1. Down the Slope
Inclined Planes

2. What is an Inclined Plane?
A tool used to move objects from one height to another.
Allows for the movement of an object without lifting it directly against gravity.

3. Principle Forces Gravitational Force (Fg) – STRAIGHT DOWN Fg║ Fg┴ Fg
Should be broken into components
Perpendicular to incline – Fg┴ = Fg cos θ
Parallel to incline – Fg║ = Fg sin θ
Fg║
Fg┴ Fg

4. Principle Forces Normal Force (FN) – PERPENDICULAR TO PLANE FN Fg║ Fg┴
Always equal to Fg┴ FN
Fg║
Fg┴ Fg

5. Principle Forces Friction Force (Ff) – OPPOSES MOTION FN Ff Fg║ Fg┴ Fg
If Ff < Fg║ then accelerates down plane
If Ff < Fg║ then not moving or constant speed FN Ff
Fg║
Fg┴ Fg

6. 0°
Fg┴ = Fg cos 0° = Fg
Fg║ = Fg sin 0° = 0 FN Fg

7. 15° FN
Fg║
Fg┴ Fg

8. 30° FN
Fg║
Fg┴ Fg

9. 45° FN
Fg║
Fg┴ Fg

10. 60° FN
Fg┴
Fg║ Fg

11. 90°
Fg┴ = Fg cos 0° = 0
Fg║ = Fg sin 0° = Fg Fg

12. As the angle increases NO CHANGE INCREASES DECREASES Fg μ Fg║
Fg┴  FN  Ff

13. What is the normal force acting on the box?
Example
A 50 newton box is sliding down a 30° incline at a constant speed.
30°
What is the normal force acting on the box?
FN = Fg┴ = Fg cos θ
FN = 50 N cos 30° = 43 N

14. Example
A 50 newton box is sliding down a 30° incline at a constant speed.
30°
What is the friction force acting on the box?
Since v = const… Ff = Fg║ = Fg sin θ
Ff = 50 N sin 30° = 25 N

15. What is the coefficient of kinetic friction in this system?
Example
A 50 newton box is sliding down a 30° incline at a constant speed.
30°
What is the coefficient of kinetic friction in this system?
Ff = μFN
μ = Ff / FN = 25N / 43 N = 0.58

16. THE END