Finding Center of Mass on a Reaction Board Using Torque Principles

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Homework Help Overview

The problem involves determining the distance from a woman's feet to her center of mass while lying on a reaction board supported at both ends. The scenario includes a specific setup with weights and a scale reading, indicating a focus on torque principles in a physics context.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the relationship between torque and the center of mass, with one suggesting a torque-based approach and another proposing an alternative method that simplifies the calculation without torque. Questions arise regarding the appropriateness of using torque principles versus standard formulas for center of mass.

Discussion Status

The discussion is active, with various approaches being explored. Some participants provide guidance on different methods, while others emphasize the importance of adhering to the torque principles as intended by the homework exercise. There is no explicit consensus on the best approach yet.

Contextual Notes

Participants note the constraints of the problem, including the specific weights and the setup of the reaction board, which may influence the calculations. There is also mention of the potential for misunderstanding the problem's requirements regarding the use of torque.

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Homework Statement


A person's center of mass is easily found by having the person lie on a reaction board. A horizontal, 3.0-m-long, 6.6kg reaction board is supported only at the ends, with one end resting on a scale and the other on a pivot. A 63kg woman lies on the reaction board with her feet over the pivot. The scale reads 23kg .

What is the distance from the woman's feet to her center of mass?

Homework Equations


T=F*d

The Attempt at a Solution


I know this is a problem that is related to torque, but I'm completely lost. Can someone help me..
 
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Let's say the distance from the woman's feet to her center of mass is d. So now you have Tup=-T down, which tells you
l(board)*23kg*g=
-(0.5*l(board)*Fg(board)+d*Fg(woman)
And then the problem becomes much easier.
 
There is a simpler way of doing this without using torque! The formula for finding a center of mass using the reaction board method is:

x = (r2-r1)/W * d

where:
x is the centre of mass
r2 is the scale after the weight has been added (23kg)
r1 is the initial scale reading (assuming uniform density, r1 = mass of the board/2)
W is the weight of the person
d is the length of the board

Therefore, your answer is 0.94 m (from her feet)

The key concept here is that the center of mass is calculated by the formula: x(cm) = x1m1 + x2m2 + x3m3... / m(total)
Because your question requires you to separate the system (woman + reaction board), you simply subtract the weight of the board.
The center of mass of the board is exactly at the midpoint, which is why the woman's height is not needed.
 
Hope that helps!
 
ksj said:
There is a simpler way of doing this without using torque...
x = (r2-r1)/W * d
Rearranging, xW = (r2-r1)d. Looks exactly like the torque equation to me.
I suggest that the object of the homework exercise is to use the principles of torque to solve it, not to look up some standard solution for reaction boards.
 

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