How Does Varignon's Theorem Simplify Calculating Moments in Statics?

[physicsnewblol]

In general, how would you find the moment of a force given:

• the magnitude of the force
• two coordinates that form a line that contains the force vector
• the pivot point

using Varignon's Theorem

 

[PhanthomJay]

In general, how would you find the moment of a force given:

• the magnitude of the force
• two coordinates that form a line that contains the force vector
• the pivot point

using Varignon's Theorem

I hope you looked up Varignon's theorem as it applies to moments. It essentially states that the moment of a force about a pivot point is equal to the sum of the moments of the components of that force about the point. You must show an attempt at your solution for further assistance.

 

[physicsnewblol]

Nevermind, I was doing the problem correctly but the book listed an incorrect answer. To answer my own question, you simply choose one of the points as the application point of the force. You then proceed to find the distance vector which is essentially the application point written in vector form. Take this vector and find the cross product with the vector representation of the force.

The problem is number 31 in Engineering Mechanics: Statics, by J. L. Meriam and L. G. Kraige. The correct answer is 518 N*m

 

[PhanthomJay]

Nevermind, I was doing the problem correctly but the book listed an incorrect answer. To answer my own question, you simply choose one of the points as the application point of the force. You then proceed to find the distance vector which is essentially the application point written in vector form. Take this vector and find the cross product with the vector representation of the force.

The problem is number 31 in Engineering Mechanics: Statics, by J. L. Meriam and L. G. Kraige. The correct answer is 518 N*m

That method of M = rF sin theta will yield the correct answer, but that is not applying Varignon's theorem, which often simplifies the solution.