Vibration Platform: Find Frequency for Rock Clatter

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To determine the frequency at which a rock begins to clatter on a vibration platform, one must analyze the maximum acceleration of the platform, which is influenced by its oscillation frequency. The rock will lose contact with the platform when the downward acceleration exceeds the gravitational pull on the rock. The problem is akin to roller-coaster dynamics, where the acceleration must be calculated based on the platform's amplitude and frequency. Understanding these relationships will help solve for the critical frequency needed for the rock to start clattering. This approach combines principles of oscillation and gravitational forces.
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Homework Statement



A vibration platform oscillates up and down with an amplitude of 10.4 cm at a controlled variable frequency. Suppose a small rock of unknown mass is placed on the platform. At what frequency will the rock just begin to leave the surface so that it starts to clatter?

Homework Equations



I need to know how to start this problem and what equations to use

The Attempt at a Solution

 
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gonzalo12345 said:
A vibration platform oscillates up and down with an amplitude of 10.4 cm at a controlled variable frequency. Suppose a small rock of unknown mass is placed on the platform. At what frequency will the rock just begin to leave the surface so that it starts to clatter?

Hi gonzalo12345! :smile:

This is like a roller-coaster problem … the rock will lose contact when the platform is accelerating downward so fast that the rock cannot fall fast enough to keep up!

So work out the maximum acceleration of the platform (it will depend on frequency, obviously). :smile:
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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