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Motion on an inclined plane
Intermediate
Component of weight along the plane drives motion.
a = g sinθResolve weight into mg sinθ along the slope and mg cosθ perpendicular. Without friction a = g sinθ; with friction a = g(sinθ − μ cosθ).
At 30° frictionless: a = 4.9 m/s².
N = mg cosθ, not mg.
In more detail
On a frictionless incline, the component of weight along the slope, mg sin θ, causes acceleration. The normal force is mg cos θ, perpendicular to the surface.
Real-world uses
- Ramps and slides are designed by calculating the acceleration down the slope.
- Skiing and sledging speeds depend on the slope angle.
- Ramps and slides use the component of weight along the slope, which sets how fast a crate slides down.
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Frequently asked questions
Why does the normal force decrease on a steeper slope?
Because only the component mg cos θ of the weight presses into the surface, and cos θ falls as the angle grows.
Does mass affect acceleration down a frictionless slope?
No. All objects accelerate at g sin θ, so mass cancels.
Why does a steeper slope give more acceleration?
The component of weight along the plane is mg sin θ, which grows as the angle increases toward 90 degrees.
Related topics in Newton's Laws & Forces
Connected bodies · Elevator problems · Pulley systems · Static friction · Kinetic friction · Angle of friction and repose