Center of Mass, Man, Woman, and Frictionless Ice

[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

 

[Doc Al]

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

 

[PeachBanana]

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

 

[Doc Al]

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.

 

[asteriatic]

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.