2 object gravitation, collision speed

In summary, two objects with masses and radii are initially at rest and separated by a distance. They begin to accelerate towards each other and the task is to determine their speed at the moment of collision. The solution involves creating differential equations and using the law of gravitation to find the velocity.
  • #1
aalasso
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Homework Statement


2 objects each with mass, m, and radius, r, are unaffected by any other objects. They are the distance L apart. At time t=0 , both are at rest. From then on they accelerate towards each other.
Determine the speed of the planets at the moment of collision.

Homework Equations


From assignment: "Use a= dv/dx * v in order to solve the problem".
Newtons law of gravitation: Fg= G m^2/(r^2)

The Attempt at a Solution



Well I would think that I'm supposed to make 1 or 2 differential equations, which I can then solve specifically by x_0=0 .
My problem is writing the equations, can anyone help, please?
 
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  • #2
I have solved a very similar problem, but am uncertain of the solution! I obtained a position-time equation, from which I could easily differentiate and find velocity... Umm refer to my post in general physics if you want to see that.
 
  • #3


I would approach this problem by first defining the variables and parameters involved. We have two objects with masses m and radii r, a distance L apart, and at rest at time t=0. We also have the gravitational constant G. From this, we can use Newton's law of gravitation to calculate the force of gravity between the two objects at any given time.

Next, I would use the given equation a= dv/dx * v to create a differential equation that describes the acceleration of the objects as they move towards each other. This equation would take into account the force of gravity between the objects, as well as their masses and distances.

Solving this differential equation would give us the velocity of the objects at any given time. To find the speed at the moment of collision, we would need to set the distance between the objects to zero, and solve for the velocity at that point in time.

However, it's important to note that this problem assumes the objects are point masses and does not take into account any other factors, such as the objects' shapes or any external forces. In reality, the collision between two objects would be much more complex and would require additional information and calculations.
 

What is the formula for calculating the gravitational force between two objects?

The formula for calculating the gravitational force between two objects is F = G * (m1 * m2)/r^2, where G is the gravitational constant, m1 and m2 are the masses of the two objects, and r is the distance between the two objects.

How does the mass of the objects affect the gravitational force between them?

The gravitational force between two objects is directly proportional to the mass of the objects. This means that as the mass of either object increases, the gravitational force between them also increases.

What is the effect of distance on gravitational force?

The gravitational force between two objects is inversely proportional to the square of the distance between them. This means that as the distance between two objects increases, the gravitational force between them decreases.

What happens to the speed of two objects after a collision?

The speed of two objects after a collision depends on the masses and velocities of the objects before the collision. In an elastic collision, the total kinetic energy of the objects is conserved and the objects will bounce off each other with equal and opposite velocities. In an inelastic collision, the objects will stick together and move with a common final velocity.

How does the gravitational force between two objects compare to other fundamental forces?

The gravitational force is the weakest of the four fundamental forces of nature. It is much weaker than the electromagnetic force and the strong and weak nuclear forces. However, it is the only force that acts on a large scale, such as between planets and stars in the universe.

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