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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?

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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.

Kloss B med masse 1,0 kg ligger oppå kloss A med masse 2,0 kg. Vi drar i kloss A med kraften 9,0 N slik at begge klossene akselererer mot høyre med a = 2,0 m/s². Det virker friksjon på begge klossene. Hva er forholdet mellom friksjonskraften på kloss B og kloss A (RB / RA)?

A) 1/2
B) 2/3
C) 1
D) 2

Determine the frictional force ratio (RB/RA) between two stacked blocks when a 9.0 N force is applied to achieve a 2.0 m/s² acceleration. The solution involves Newton's second law and proportional distribution of frictional forces. Ideal for students in Grades 10-12.

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