Let's break this problem down step by step:

Given:

• Two blocks with masses:
  • Block 1: 3 kg
  • Block 2: 2 kg
• A force of 20 N is applied horizontally to the 3 kg block (Block 1).
• We are asked to find the force that the 2 kg block (Block 2) exerts on the 3 kg block (Block 1).

Step 1: Finding the acceleration of the system

First, let's calculate the total mass of the system: $m_{\text{total}} = m_1 + m_2 = 3 \, \text{kg} + 2 \, \text{kg} = 5 \, \text{kg}$ Using Newton's second law ($F = ma$), the acceleration of the system is: $a = \frac{F_{\text{total}}}{m_{\text{total}}} = \frac{20 \, \text{N}}{5 \, \text{kg}} = 4 \, \text{m/s}^2$ So, the system accelerates at $4 \, \text{m/s}^2$.

Step 2: Finding the force between the blocks

Now, we need to find the force that the 2 kg block exerts on the 3 kg block. This is an internal force, and we can use the equation $F = ma$ for the 3 kg block.

The force exerted by the 2 kg block on the 3 kg block is the force required to accelerate the 3 kg block at the same acceleration of $4 \, \text{m/s}^2$: $F_{\text{2 on 3}} = m_1 \cdot a = 3 \, \text{kg} \cdot 4 \, \text{m/s}^2 = 12 \, \text{N}$ So, the force that the 2 kg block exerts on the 3 kg block is 12 N.

Final Answer:

The 2 kg block exerts a 12 N force on the 3 kg block.

Would you like more details on this solution or have any further questions?

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Here are some follow-up questions for you:

1. How does the force exerted by the 2 kg block affect the motion of both blocks?
2. What would happen if the applied force was greater than 20 N?
3. How would the solution change if the blocks were in a frictionless environment?
4. What role does Newton’s third law play in this situation?
5. How would the scenario change if there was friction acting on the blocks?

Tip: When multiple objects are involved in a system, always consider the total mass and the acceleration of the entire system to find forces acting between the objects.