Acceleration on an incline with friction

[luftey]

A box of books is initially at rest a distance D = 0.545 m from the end of a wooden board. The coefficient of static friction between the box and the board is μs = 0.302, and the coefficient of kinetic friction is μk = 0.238. The angle of the board is increased slowly, until the box just begins to slide; then the board is held at this angle. Find the speed of the box as it reaches the end of the board.



a=(m2g-μm1)/(m1+m2)

The Attempt at a Solution

My homework let's me try another version of the problem (it's online). For that, I did the average of the two frictions plus the distance. It gave the correct anwser, however; that doesn't seem to work for this version of the problem. The above equation is the closest thing that I could find in my book, but, it requires mass which I don't have. Would mass be canceled out I'm guessing? Any help would be appreciated :D

 

[HallsofIvy]

The "average of the two frictions" plays no roll here. They never apply at the same time. Static friction only applies to an object that is not moving, kinetic friction only applies to an object that is moving. Use the static friction to find when the angle at which the object begins to slide. Then use the kinetic friction to find its acceleration at that angle. This problem, like any problem involving gravity, does NOT require the object's mass. ma= F and F, the force, both force of gravity and the two friction forces, will be a multiple of mass.

 

[luftey]

Ok thanks, makes sense about the two frictions. I guess it was just blind luck that that worked ;p

How exactly would one find that angle where the object begins to slide? Would it be using the distance(sin)"beta"? I'm pretty sure I can solve it once I figure out how to find it at what angle.

Also, for the "m" in f=ma, I don't really get how it would be a multiple of mass if you can't find a mass for it.edit:I found the angle to be 17.95 deg, would that be correct?