Solving M_x=U_x |r X R|: Need Help?

[suspenc3]

Homework Statement

See attachment

Homework Equations

I was thinking : $$M_x=U_x |r X R|$$

where r is going to be the distance from any point on the x-axis to any point on the line of action of the force

The Attempt at a Solution

Im not really sure how to exactly do this problem...Ive been plugging in numbers hoping for the best but nothing good has come out of it...Any help would be appreciate.

 

[PhanthomJay]

Attachment, please, is missing.

 

[m2003]

Hello,

Thank you for reaching out for help with this problem. Solving for M_x in the equation M_x=U_x |r X R| can be a bit tricky, but with some guidance, I'm sure you will be able to solve it successfully.

First, let's break down the equation. M_x represents the moment about the x-axis, U_x is the unit vector in the x-direction, and |r X R| is the cross product of the position vector r and the force vector R. Essentially, we are trying to find the moment about the x-axis caused by the force R at any point along its line of action.

To solve this, we can use the following steps:

1. Identify the position vector r: This vector represents the distance from any point on the x-axis to any point on the line of action of the force. You can either use specific coordinates or variables to represent this vector.

2. Identify the force vector R: This vector represents the magnitude and direction of the force. Again, you can use specific values or variables to represent this vector.

3. Find the cross product of the position vector and the force vector: This will give you a new vector that is perpendicular to both r and R. You can use the right-hand rule to determine the direction of this vector.

4. Calculate the magnitude of the cross product: This can be done by taking the magnitude of the position vector and multiplying it by the magnitude of the force vector, and then multiplying it by the sine of the angle between the two vectors.

5. Multiply the magnitude of the cross product by the unit vector in the x-direction (U_x): This will give you the magnitude of the moment about the x-axis caused by the force R.

I hope this helps guide you in solving the problem. If you are still having trouble, please feel free to ask for more specific help or clarification. Good luck!