Velocity of two spheres under gravitational attraction

AI Thread Summary
To estimate the collision velocity of two solid copper spheres, the masses are calculated using the density and volume of copper. The gravitational force between the spheres, which varies with distance, can be analyzed using Newton's law of gravitation. A more straightforward approach involves applying conservation of energy, equating the loss in gravitational potential energy to the gain in kinetic energy. This method simplifies the calculations without needing to solve complex differential equations. The discussion emphasizes the importance of understanding energy conservation in gravitational interactions.
Jimmy Jazz
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Homework Statement


Two solid copper spheres of radii 1 and 2 cm are released from rest in free space, their centers being 20 cm apart. Estimate the velocity with which they collide

Homework Equations


density =mass/volume
F=GMm/r^2

The Attempt at a Solution


Find mass of each from density of copper and volume.
With mass and separation I can find force and initial acceleration towards each other.
This force changes with distance, so how would I take account of this in my solution?

Many thanks for any prompts.
 
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Jimmy Jazz said:
This force changes with distance, so how would I take account of this in my solution?
The short answer is to write down and solve a differential equation, but there is an easier way. What conservation law can you apply usefully?
 
Thanks for responding so I can equate the loss in potential energy with the gain in kinetic energy?
I am just going to look at the formulas for this now
 

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