How do masses affect the acceleration of the center of mass?

AI Thread Summary
The discussion focuses on calculating the acceleration of the center of mass for two particles with given vector positions. The first particle has a mass of 4.00 g and the second 5.95 g, with their positions defined by specific equations in the xy plane. An initial attempt to find acceleration resulted in -4i + 4j, which was deemed incorrect due to neglecting the effect of the particles' masses on the center of mass calculation. The importance of incorporating mass into the center of mass position definition is emphasized. Proper calculation requires considering both the position and mass of each particle to accurately determine the center of mass acceleration.
Kump
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Homework Statement



The vector position of a 4.00 g particle moving in the xy plane varies in time according to
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1 = (3i+3j)t +2jt^2
where t is in seconds and
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is in centimeters. At the same time, the vector position of a 5.95 g particle varies as
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2 = 3î − 2ît^2 − 6ĵt.
Determine the acceleration of the center of mass at t = 2.40.

Homework Equations

The Attempt at a Solution


A=-4i+4j
i took the second derivative of position to give me acceleration. This resulted in -4i+4j which is wrong[/B]
 

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Can you show the details of how you arrived at your solution? Helpers won't simply confirm or deny a solution without work shown.
 
Kump said:

Homework Statement



The vector position of a 4.00 g particle moving in the xy plane varies in time according to
View attachment 2326741 = (3i+3j)t +2jt^2
where t is in seconds and View attachment 232675 is in centimeters. At the same time, the vector position of a 5.95 g particle varies as
View attachment 2326762 = 3î − 2ît^2 − 6ĵt.
Determine the acceleration of the center of mass at t = 2.40.

Homework Equations

The Attempt at a Solution


A=-4i+4j
i took the second derivative of position to give me acceleration. This resulted in -4i+4j which is wrong[/B]
You ignored the masses. How is the position of the center of mass defined?
 
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