1. Forces on an inclined plane

2. Newton’s 2nd law
In all physics problems with forces, use Newton’s 2nd law.
Remember that Fnet is the sum of ALL forces.
If the object is not moving, 𝐹 𝑛𝑒𝑡 = 0
𝐹 𝑛𝑒𝑡 =𝑚𝑎

3. Inclined Planes A tilted surface is an inclined plane
Tilt your coordinate axis to the incline.
Objects will almost always accelerate down an inclined plane. There are exceptions! Read the problem carefully.
There are always AT LEAST two forces acting on any object positioned on an inclined plane.
Gravity
Normal Force

4. Inclined Planes
Normal Force 𝐹 𝑁 - Always perpendicular to the surface.

5. Inclined Plane
Gravity - 𝐹 𝑔 Always straight down. You will have to resolve gravity into its vector components.
𝐹 𝑔 will be your Resultant
These components
Can be placed in a triangle
x component = Fg sin 𝜃
y component = Fg cos 𝜃 𝜃 𝜃
𝐹 𝑔𝑦
𝐹 𝑔
𝐹 𝑔𝑥

6. Inclined Plane – Free body diagram
If there is NO friction, 𝐹 𝑔𝑥 = Net force
𝐹 𝑔𝑦 = Normal force
Remember: 𝐹 𝑔 =𝑚𝑔
𝐹 𝑁
𝐹 𝑔𝑥 𝜃 𝜃
𝐹 𝑔𝑦
𝐹 𝑔

7. Steps for solving inclined plane problems
Draw free body diagram
Label all vectors/forces
Resolve 𝐹 𝑔 into its components
Remember 𝐹 𝑛𝑒𝑡 = sum of ALL forces. Generally, 𝐹 𝑁 𝑎𝑛𝑑 𝐹 𝑔𝑦 will cancel each other out.
𝐹 𝑛𝑒𝑡 =𝑚𝑎 Substitute and simplify as needed.
If object is sliding, find acceleration.

8. Examples
A100-kg crate is sliding down an inclined plane. The plane is inclined at an angle of 30 degrees. The coefficient of friction between the crate and the incline is 0.3. Determine the net force and acceleration of the crate.

9. Examples
The two diagrams below depict the free-body diagram for a 1000-kg roller coaster on the first drop of two different roller coaster rides. Use the above principles of vector resolution to determine the net force and acceleration of the roller coaster cars. Assume a negligible effect of friction and air resistance.