- #1

fog37

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The classic problem of a block dropped on a vertical spring from a height ##h## above the scale: find the overall compression distance of a spring when a block is dropped on it and brought to rest. This problem is easy to solve using conservation of energy, potential gravitational energy and potential elastic energy. This is the energy approach.

What if we tried to solve the problem only using forces and body diagrams? I have been stuck thinking about it. How would we set the problem up? When the spring is fully compressed, the forces involved would be the weight of the block ##W## pointing down, the spring force ##F_s = k \Delta x## pointing up and the normal force ##F_N## pointing up.

We can first find the velocity of impact of the block with the spring: $$v_f = v_0 -2*9.8 (h) = -19.6 (h)$$ Then we can find the deceleration ##a_{net}## that the block experience going from ##v_f## to ##0##.

Third, we can set up the force equation $$F_{net} = m a_{net} =F_N + k \Delta x - mg$$

We know ##a_{net}##, ##g##, ##k##, ##m##, but we don't know the normal force ##F_N## so we cannot find ##\Delta x##...

Using the energy approach, the mass ##m## does not matter...

Thanks for any hint.