帮我讲解这道题---Okay, here is the extracted content from the image in plain text format. **Problem Description:** As shown in the figure, a wooden board of mass $m_1 = 1 \, \text{kg}$ is initially at rest on a smooth horizontal surface. A light spring with spring constant $k = 20 \, \text{N/m}$ is fixed to a vertical wall on the right side, and the spring is in its natural state. A small object of mass $m_2 = 4 \, \text{kg}$ slides onto the left end of the wooden board with an initial horizontal velocity to the right $v_0 = \frac{5}{4} \, \text{m/s}$. The wooden board just contacts the spring when the two objects reach a common velocity. The wooden board is long enough, and the coefficient of kinetic friction between the object and the wooden board is $\mu = 0.1$. The maximum static friction is equal to the kinetic friction. The spring is always within its elastic limit. The relationship between the spring's potential energy $E_{\text{p}}$ and its deformation $x$ is $E_{\text{p}} = \frac{1}{2}kx^2$. Take the gravitational acceleration $g = 10 \, \text{m/s}^2$. The results can be expressed using radicals. **Mathematical Formula:** $E_{\text{p}} = \frac{1}{2}kx^2$ **Diagram Description:** * Type: Schematic diagram of a mechanical system. * Elements: * A horizontal ground surface shown with hatching. * A long rectangular block labeled $m_1$ (wooden board) on the ground. * A smaller rectangular block labeled $m_2$ (small object) on the left end of $m_1$. * An arrow labeled $v_0$ pointing to the right, originating from $m_2$. * A horizontal spring connected to the right end of $m_1$ and a vertical wall on the right. * The vertical wall is shown with hatching. * The spring appears to be in its natural length in the initial setup shown in the diagram. **Questions:** (1) Find the magnitude of the velocity $v_1$ of the wooden board when it first contacts the spring, and the distance $x_1$ between the right end of the wooden board and the left end of the spring just before the wooden board starts moving. (2) After the wooden board contacts the spring, find the compression $x_2$ of the spring when the object and the wooden board are just about to have relative sliding, and the velocity $v_2$ of the wooden board at this moment. (3) It is known that the time taken for the wooden board's rightward velocity to decrease from $v_2$ to $0$ is $t_0$. Find the internal energy $\Delta U$ converted due to friction in the process from when the wooden board has velocity $v_2$ until its acceleration is the same as the object's acceleration for the first time (express using $t_0$).