Help with Center of Mass (Calc II problem)

In summary, the center of mass is the average position of all the mass in a system and is calculated by multiplying individual masses by their respective distances from a reference point and dividing by the total mass. It is important in understanding the motion of a system and predicting the behavior of objects in different situations. The center of mass can be located outside the physical boundaries of an object if the mass is not evenly distributed, and it is related to stability as a lower center of mass results in a more stable object.
  • #1
kiwwi
1
0

Homework Statement


Find the centroid (center of mass) of the region in the first quadrant bounded by y=x, y=3x, x=n (>0)


Homework Equations





The Attempt at a Solution



No idea how to start the question, since I have to get the area of the region but
the graph does not intersect the second time. So it would be an area to inifinity.
 
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  • #2
There are three lines.
 
  • #3
The x boundaries of the region are x=0 and x=n, aren't they? There's a third curve x=n. Both lines hit it. You can make a better start than that.
 

Related to Help with Center of Mass (Calc II problem)

1. What is the definition of center of mass?

The center of mass is the average position of all the mass in a system. It is the point where the entire mass of an object can be considered to be concentrated.

2. How is center of mass calculated?

In order to calculate the center of mass, the individual masses in a system must be multiplied by their respective distances from a reference point, and then divided by the total mass of the system.

3. What is the importance of center of mass?

The center of mass is important because it helps us understand the overall motion of a system. It also helps in predicting the behavior of objects in different situations, such as collisions or rotations.

4. Can center of mass be located outside the physical boundaries of an object?

Yes, the center of mass can be located outside the physical boundaries of an object. This can occur if the mass is not evenly distributed within the object.

5. How is center of mass related to stability?

The lower the center of mass is in an object, the more stable it is. This is because a lower center of mass means there is less potential for the object to tip or fall over due to external forces.

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