1. Motion of an Object on an Inclined Surface

2. While working on a house repair project for Habitat for Humanity, you place your toolbox on a board that is slanted (one end on the ground, the other end resting on a bucket). 1)What will be the resulting motion of the toolbox? 2)What forces are acting on the toolbox? FNFN FfFf FgFg It will either: a) remain at rest, or b) accelerate down the ramp.

3. FNFN FfFf FgFg If we want to analyze the motion of this toolbox, the normal x-y coordinate axis doesn’t really fit too well. Neither of the axes line up with the ramp, making it difficult to figure out what is going on.

4. FNFN FfFf FgFg By rotating the coordinate plane so that one axis is parallel to the ramp, it can be seen that the gravitational force can be resolved into two useful components. (The other two forces do not need to be; they are parallel to the axes.)

5. F g ( ‖) F g ( ⊥) FgFg Component of F g PARALLEL to the ramp [ F g ( ‖) ] Component of F g acting PERPENDICULAR to the ramp [ F g ( ⊥) ] Adding these components together produces the entire F g vector.

6. F g ( ‖) F g ( ⊥) FgFg These angles (Ѳ) are the same!

7. F g ( ‖) F g ( ⊥) FgFg F g ( ‖) FgFg

8. F g ( ⊥) FgFg

9. Example: A 45.0 kg polar bear cub slides down an icy (frictionless) slope. If the cub starts from rest and slides 3.0 meters down the 25° incline, what speed is it moving at the bottom?

10. FNFN FgFg F g ( ‖)

11. FNFN FgFg

12. At this time, go back and finish the lab activity.

13. The bear hits a rough patch on the way down, producing a frictional coefficient of 0.150 between its fur and the slope. What frictional force will act on the bear?

14. FNFN FgFg FfFf F g ( ⊥)

15. FNFN FgFg FfFf