Inclined Plane: Forces and Friction

Change the angle, the friction and the mass, and see how the forces on the box add up to its acceleration.

Acceleration (a)—
Time—
Speed—
The box starts to slide when—
Weight mgNormal force NFriction fNet force F

The same μ is used for static and kinetic friction.

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Show the working and the notes

Resolve the weight. The weight mg points straight down. Along the ramp it has a component mg sin θ (pulling the box down the slope), and into the ramp a component mg cos θ.

The normal force. The ramp pushes back at right angles to the surface: N = mg cos θ (there is no acceleration into the ramp).

Friction. It acts up the slope. When the box is sliding, f = μN = μmg cos θ. When the box is at rest, friction is only as big as it needs to be, mg sin θ, and it has a maximum of μN.

F = mg sinθ − μmg cosθ, so a = g (sinθ − μ cosθ)

The mass cancels. Try a different mass: the forces change, but the acceleration does not. The box starts to slide when tan θ is greater than μ.

Energy. The box loses gravitational potential energy mgh. Some becomes kinetic energy and the rest is heat from friction: mgh = ½mv² + f d. The bars show this adding up.

The box slides from rest along 2.0 m of the ramp. Time and speed use the exact results t = √(2d/a) and v = at.

Learn more in the Forces lesson. Original idea by Physics High.