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

In summary, to find the center of mass of the boat in this problem, we need to calculate the weighted average of the man's and boat's positions, with the boat's position being determined by its center of mass. However, when finding the man's position after moving to the right edge of the boat, we need to consider the movement of both the man and the boat and use the equation m[man]*x[man] = -m[boat]*x[boat] to find the correct answer.
  • #1
mohabitar
140
0
HZZj0.png


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?
 
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  • #2
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.
 
  • #3
What is really x[boat] ?
What did you put in your forumla ?
 
  • #4
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)
 
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  • #5
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?
 
  • #6
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
 

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

What is the center of mass?

The center of mass is a point in an object where all of its mass can be considered to be concentrated. It is the average position of all the particles that make up the object.

What factors affect the center of mass?

The center of mass is affected by the distribution of mass within an object. Objects with more mass on one side will have a center of mass closer to that side. It is also affected by the shape and size of the object.

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 the object. This is done by multiplying the position of each particle by its mass, adding all these values together, and then dividing by the total mass of the object.

Why is the center of mass important?

The center of mass is important because it helps us understand the stability and motion of objects. It is also used in many engineering and physics calculations, such as determining the torque needed to rotate an object.

Can the center of mass be outside of an object?

Yes, the center of mass can be outside of an object. This can happen when the object has an irregular shape or when the mass is not evenly distributed. In some cases, the center of mass may even be located outside of the physical boundaries of the object.

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