Understanding Moments: Exploring a Common Statics Question

[eurekameh]

Here is my question:
http://imageshack.us/photo/my-images/31/unledasm.png/
On this figure, there is a 50 N force on the bigger pulley. When summing up the moments about the x-axis, why isn't -50(0.15) [circled on figure] the same as (-50cos45)(0.15) + (-50sin45)(0.15), which is the sum of the moments of its components?

 

[PeterO]

Here is my question:
http://imageshack.us/photo/my-images/31/unledasm.png/
On this figure, there is a 50 N force on the bigger pulley. When summing up the moments about the x-axis, why isn't -50(0.15) [circled on figure] the same as (-50cos45)(0.15) + (-50sin45)(0.15), which is the sum of the moments of its components?

I have a 22" monitor, but that image is still too small to read anything?

 

[PhanthomJay]

Here is my question:
http://imageshack.us/photo/my-images/31/unledasm.png/
On this figure, there is a 50 N force on the bigger pulley. When summing up the moments about the x-axis, why isn't -50(0.15) [circled on figure] the same as (-50cos45)(0.15) + (-50sin45)(0.15), which is the sum of the moments of its components?

I was able to see the image. The 50 N force is applied to the pulley tangent to its circumference at a point 45 degrees counterclockwise from its vertical z axis. It is not applied at the top of the pulley. When you break it into its components, the perpendicular distance is not 0.15 m. Either calculate the perpendicular distance, or use the cross product rule, when calculating the sum of moments this way, and you get the same result.

 

[eurekameh]

I was able to see the image. The 50 N force is applied to the pulley tangent to its circumference at a point 45 degrees counterclockwise from its vertical z axis. It is not applied at the top of the pulley. When you break it into its components, the perpendicular distance is not 0.15 m. Either calculate the perpendicular distance, or use the cross product rule, when calculating the sum of moments this way, and you get the same result.

This helped me. Thanks.

 

[rwisz]

The reason why -50(0.15) is not the same as (-50cos45)(0.15) + (-50sin45)(0.15) is because moments are calculated using the perpendicular distance from the line of action of the force to the axis of rotation. In this case, the line of action of the force is not perpendicular to the x-axis, so the perpendicular distance used in the moment calculation would be different.

Additionally, the components of the force (-50cos45) and (-50sin45) are not located at the same point as the original force, so their moments would also be different.

It is important to remember that moments are not simply the product of the force and the distance, but also take into account the direction and location of the force. Therefore, it is necessary to carefully consider all components and their respective perpendicular distances when calculating moments.