Inclined Plane Calculator
Calculate forces on an object on an inclined surface.
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Enter the mass in kg, the angle of the incline in degrees, and the coefficient of friction. The calculator shows the gravitational components parallel and perpendicular to the slope, the friction force, and the net force.
About Inclined Plane
An inclined plane decomposes gravitational force into components parallel and perpendicular to the surface. The parallel component (mg sin theta) tends to slide the object down, while the perpendicular component (mg cos theta) determines the normal force. Friction, equal to the friction coefficient times the normal force, opposes the parallel component. When the parallel force exceeds friction, the object accelerates. Inclined plane analysis is fundamental in engineering, construction, and transportation.
Frequently Asked Questions
How do you calculate forces on an inclined plane?
Gravity is decomposed into two components: parallel to the slope (mg sin theta) which drives motion, and perpendicular (mg cos theta) which determines normal force and thus friction.
What happens when the parallel force exceeds friction?
The object accelerates down the slope. The net force equals the parallel gravitational component minus the friction force. The resulting acceleration is the net force divided by mass.
What is the critical angle for sliding?
An object starts sliding when tan(theta) exceeds the coefficient of static friction. This critical angle is arctan(mu_s).