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

• Kump
In summary, the conversation discusses determining the acceleration of the center of mass of two particles with different masses and vector positions in the xy plane. The attempted solution uses the second derivative of position, resulting in -4i+4j, but it is incorrect as it ignores the masses. The helper asks for more details on how the solution was obtained and reminds the student to consider the masses when finding the position of the center of mass.
Kump

## Homework Statement

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

## 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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Last edited:
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.

## 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?

## 1. What is the center of mass?

The center of mass is the point in a system where the mass is evenly distributed in all directions. It is also known as the center of gravity.

## 2. How is the center of mass calculated?

The center of mass can be calculated by finding the weighted average of the positions of all the particles in a system, where the weight is the mass of the particle.

## 3. Why is the center of mass important?

The center of mass is important because it helps us understand the motion of a system and how external forces affect its overall movement. It is also used in calculations for rotational and translational motion.

## 4. Can the center of mass be outside of an object?

Yes, the center of mass can be outside of an object if the mass is unevenly distributed. For example, a crescent moon has its center of mass outside of its physical shape.

## 5. How does the center of mass affect the stability of an object?

The lower the center of mass is for an object, the more stable it will be. This is because the distance between the center of mass and the base of support is smaller, making it harder for the object to topple over.

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