Down the Slope Inclined Planes

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.

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

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

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

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

15° FN Fg║ Fg┴ Fg

30° FN Fg║ Fg┴ Fg

45° FN Fg║ Fg┴ Fg

60° FN Fg┴ Fg║ Fg

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

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

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

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

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

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