A 200 lb man lies against the cushion on a Rotor ride, which is inclined at θ=10°. The coefficient of static friction is μs=0.3. Radius is 8 ft. Find minimum speed so that the man does not slip down.
ΣFn = man
ΣFz = 0
an = v2/r
The Attempt at a Solution
OK, so I've done several of these problems without any issues. But now I'm running into a problem finding minimum velocity.
Here's my setup:
ΣFn = mv2/r
FnormalCos80-0.3FnormalCos10 = 6.21v2/8
ΣFz = 0
FnormalSin80+0.3FnormalSin10 = 200
The positive z axis is up, and the positive n axis is to the left.
The issue is that once I plug the normal force into my first equation, the left hand side becomes negative. This is the same approach I've taken with other problems, but with larger angles. I feel like I'm going insane. Can someone please help me out? Thanks.