A homogeneous rod of length L is acted upon by two forces `F_(1) and F_(2)` applied to its ends and directed opposite to each other. With what force F will the rod be stretched at the cross section at a distance l from the end where `F_(1)` is applied?

Explanation

To solve the problem, we need to determine the force \( F \) that will stretch the rod at a cross-section located at a distance \( l \) from the end where the force \( F_1 \) is applied. We will follow these steps:

### Step 1: Understand the forces acting on the rod
We have a homogeneous rod of length \( L \) with two forces \( F_1 \) and \( F_2 \) applied at its ends, directed opposite to each other. We assume \( F_2 > F_1 \).

### Step 2: Define the mass per unit length
Let the mass per unit length of the rod be \( \lambda \) (in kg/m). The total mass of the rod can be expressed as:
\[
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