Finding Force with friction on a slope

[PAstudent]

1. Homework Statement

I was wondering if my phi angle was in the right position from the picture. Also, it is correct that my normal force FN is perpendicular to the surface?

Homework Equations

Newton's second law
fk=ukFN[/B]

The Attempt at a Solution

Refer to picture[/B]

 

[TSny]

The angle Φ is not correctly indicated in your diagram. Note that Φ is the angle F makes to the vertical direction. Your normal force is correctly drawn.

 

[PAstudent]

So the angle would just be on the other side of that Force vector

 

[TSny]

I'm not sure exactly what you mean. Could you be more specific or attach another figure?

 

[PAstudent]

 

[TSny]

That's still not quite right. You now have Φ as the angle between F and your y axis. But Φ is the angle between F and the vertical direction.

 

[PAstudent]

I get what you are saying about the vertical direction, but I just don't get how that vector wouldn't be in that quadrant

 

[TSny]

You have F in the correct quadrant of your x-y coordinate system. But you do not have the angle Φ indicated correctly. Φ is not the angle between F and the y axis. Φ is the angle between F and the vertical direction. The vertical direction is along the same line that mg acts. Draw a dotted line along mg and extend it upward into the same quadrant that F is in.

 

[PAstudent]

 

[TSny]

You rotated F to the wrong side of the vertical. In the original figure, F points up and to the left. You now have F pointing up and to the right.

 

[PAstudent]

Hopefully this is correct. Sorry to put you through all of that. I just struggle with these type of angle concepts

 

[TSny]

Yes, your free body diagram is now correct. You just need to find the angle that F makes to the x-axis (or y axis).

 

[PAstudent]

Thank you for all your help