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Lotto

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- Homework Statement
- On a long horizontal board lying on the floor of a spacious room, there are ##N## small discs, each with a mass of ##m##. The first disc is at the edge of the board, and the distance between the discs is ##l##. Initially, we give the board with the discs an initial velocity ##v_0##, so that the discs remain stationary, and then we release it. There's a layer of oil between the board and the discs. The magnitude of the force that slows down a disc is directly proportional to its velocity, ##F(v) = b · v##. The coefficient of friction between the board and the floor is ##\mu##. The masses of the discs are negligible compared to the mass of the board. We can consider the discs as point masses.

How many discs will slide off the board until all objects come to a complete stop?"

- Relevant Equations
- According to the solution, the relevant equation is ##ma=-b(v-v_0)##, where ##v## is a velocity of a single disc relative to the ground.

I don't undertand the equation. It is Newtons's second law of motion, so it decribes a force that acts on a single disc relative to the ground. So when the force is proportional to velocity, shouldn't it be ##-bv##? Because the dics's velocity is ##v## relative to the ground. Relative to the board, it is ##v-v_0##, but the equation is valid only with respect to the ground. So what do I get wrong about the equation?