Man on a Boat: Finding the Center of Mass

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In summary, the problem asks for the location of the center of mass of a system consisting of a man and a boat before and after the man moves from one end to the other. The solution can be found by considering the location of the C.O.M. before and after the man moves, as well as the behavior of the C.O.M. in a closed system.
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aszymans
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Homework Statement


A man with mass m1 = 60 kg stands at the left end of a uniform boat with mass m2 = 165 kg and a length L = 3.6 m. Let the origin of our coordinate system be the man’s original location as shown in the drawing. Assume there is no friction or drag between the boat and water.



Homework Equations


If the man now walks to the right edge of the boat, what is the location of the center of mass of the system


The Attempt at a Solution


I tired using the equation xcom = m1x1+m2x2 / Mtotal
60*3.6 + (1.8)(165)/(165+60) which = 2.28 which is wrong
 
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  • #2
Why don't you use moments about the centre of mass rather than plugging in numbers in a formula?
 
  • #3
aszymans said:

Homework Statement


A man with mass m1 = 60 kg stands at the left end of a uniform boat with mass m2 = 165 kg and a length L = 3.6 m. Let the origin of our coordinate system be the man’s original location as shown in the drawing. Assume there is no friction or drag between the boat and water.

<snip>

I tired using the equation xcom = m1x1+m2x2 / Mtotal
60*3.6 + (1.8)(165)/(165+60) which = 2.28 which is wrong

First determine the location of the C.O.M. before the man moves. Remember, the coordinate system is fixed to the man's original location in space, not to the man himself.

Next, consider whether the system comprising the man and boat is open or closed with respect to forces; are there only internal forces acting, or are there external forces acting on the system components? What do you know about the behavior of the center of mass of a closed (or isolated) system?
 

1. What is the center of mass?

The center of mass is the point at which an object can be balanced or suspended without any rotation occurring. It is the point of the object that responds to external forces as if all of the object's mass were concentrated at that point.

2. How is the center of mass calculated?

The center of mass can be calculated by finding the weighted average of the individual masses and their respective distances from a chosen reference point. The formula for calculating the center of mass is: xcm = (∑mixi) / (∑mi) where xcm is the x-coordinate of the center of mass, mi is the mass of each individual component, and xi is the x-coordinate of each individual component.

3. Why is finding the center of mass important?

Finding the center of mass is important because it helps in understanding how an object will behave when subjected to external forces. It also allows for the prediction of an object's motion and stability.

4. What factors affect the center of mass of an object?

The center of mass of an object can be affected by the distribution of mass within the object, as well as the shape and size of the object. The position and orientation of an object also play a role in determining its center of mass.

5. How does finding the center of mass apply to a man on a boat?

For a man on a boat, the center of mass is important for maintaining balance and stability. If the man moves to one side of the boat, the center of mass will shift, potentially causing the boat to tip over. By finding the center of mass, the man can position himself to keep the boat stable.

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