Let's solve this step-by-step.

We are given:

• Block B (on top of A) with mass $m_B = 1.0 \, \text{kg}$
• Block A with mass $m_A = 2.0 \, \text{kg}$
• A force $F = 9.0 \, \text{N}$ is applied to block A, causing an acceleration $a = 2.0 \, \text{m/s}^2$ to the right.
• Frictional forces act on both blocks.

We are asked to find the ratio of the frictional force on block B to the frictional force on block A, i.e., $\frac{R_B}{R_A}$.

Step 1: Calculate the net force required for the system to achieve the acceleration

The total mass of the two blocks is: $m_{\text{total}} = m_A + m_B = 2.0 + 1.0 = 3.0 \, \text{kg}$ The net force needed to produce an acceleration $a = 2.0 \, \text{m/s}^2$ is: $F_{\text{net}} = m_{\text{total}} \cdot a = 3.0 \times 2.0 = 6.0 \, \text{N}$

Step 2: Determine the total frictional force

Since an external force of 9.0 N is applied, and the system only needs 6.0 N to achieve the required acceleration, the remaining 3.0 N must be countered by frictional forces. Therefore, the total frictional force $R_{\text{total}}$ acting on both blocks is: $R_{\text{total}} = 9.0 - 6.0 = 3.0 \, \text{N}$

Step 3: Determine the frictional forces on each block

Each block experiences a frictional force proportional to its mass since both blocks are accelerating together. Thus, we can find the frictional force on each block by considering the mass ratio.

Frictional force on block A

$R_A = R_{\text{total}} \cdot \frac{m_A}{m_{\text{total}}} = 3.0 \cdot \frac{2.0}{3.0} = 2.0 \, \text{N}$

Frictional force on block B

$R_B = R_{\text{total}} \cdot \frac{m_B}{m_{\text{total}}} = 3.0 \cdot \frac{1.0}{3.0} = 1.0 \, \text{N}$

Step 4: Calculate the ratio $\frac{R_B}{R_A}$

$\frac{R_B}{R_A} = \frac{1.0}{2.0} = \frac{1}{2}$

Answer

The correct answer is: A) 1/2

Would you like further clarification or details on any part of this solution?

Here are five related questions to deepen your understanding:

1. How would the frictional forces change if the acceleration was increased?
2. What would happen to the frictional forces if the mass of block B was doubled?
3. How does the direction of the applied force affect the frictional forces?
4. What would the ratio $R_B / R_A$ be if there was no friction on block A?
5. How would the answer change if the force was applied to block B instead of block A?

Tip: When solving for frictional forces in a system with multiple objects, distributing friction proportionally based on mass can simplify the calculation process.