Equilibrium of Forces and Moments: Analysis of a Sanding Mechanism

[nod32]

Homework Statement

As a block of wood is sanded, it exerts on the disk of the sander a force F of magnitude 1.8N. Knowing that the belt forces (B is 11N and C is 18N) exerted on the 5cm diameter pulley lie in a plane parallel to the yz plane, replace F and the belt forces with an equivalent force-couple system at O.

Homework Equations

Sum of moments = moment created by F + moment created by pulley

The Attempt at a Solution

I've combined the forces to get the equivalent force by splitting up the forces into their components.

My question is about the moments. I'm not sure how to interpret the moment the pulleys are creating. At first i just thought to find the moment each force creates, but it doesn't seem logical as they are opposing each other (?). Would I use the difference between the 2 forces? And if so, how would I know their directions? Thanks

 

[nvn]

nod32: Yes, in the real world, forces and moments oppose each other everywhere. That is Newton's third law. No, do not use the difference between the two forces. You need a free-body diagram. You could draw on top of the picture, in this case, if you wish. Break each force into its x, y, and z components and draw them on the diagram; and draw the location dimension of each force component from point O. Then perform summation of forces, and summation of moments about point O. Also, see the last paragraph of post https://www.physicsforums.com/showpost.php?p=2946515".

 

[nod32]

Thanks for your reply. I can see now why you wouldn't use the difference, because they end up canceling out when you add them anyway.

I have one more questions about mechanical equilibrium. I'm working on a more complex problem now and I have to find reaction forces to two given forces. I understand the concept, but the step I usually seem to get stuck at is knowing which equations to use.

For example, knowing which point to take a moment about to to set to zero. Is there a rule of thumb you could use? Like use a moment location that would cancel out the most forces?

Hope that makes sense

 

[nvn]

nod32: Yes, although you can take moments about any axis, it is usually good to take moments about an axis that cancels out the most forces.

 

[DeeNos]

The moment created by the pulleys can be determined by finding the distance from the point of rotation (O) to the line of action of the force. In this case, the line of action is parallel to the yz plane, so the distance can be calculated as the radius of the pulley (2.5cm) multiplied by the sine of the angle between the y-axis and the line of action. This angle can be found by using trigonometry and the given forces B and C.

Once you have the moment created by the pulleys, you can add it to the moment created by the force F (calculated as the magnitude of the force multiplied by the perpendicular distance from O to the line of action of the force) to find the total moment at O. This will give you the equivalent force-couple system at O.

It is important to note that the direction of the moment created by the pulleys will depend on the direction of rotation of the pulley and the direction of the force applied by the belt. This can be determined by considering the right-hand rule, where the thumb points in the direction of the force and the fingers curl in the direction of rotation.