# Center of Mass, Man, Woman, and Frictionless Ice

• PeachBanana
In summary, a 58 kg woman and 78 kg man are positioned 8.00 m apart on frictionless ice. Their center of mass is 4.6 m from the woman. If the man pulls on a rope and moves 2.6 m, he will end up 1.9 m from the woman. When he collides with the woman, he will have traveled a total distance of 3.4 m from their initial positions.
PeachBanana

## Homework Statement

A 58 kg woman and an 78 kg man stand 8.00 m apart on frictionless ice. How far from the woman is their CM? 4.6 m

If each holds one end of a rope, and the man pulls on the rope so that he moves 2.6 m, how far from the woman will he be now? Use two significant figures in answer. 1.9 m

How far will the man have moved when he collides with the woman?

## Homework Equations

mass man * Δx man = mass woman * -Δx woman

## The Attempt at a Solution

This can't be right because it's too close to letter B's answer.

I'm assuming because the ice is frictionless that they'll just keep going until the hit each other.

(78 kg)(x) = -(58 kg)(4.6 m)

x = -3.42 m

8.00 m - 2.6 m - 3.42 m = 1.98 m

Last edited:
Think this way: When they finally hit each other, where will they both end up? How far from their starting points is that?

DocAl:

The man starts 8.00 m apart from the woman and I knew he was 4.6 m from her CM. 8.00m - 4.6m = 3.4m

Thank you

I'll rephrase: The man was initially 3.4 m from the center of mass, so when they collide he will have traveled 3.4 m.

The man will have moved 1.98 m when he collides with the woman.

I would like to point out that the calculation in the attempt at a solution is incorrect. The equation used is based on the assumption that the center of mass remains at a constant position, which is not the case in this scenario. Since the man is pulling on the rope, the center of mass will shift towards him as he moves.

To accurately calculate the position of the center of mass at any given time, we need to use the formula:

CM = (m1x1 + m2x2) / (m1 + m2)

Where m1 and m2 are the masses of the man and woman, and x1 and x2 are their respective positions.

Using this formula, we can calculate that the center of mass will be at 2.74 m from the woman when the man has moved 2.6 m.

Furthermore, when the man collides with the woman, the center of mass will be at their midpoint, which is 4 m from the woman.

In summary, as a scientist, I would like to clarify that the position of the center of mass is constantly changing in this scenario, and it is important to use the correct formula to accurately calculate its position.

## 1. What is the center of mass?

The center of mass is a point within an object where all of its mass can be considered to be concentrated. It is the point at which the object can be balanced and will remain in equilibrium when placed on a surface.

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

The center of mass is important because it affects the stability and motion of an object. It determines how an object will move and how it will respond to external forces.

## 3. 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 that make up an object. This can be done by dividing the sum of the mass of each particle multiplied by its position by the total mass of the object.

## 4. How does the center of mass differ between a man and a woman?

The center of mass for a man is typically lower and closer to the hips, while for a woman it is typically higher and closer to the chest. This is due to differences in body composition and weight distribution between genders.

## 5. Why is it easier to move on frictionless ice?

Frictionless ice has no resistance to movement, so it requires less force to move on it compared to a surface with friction. This is because friction acts as a force that opposes motion, making it more difficult to move on surfaces with friction.

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