How far from the end of the pier are you?

[dch1runs]

1. You are standing at the very rear of a 6.0m long, 120kg raft that is at rest in a lake with its prow only .5m from the end of the pier. Your mass is 60kg. Neglect friction between the raft and the water. A) How far from the end of the pier is the center of mass of the you-raft system? B) You walk to the front of the raft and then stop. How far from the end of the pier is the center of mass now? C) When you are at the front of the raft, how far from the end of the pier are you?



2. xcm= (m2*d)/(m2+m1)
where m1 and m2 are mass one and mass two, xcm is center of mass, and d is the difference in position of the particles.



3.A) By defining the pier as the origin and then I find the following equation. xcm= 60kg(5.5m)/180kg= 1.833m from the pier B) 60kg(0)/180kg = 0 C) .5m
I thought I had A) and C) right, but B) makes me second guess myself. What did I miss here?

 

[ehild]

2. xcm= (m2*d)/(m2+m1)
where m1 and m2 are mass one and mass two, xcm is center of mass, and d is the difference in position of the particles.

The formula for xcm is wrong. You need to determine xcm with respect to the end of the pier.


ehild

 

[dch1runs]

Should it be xcm= (m2*d)/(m2+m1) + .5?

 

[ehild]

1

2. xcm= (m2*d)/(m2+m1)
where m1 and m2 are mass one and mass two, xcm is center of mass, and d is the difference in position of the particles.

This is the distance of the CM from the first particle if there are two particles d distance apart.

What are the "particles" in this case, and what are their positions?

ehild

 

[rwisz]

It seems like you have made a mistake in your calculation for part B. The correct calculation would be:
xcm = (m2*d)/(m1+m2) = (120kg*5.5m)/(60kg+120kg) = 4.125m from the pier.
This is because when you move to the front of the raft, the distance (d) between your position and the center of mass (which is now at the rear of the raft) is 5.5m.
Therefore, the center of mass is now 4.125m from the end of the pier.
I hope this helps clarify the situation.