Solving Tilted Axis Friction Problems

[Maximillien]

Okay I was just wondering exactly how I'm supposed to know of where to put my forces once I get them from what I'm given in the problem because I know how to break up for example the W in my problem into its components or units (I,J) I just don't know which direction to put them on the titled axis. Because for example on my picture the W Force is pointing down yet my book says = 16.38i - 11.47 j and the F force is pointing right but my book says the components are = -3.83i - 3.21j...

I got those numbers just not where they go on the tilted axes. Thanks in advance for any help.

 

[awvvu]

Remember that weight always points straight down, no matter how you rotate the axes. I guess you're doing that in the diagram, but it's hard to read it.

Are i and j still unit vectors in the unrotated axes or the rotated ones? I'm assuming the book means rotated, since weight is just in the j direction unrotated. So, you have to break up the weight force into components on your rotated axes. On the bottom picture, there should be the weight force along -i and -j. (assuming +i is up the ramp, +j is northwest perpendicular)

 

[Moetasim]

I understand your confusion about where to place the forces on a tilted axis. The key to solving these types of problems is to carefully consider the orientation of the axis and the direction of the forces. In this case, it seems like the W force is acting downwards and to the left, while the F force is acting to the right and downwards. Therefore, the components of the W force should be placed on the negative side of the tilted axis, while the components of the F force should be placed on the positive side. It may also be helpful to draw a diagram or use a coordinate system to visualize the forces and their directions. I recommend double-checking your calculations and considering the direction of the forces to ensure accurate placement on the tilted axis. I hope this helps. Good luck with your problem!