The initial kinetic energy of the system is K. The final kinetic energy of the system is K/n. What is the value of n?

Break Down the Problem

1. We know the initial kinetic energy $K$ and the final kinetic energy $\frac{K}{n}$.
2. We need to find $n$ in terms of the relationship between the initial and final kinetic energies.

Relevant Concepts

3. The kinetic energy $K$ is given by the formula: $K = \frac{1}{2} mv^2$ where $m$ is the mass and $v$ is the velocity.

Analysis and Detail

4. We can determine the change in kinetic energy: $\text{Initial Kinetic Energy} = K$ $\text{Final Kinetic Energy} = \frac{K}{n}$ To find $n$, we can set up the equation: $K = n \cdot \frac{K}{n}$ This shows that $K$ is multiplied by $n$ to reach the initial condition again.

Verify and Summarize

5. By simplifying the equation, we find: $\frac{K}{n} = K \Rightarrow 1 = n$ Thus, $n$ must equal 1.

Final Answer

The value of $n$ is $1$.