Center of Mass Force Problem

In summary, the conversation discusses how to calculate the recoil distance of a canoe when a person walks from one end to the other. The center of mass of the person and canoe is initially at the center, but shifts when the person moves. To find the recoil distance, the equation Xcm = X'cm can be used, where Xcm is the initial center of mass and X'cm is the center of mass after the person moves. This equation can be solved for x, which represents the distance of the center of mass from the starting end of the canoe.
  • #1
uchicago2012
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I am floating in a canoe in still water. I carefully walk from one end of the canoe to the other. If my mass is M and the canoe's is Mc, how far does the canoe recoil?

I've solved more complicated problems but this one confuses me. Isn't recoil the velocity of a body after collision? I would have thought I would need at least one velocity. Obviously the center of mass shifts from end of the canoe to the other. I'm confused on how to approach this problem.
 
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  • #2
If you measure the distance of the center of mass from the end from which you have started walking, and L is the length of the canoe, the center of mass of you and canoe before you start walking is

Xcm = (Mc*L/2)/(M + Mc)

When you move to the other end of the canoe, the center of mass will be

X'cm = [M*L + Mc*(L/2 - x)]

Since there is no external force acting on the canoe Xcm = X'cm.

Now solve for x.
 

1. What is the center of mass and why is it important?

The center of mass is the point at which the entire mass of an object can be considered to be concentrated. It is important because it helps in understanding the motion and stability of an object.

2. How do you calculate the center of mass of an object?

The center of mass can be calculated by dividing the total mass of an object by the sum of the individual masses multiplied by their respective distances from a reference point.

3. What is the relationship between center of mass and force?

The center of mass is the point at which all external forces can be considered to act on an object. The net force acting on an object is equal to the mass of the object multiplied by its acceleration towards the center of mass.

4. How does the center of mass affect the stability of an object?

The lower the center of mass, the more stable an object will be. This is because a lower center of mass means a smaller distance between the applied force and the pivot point, resulting in a smaller moment of force and less likelihood of tipping over.

5. Can the center of mass be outside of an object?

No, the center of mass will always be within the boundaries of an object. It may be located on the surface or inside the object, but it cannot be outside of the object.

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