Conclusion

This lesson not only walks you through the application of Newton's Second Law of Motion but also helps you understand the dynamics of force and acceleration in a two-block system. By breaking down complex problems into manageable steps, we aim to enhance your physics problem-solving skills, making you better prepared for exams and real-world applications. Stay tuned for more physics lessons that challenge and build your understanding of the physical world around us.