### θ inclination 90 o - θinclination

```Forces
Problems
1.Flip is an gymnast hanging from a bar by both arms. He weighs 650N. What is the tension
in each of Flip's arms?
2. Sid is hanging a painting on the wall.If the painting weighs 126N, what is the tension in
each side fo the wire supporting the painting?
90o
3. Michelle likes to swing on a tire tied to a tree branch in her yard. If Michelle and the tire
have a combined weight of 825 N. Her friend Elwiln pulls her back far enough for her to
make an angle of 30.0o. What is the tensions in the rope supporting Michell and the tire?
T?
30o
825N
FT
FTy
It's not moving at this moment
∴ FTy = Fg
Fap
Fg
4. Brian is walking in the hall and doesn't realize that Joe (in front of him) just spilled some
chocolate milk.
Brian weighs 420N, the coefficient of sliding friction (kinetic) is 0.040. What is the force of
sliding friction between Brian and the slippery floor?
5. Jessica pushes an 82 kg book case across a wooden floor.
The force of friction is 320 N. What is μk?
6.
At the zoo, a 900 kg polar bear slides down a wet slide inclined at an angle of
25.0o to the horizontal. μk = 0.050. What is the frictional force that impedes the
bear's motion down the slide?
hint: the force of friction is parallel to the surface so find the
applied force parallel to the surface!
25o
FN
25o
Fg
FN
Fgx or F//
T
Fgy or FΤ
25o
Fg
FN
Fgx or F//
T
Fgy or FΤ
25o
Fg
Always remember that Fg is
the hypotenuse of the trig ratios /
on the right angle triangle!!!!!!!!!!!!!!!!!
FN
o
65
T
Fgy or FΤ
Fgx or F//
25o
25o
Fg
Fgx = Fg cos 65
Fgy = Fg sin 65
as 65o is the angle of depression to the // plane.
Math activity:
conjecture question on complementary angles.
What is the relationship between cos and sin of complementary angles?
where A + B = 90o
A
B
3 examples:
Solving force problems on an inclined plane
The tricky part on inclined plane questions is determining
the angle of depression for Fg and applying the proper
trig ratio (sin or cos).
Fgx is // to the plane
Fgy is 90o to the plane
Fg
Solving force problems on an inclined plane
Fgx is // to the plane
Fgy is 90o to the plane
What is FN equal to?
FN
Fg
A
FN
Fg
Fgx (or F down)
I choose the complementary angle to the angle of
inclination so that
Fgx is Fg cosA and
Fgy (and FN) = Fg sin A
```