Walking on a canoe, finding its mass.

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Homework Help Overview

The problem involves a canoeist walking on a canoe and aims to determine the mass of the canoe based on the distances involved as the canoeist moves. The context includes concepts from mechanics, particularly relating to center of mass and motion in a system with multiple masses.

Discussion Character

  • Exploratory, Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • Participants discuss the need for additional assumptions regarding the system's dynamics, such as whether the canoe is moving, the uniformity of mass distribution, and the nature of the canoeist's movement. Some suggest that the problem may relate to center of mass principles, while others express uncertainty about how to apply these concepts and what distances to consider.

Discussion Status

There is an ongoing exploration of the problem with various interpretations being considered. Some participants have attempted calculations based on their understanding of center of mass, while others are questioning the assumptions made in these calculations. Guidance has been offered regarding the need to clarify the system's conditions and the implications of those assumptions.

Contextual Notes

Participants note the lack of specific information about the canoe's movement and the conditions under which the canoeist is walking. There is also mention of potential simplifications, such as treating the canoeist as a point mass and the canoe as a thin rod, which may influence the analysis.

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Homework Statement



A 61.7 kg canoeist stands in the middle of her canoe. The canoe is 3.9 m long, and the end that is closest to land is 2.5 m from the shore. The canoeist now walks toward the shore until she comes to the end of the canoe. Suppose the canoeist is 3.4 m from shore when she reaches the end of her canoe. What is the canoe's mass?


Homework Equations



I don't know

The Attempt at a Solution


1.95m/.9m * Mp

I tried taking a ratio of how far the canoeist moved to how far the canoe moved in the opposite direction and multiply that by the mass of the conoeist. I got 133.68 kg but that's wrong. How do I do this problem?
 
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several additional assumptions may be required to solve this one as there are so many unknowns here. eg. is the canoe moving? mass distribution on canoe uniform? how steady is the canoeist moving? is the canoesit moving at constant speed or accelerating? frictionless water?

from the wording, this looks to me like a "center of mass" problem...try that
 
I thought of that a realized I don't know how to go about it being a center of mass problem. The only thing I really undestand is its the sum of the mass*d/total mass of the system. In this case I don't know what distances to use. Distance from the shore? Distance from the center of the canoe? Just not sure how to go about it. Any help is appreciated.
 
I did the following...
Mc=Mass canoe
Mp=Mass person
4.45= distance from shore+half distance of canoe
Cm=Cm

(Mc+Mp)*4.45/(Mc+Mp)=Cm
Cm=4.45m
4.45=3.4Mp+5.35Mc/(Mp+Mc)
4.45Mp+4.45Mc= 3.4Mp+5.35Mc
1.05Mp=.9Mc
1.1667Mp=Mc
Mc= 71.983kg

Is this correct? or am I not suppose to assume the Cm is the same?
 
ok, in order to do this as a "center of mass" problem, you do need to make quite a few assumptions. given the lack of info provided, I am guessing that we are to assume that (if it is indeed a center of mass problem) the person is "point mass" while the canoe is just a thin rod with uniform mass distribution. perhaps the person somehow rolls fritionlessly towards one end from the middle without doing anything silly like undergo large acceleration...etc..

ok, (if this is indeed a center of mass problem...of course I don't know) the key concept here is that the position of the centre of mass of a system remain at the same place IF no external force acts on the system. so in this case, taking in all our assumptions (basically to say that there is no external force present)...the change in the internal structure of the system gives rise to change in the location of the center of mass , but since location of it can't change (no external force) the entire system must be shifted relatively to the original coordinate grid.
 

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