How Do You Calculate Force Components and Moments in Vector Problems?

[greg997]

Hi,
I ve got two questions.

1. how to find the component of the force F in the direction of the displacement s?

I have two vectors and angle between them.


2. how to find moment of force F when applied at position r= 2a+7b-3c


No idea how to start:(. Thanks for helping me.

 

[LowlyPion]

1) It very much depends on the angle doesn't it? Then which axes you choose to determine he result. I usually choose the axes that make calculation the easiest - like along one of the vectors.

2) Moment is r X F. Your interest then will be in the cross product between the displacement and the force.

 

[nlightner]

Sure, I'd be happy to help with your questions on vectors and forces. Let's start with the first question about finding the component of force in the direction of displacement. To do this, we need to use the concept of vector projection. The component of a vector in a certain direction is equal to the magnitude of the vector multiplied by the cosine of the angle between the vector and the direction. So, in this case, we can find the component of force F in the direction of displacement s by taking the magnitude of F and multiplying it by the cosine of the angle between F and s. This will give us the component of F in the direction of s.

For your second question about finding the moment of force F when applied at position r, we can use the formula for calculating moment of a force, which is given by the cross product of the force vector and the position vector. So, in this case, we would take the cross product of F and r to find the moment of force F at position r.

I hope this helps you get started on your questions. Remember, when dealing with vectors and forces, it's important to consider both magnitude and direction, and to use the appropriate formulas and concepts to solve the problem. Let me know if you have any further questions or need clarification on anything. Good luck!