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Let's analyze the problem step-by-step.

Given dataLet's analyze the problem step-by-step.

Given 
- Mass of the child, \( m_{\text{child}} = 20 \, \text{kg} \)
- Mass of the sledge, \( m_{\text{sledge}} = 40 \, \text{kg} \)
- Horizontal pulling force exerted by the child, \( F = 12 \, \text{N} \)
- The system (child + sledge) accelerates together towards the pole with an equal acceleration \( a \).

### Step 1: Calculate the Acceleration of the System

The total mass of the system:
\[
m_{\text{total}} = m_{\text{child}} + m_{\text{sledge}} = 20 + 40 = 60 \, \text{kg}
\]

Using Newton's Second Law for the entire system:
\[
F = m_{\text{total}} \cdot a
\]
\[
a = \frac{F}{m_{\text{total}}} = \frac{12 \, \text{N}}{60 \, \text{kg}} = 0.2 \, \text{m/s}^2
\]

### Step 2: Calculate the Frictional Force Between the Child and the Sledge

For the child alone, the frictional force \( f \) between the child and the sledge is what accelerates the child forward, since the only external force the child experiences horizontally (apart from the rope tension) is friction.

Applying Newton's Second Law to the child:
\[
f = m_{\text{child}} \cdot a
\]
\[
f = 20 \, \text{kg} \cdot 0.2 \, \text{m/s}^2 = 4 \, \text{N}
\]

### Answer
The frictional force between the child and the sledge is:
\[
\boxed{4 \, \text{N}}
\]

Thus, the correct answer is **A. 4.0 N**.

Would you like more details or have questions on any steps?

---

1. How would the answer change if the sledge's mass were different?
2. What if there were friction on the horizontal surface? How would that affect the acceleration?
3. How does the force of friction relate to Newton’s third law in this scenario?
4. What would happen if the child exerted a larger pulling force on the rope?
5. How would you calculate the tension in the rope?

**Tip:** In physics problems, separating the system into components (child and sledge) helps isolate forces effectively, especially when dealing with internal forces like friction.

A child of mass 20 kg stands on the rough surface of a sledge of mass 40 kg. The sledge can slide on a horizontal frictionless surface. The child pulls on the rope with a horizontal force of 12 N, causing the child and the sledge to move with equal acceleration towards the pole. What is the frictional force between the child and the sledge?

Learn how to calculate the frictional force between a child and a sledge on a frictionless surface. This problem involves Newton's Second Law, where a child pulls on a rope with 12 N, causing an equal acceleration. Suitable for high school physics students.

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