Find the Center of Mass: Tutorials & Problem Solutions

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Discussion Overview

The discussion revolves around finding the center of mass of various objects and related problems, including practical scenarios like a person moving on a boat. Participants seek resources for learning and examples for practice, while also exploring the implications of motion and momentum in these contexts.

Discussion Character

  • Exploratory
  • Homework-related
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant requests resources for learning about the center of mass, specifically for objects like spheres and cubes, and practical problems involving movement on a boat.
  • Another participant suggests breaking objects into simple shapes and using their distances to the center of mass, referencing Wikipedia as a resource.
  • A participant expresses the need for more examples with solutions, particularly for problems involving the movement of a person on a boat.
  • One participant notes that the problem of a person moving on a boat relates to conservation of momentum rather than center of mass directly.
  • A hypothetical scenario is presented involving a physicist and his girlfriend swapping seats on a boat, with a focus on how to analyze the situation using conservation of momentum.
  • Another participant questions the clarity of the scenario, asking for specifics about the type of displacement and the need for additional information to analyze the motion correctly.

Areas of Agreement / Disagreement

Participants express differing views on the relationship between center of mass and the problem of a person moving on a boat, with some emphasizing conservation of momentum. The discussion remains unresolved regarding the best approach to analyze the presented scenario.

Contextual Notes

Some participants highlight the need for clarity in the problem setup, including the type of displacement and the conditions necessary for applying conservation principles. There are also indications of missing assumptions regarding the motion of the boat and the individuals involved.

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Hey guys, does anyone know a good website teaching center of mass? I need to know how to find the center of mass of objects like spheres, cubes etc. and also do problems such as "a man is standing on a boat and moves from one side to the other, how far does the boat move." Stuff like that. Thanks so much!
 
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It's really a very simple problem - just split the object into simple shapes and then add all the distances to the centre of each shape * the mass of the shape.

wiki has a good article http://en.wikipedia.org/wiki/Center_of_mass
 
I looked at Wikipedia before posting, and I understand the examples on there. I need more examples though that have solutions so I can practice.
Also, there aren't any examples like how far does a boat/person on the boat move if the boat/person moves.
 
I guess I should have included translation motion in the subject too
 
Yea, the boat/person moving definitely isn't center of mass; that problem relies on conversation of momentum.
 
Hmmm how would you set up the following situation in conservation of momentum terms?

A young physicist weighing 80 kg enjoys the sunset together with his girl friend on a rowboat floating on a calm lake. The boat weighs 30 kg and does not move. The young couple swap their seats which are symmetrically located with respect to the boat's center of mass. The man observes the boat shifting by 40 cm with respect to a spatially fixed buoy. With that the physicist can tell his girl friend how much she weighs.
 
AROD said:
A young physicist weighing 80 kg enjoys the sunset together with his girl friend on a rowboat floating on a calm lake. The boat weighs 30 kg and does not move. The young couple swap their seats which are symmetrically located with respect to the boat's center of mass. The man observes the boat shifting by 40 cm with respect to a spatially fixed buoy. With that the physicist can tell his girl friend how much she weighs.

I can't even understand the question. 'Shifting' how? Horizontally? Vertically? Are we talking about the boat getting a velocity? In that case, we need a time as well as a distance. If it's a vertical displacement, then we need the distances of the lovebirds from the centre of mass in order to know the moment. It all sounds a bit odd.
 

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