Two masses accelerate towards each other

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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.
 
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FAQ: Two masses accelerate towards each other

What causes two masses to accelerate towards each other?

Two masses accelerate towards each other primarily due to the gravitational force. According to Newton's Law of Universal Gravitation, every mass attracts every other mass with a force that is proportional to the product of their masses and inversely proportional to the square of the distance between their centers.

How can we calculate the acceleration of each mass?

The acceleration of each mass can be calculated using Newton's Second Law of Motion, F = ma, where F is the gravitational force between the two masses. For mass m1, the acceleration a1 is given by a1 = F / m1, and for mass m2, the acceleration a2 is given by a2 = F / m2. The gravitational force F can be calculated using the formula F = G * (m1 * m2) / r^2, where G is the gravitational constant and r is the distance between the centers of the two masses.

What happens to the acceleration as the masses get closer?

As the masses get closer, the gravitational force between them increases because the force is inversely proportional to the square of the distance between the masses. This increased force results in greater acceleration for both masses as they approach each other.

Do the masses accelerate at the same rate?

No, the masses do not accelerate at the same rate unless they are of equal mass. The acceleration of each mass is inversely proportional to its own mass. Therefore, the smaller mass will accelerate more than the larger mass if the two masses are different.

Can this concept be applied to other forces besides gravity?

Yes, the concept of two masses accelerating towards each other can be applied to other forces, such as electrostatic forces between charged particles. The fundamental principles of force, mass, and acceleration remain the same, although the specific force law (e.g., Coulomb's law for electrostatics) may differ from the gravitational force law.

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