Two masses accelerate towards each other

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To solve the problem of two masses accelerating towards each other, it's essential to start with a clear diagram illustrating their positions. Simply applying F=ma is insufficient; a deeper understanding of the dynamics involved is required. The discussion emphasizes the need to derive an ordinary differential equation (ODE) to approach the solution effectively. Participants are encouraged to demonstrate their initial understanding and outline their problem-solving strategy. Following the forum's homework guidelines is crucial for receiving assistance.
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Homework Statement
Hey, I have problem which I have no idea how to solve:
https://ibb.co/5n8JX6m
As you can see: There are 2 equal masses m connected by a massless string with length 2l. Now a constant force F attacks at the center of the string (at P) and pushes the string upwards so that the masses accelerate in x direction towards each other. Find a formula for the acceleration a depending on the time. Thank you for hints and solutions :)
Relevant Equations
F=ma
.
 
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Start with a diagram of the general position, not the initial position.
But I see no way to get a solution in closed form. Try to get an ODE at least.
 
Last edited:
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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