How Far Does m1 Travel Before Colliding with m2?

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Homework Help Overview

The problem involves two small particles, m1 and m2, that attract each other with a force inversely proportional to the cube of their separation. The original poster seeks to determine the distance m1 travels before colliding with m2, given that m1 has an initial velocity towards m2, which is at rest a distance d away.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • The original poster attempts to use the center of mass as the collision point, calculating its position based on the masses and distance. Some participants question this assumption, suggesting that the center of mass does not necessarily represent the collision point due to the initial conditions of the particles.

Discussion Status

Participants are actively engaging with the original poster's reasoning, providing insights about the movement of the center of mass and the implications of the initial velocities of the particles. There is a recognition that the center of mass moves and that this affects the distance traveled by m1 before the collision.

Contextual Notes

Participants note that the problem specifies the particles as small, which may imply certain assumptions about their sizes and interactions. There is also mention of the need to consider the forces acting on the particles and the nature of their motion, indicating that the problem may involve more complex dynamics than initially assumed.

postfan
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Homework Statement



Two small particles of mass m1 and mass m2 attract each other with a force that varies with the inverse cube of their separation. At time t0, m1 has velocity v directed towards m2, which is at rest a distance d away. At time t1, the particles collide.
How far does m1 travel in the time interval (t0 and t1)? Note: you may use t1 and t0 in your answer. Enter m1, m2, t1 and t0 for masses and times.

Homework Equations





The Attempt at a Solution



I used the center of mass as the collision point, so I calculated (taking x=0 at m1) it to be m2*d/(m1+m2). What did I do wrong?
 

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Why did you assume that the C.O.M. would be the collision point? If you jumped off the Brooklyn Bridge, is it reasonable to assume that you would travel to almost the center of the earth?
 
The title of the question literally was 'Center of Mass', in that case what should I do?
 
postfan said:
I used the center of mass as the collision point, so I calculated (taking x=0 at m1) it to be m2*d/(m1+m2). What did I do wrong?
You are overlooking that in the reference frame you are given m1 has an initial velocity but m2 does not. The COM of the system is therefore moving. This increases the distance m1 moves to the collision point.
Even without that complication, I don't believe your formula is right. What is the ratio of the two accelerations? If both started at rest, what would that mean about the ratio of the distances moved?
SteamKing said:
Why did you assume that the C.O.M. would be the collision point?
Because it tells you they are small particles, not bothering to give the actual sizes.
 
The particles will collide at the CM, but the CM moves with a constant velocity, and you need to figure out the time when they collide. It depends on the force of interaction between them, so you need to consider how the particles move, either solving the the dynamical equations F=m1a1 and -F=m2a2, or using conservation of energy. The force of interaction is conservative.

ehild
 

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