What variables are needed to find a moment?

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Homework Help Overview

The discussion revolves around determining the variables necessary to calculate the moment at the origin produced by a force applied at a specific position vector. The subject area is mechanics, specifically focusing on the concept of moments and cross products in vector analysis.

Discussion Character

  • Exploratory, Mathematical reasoning, Assumption checking

Approaches and Questions Raised

  • Participants explore the relationship between the variables involved in the moment calculation, questioning which specific components are necessary. There is an attempt to clarify the roles of the force components and the position vector components in the cross product equation.

Discussion Status

Participants are actively engaging with the mathematical expressions involved in the problem. Some have provided insights into the implications of setting certain force components to zero, while others are clarifying the definitions of the variables involved. There is a recognition of the need for specific variables to arrive at a numerical answer, but no consensus has been reached on the complete set of necessary variables.

Contextual Notes

There is an indication that additional information, such as coordinate direction angles, could influence the variables needed for the calculation. Participants are also navigating the distinction between scalar and vector representations of the force.

Alex Katko
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Homework Statement


You wish to find the moment at the origin produced by a force, ̅F= {Fi}̂, that is applied at r= {̂ai+bj +ck ̂}. Which variables (F,a ,b,c , ) do we need to know to find a numerical answer? Explain using math and figures.

Homework Equations


Mo = r x F

The Attempt at a Solution


I know that the above equation is used to find a moment. Therefore, to me it makes sense that all variables (a,b,c,F) are needed unless you were given some sort of extra information (coordinate direction angles). Needing all the variables seems to be too simple. Any advice or hints are appreciated!
 
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Alex Katko said:

Homework Statement


You wish to find the moment at the origin produced by a force, ̅F= {Fi}̂, that is applied at r= {̂ai+bj +ck ̂}. Which variables (F,a ,b,c , ) do we need to know to find a numerical answer? Explain using math and figures.

Homework Equations


Mo = r x F

The Attempt at a Solution


I know that the above equation is used to find a moment. Therefore, to me it makes sense that all variables (a,b,c,F) are needed unless you were given some sort of extra information (coordinate direction angles). Needing all the variables seems to be too simple. Any advice or hints are appreciated!
Perform the cross product algebra and see what happens.
 
haruspex said:
Perform the cross product algebra and see what happens.
Performing the cross product gives me: (bFz-cFy)i + (cFx - aFz)j + (aFy - bFx)k. All variables (the 3 components of F and a,b,c show up).
 
Alex Katko said:
Performing the cross product gives me: (bFz-cFy)i + (cFx - aFz)j + (aFy - bFx)k. All variables (the 3 components of F and a,b,c show up).
You are given ##\vec F=F\hat i##. So what are Fx, Fy and Fz?
 
haruspex said:
You are given ##\vec F=F\hat i##. So what are Fx, Fy and Fz?
Ohh i think i am understanding. Fx = Fi. Fy = 0 Fz = 0
 
Alex Katko said:
Ohh i think i am understanding. Fx = Fi. Fy = 0 Fz = 0
Almost. Fx=F, a scalar. There is no variable Fi.
 
haruspex said:
Almost. Fx=F, a scalar. There is no variable Fi.
If Fy and Fz are both zero, then the croos product becomes cFxi - bFxj. Therefore, the variables needed are F,c, and b
 
Alex Katko said:
If Fy and Fz are both zero, then the croos product becomes cFxi - bFxj. Therefore, the variables needed are F,c, and b
Yes.
 

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