What is the Correct Center of Mass Calculation for a Man and a Boat?

[mohabitar]

This should be easy enough, but the fact that the guy is standing at x=0 is confusing me. The center of mass should be m[guy]*x[guy]+m[boat]*x[boat] / total mass

But since x[guy] is zero, then its just 162*3.4/(163+53) which comes out to 2.55, which is incorrect, since it has to be less than 1.7(center of mass of the boat alone). What am I missing?

 

[Mindscrape]

Basically what you want to do is find the center of mass of the boat, which should be intuitive because it is symmetric, and then use that as the length of "x[boat]". You are basically condensing the boat mass into its c.o.m. and then using that as the effective mass and position of the entire boat, then it's like finding the c.o.m. of a couple point masses.

 

[Quinzio]

What is really x[boat] ?
What did you put in your formula ?

 

[Alok Singh]

The force at c o m =(due to left portion)=53x+xsquare#/2.The force at com due to right portion=(3.4-x)(3.4-x)/2#.
Equating LHS and RHS--
53x+xsquare#/2=(xsquare+3.4square-6.8x)#/2
[#=162/3.4]





53x +xsquare/2# = xsquare/2+1.7*3.4-3.4x


CALCULATE IT AND YOU GET THE ANSWER,I AM HALF ASLEEP, IT'S 1:40am (AND THE ANSWER IS LESS THAN ZERO)

 

[mohabitar]

Related to the same problem, After walking to the right edge of the boat, how far has the man moved from his original location?

So while the man moves to the right, the boat moves as well, so we have to account for that, and just find the movement of the man from the original location. I'm using x[man]=-m[boat]*x[boat] / m[man], but that's not giving me the right answer. How would I approach this one?

 

[Alok Singh]

look:the time period in which the man as well as the boat move is the same as the man is responsible for the movement of the boat.
Average velocity=Total distance/time .Time is constant in both the cases so the velocity is proportional to the distance moved.
p=mv, also mass of man*distance=-mass of boat*distance
the total distance covered by man = distance traveled by him + distance traveled by boat
let the distance traveled by him be x,thus the distance traveled by boat=3.4-x
m1v=m2v, 53x=(3.4-x)162
53x=3.4*162-162x=>215x=550.8=>2.561m