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To solve this problem, we need to find the final change in internal energy when the block comes to a stop due to friction.

Here’s how we can approach it step by step:

### Given Data:
- Mass of the block, \( m = 2.6 \, \text{kg} \)
- Initial velocity, \( v = 2.5 \, \text{m/s} \)
- Coefficient of kinetic friction, \( \mu_k = 0.03 \)
- Final velocity, \( v_f = 0 \, \text{m/s} \) (since the block comes to a stop)

### Step 1: Calculate the initial kinetic energy
The change in internal energy will be equal to the initial kinetic energy lost, which is converted into thermal energy due to friction.

The kinetic energy \( K \) of the block is given by:
\[
K = \frac{1}{2} m v^2
\]
Substitute the given values:
\[
K = \frac{1}{2} \times 2.6 \, \text{kg} \times (2.5 \, \text{m/s})^2
\]
\[
K = 1.3 \times 6.25 = 8.125 \, \text{J}
\]

### Step 2: Conclusion
The initial kinetic energy of the block is 8.125 J, and since the block comes to a complete stop due to friction, all of this energy is transferred into internal energy. 

Thus, the **final change in internal energy** is \( 8.13 \, \text{J} \) (rounded to two decimal places).

Would you like more details or have any questions?

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Here are 5 related questions to expand your understanding:

1. How would the result change if the coefficient of friction was increased?
2. Can you explain how the kinetic energy formula is derived?
3. What happens to the internal energy when the block moves with constant velocity?
4. How does the friction force affect the motion of the block in terms of energy?
5. How would the energy transformation be different if the block were on an inclined plane?

**Tip**: Always remember that the work done by friction converts mechanical energy into internal energy, which often manifests as heat.

The friends consider a block of mass 2.6 kg set in motion by an external force. The initial velocity is 2.5 m/s, and the coefficient of kinetic friction is 0.03. What do they find as the final change in internal energy of the system once the block comes to a complete stop?

Learn how to calculate the final change in internal energy of a block when it comes to a stop due to friction. Using key physics principles like kinetic energy and energy transformation, this problem demonstrates how the initial kinetic energy of 8.13 J is fully transferred into internal energy. Suitable for Grades 10-12.

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