**Incline Planes**

Learn the forces involved in incline planes with and without friction. See how to solve for acceleration of an object created by the net force.

__Forces on an incline__

**F**_{w}: Weight- Longest Vector Straight Down

__Every other force is the result of the weight__

**F**_{⟘ }: Perpendicular Force- Force pushing into the hill

**F**_{⸗ }: Parallel Force- Force pushing down the hill

**F**_{N}: Normal Force- Reaction to the force pushing into the hill (F
_{⟘})and equal and opposite to it

- Reaction to the force pushing into the hill (F
**F**_{f}: Force of Friction- Reaction to the force pushing down the hill (F
_{⸗ })

- Reaction to the force pushing down the hill (F
**Ө : Angle of Incline**- Same as angle in the right triangle

### Incline Planes and Trig Functions

Depending what the incline plane question is asking you will use the SOH CAH TOA trig functions. The most common case will be when you are given a mass on a hill and provided the hills incline(Ө). Start by finding weight (F_{W} = mg (g = 9.8 m/s^{2}). Because you have weight and an incline angle, you now can find other forces involved. These are the most common rearranged forms.

**F**_{⟘ }= (cos**Ө)(hyp)****F**_{⸗ }= (sin**Ө)(hyp)****F**_{N}= F_{⟘ }= (cos**Ө)(hyp)**

Depending on how a the questions is asked you may need any of the trig functions including tangent.

### Example Problems (Incline Plane)

**1) How much a 1.5 kg block accelerate down a 15° frictionless incline plane?**

**2) How much would the block accelerate if it was wood and the incline was wood and there was friction?**

**3) How fast would the block be going after 3 seconds with friction?**

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