1. 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? 90 o 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 30.0 o. What is the tensions in the rope supporting Michell and the tire? 30 o 825N T? F Ty Fg Fap FTFT It's not moving at this moment ∴ F Ty = Fg

2. 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 μ k ? 6. At the zoo, a 900 kg polar bear slides down a wet slide inclined at an angle of 25.0 o to the horizontal. μ k = 0.050. What is the frictional force that impedes the bear's motion down the slide? 25 o hint: the force of friction is parallel to the surface so find the applied force parallel to the surface!

3. FN Fg 25 o

4. FN Fg Fgx or F// Fgy or FΤ T 25 o

5. FN Fg Fgx or F// Fgy or FΤ T 25 o Always remember that Fg is the hypotenuse of the trig ratios / on the right angle triangle!!!!!!!!!!!!!!!!!

6. FN Fg Fgx or F// Fgy or FΤ T 25 o Fgx = Fg cos 65 Fgy = Fg sin 65 as 65 o is the angle of depression to the // plane. 25 o 65 o

7. Math activity: conjecture question on complementary angles. What is the relationship between cos and sin of complementary angles? A B where A + B = 90 o 3 examples:

8. The tricky part on inclined plane questions is determining the angle of depression for Fg and applying the proper trig ratio (sin or cos). Fg Fgx is // to the plane Fgy is 90 o to the plane Solving force problems on an inclined plane

9. Fg Fgx is // to the plane Fgy is 90 o to the plane What is F N equal to? Solving force problems on an inclined plane FNFN

10. A helpful hint FN Fgx (or F down) Fg θ inclination 90 o - θinclination I choose the complementary angle to the angle of inclination so that Fgx is Fg cosA and Fgy (and FN) = Fg sin A A