Object on an Inclined Plane
If an object of mass m is placed on a smooth inclined plane (i.e. frictional force F = 0) and released it will slide down the slope. To find the acceleration of the particle as it slides we resolve in the direction of motion.
F = ma
mg cos(90 — θ) = ma
g cos(90 — θ) = a
g sin(θ) = a
We can see that the particle’s mass does not affect the acceleration but only the angle of the slope does.
If a particle of mass m is placed on a rough inclined plane (i.e. the frictional force F is not 0), if sliding of F is large enough.
We resolve perpendicular to the plane, where acceleration is zero.
F = ma,
R – mg cos θ = m×0
R = mg cos θ
We resolve in the direction of the slope, if the particle is at rest then
F = ma
mg cos(90 – θ) – F = m × 0
mg sin θ = F
Where F is the force of friction. We know that the maximum frictional force is given by Fmax = uR
Therefore
F ≤ uR
mg sin(θ) ≤ u mg cos(θ),
sin(θ)/cos(θ)=tan(θ)
tan(θ) ≤ u
Therefore the particle will remain at rest until tan(θ) > u, at this point it will accelerate down the slope.
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Inclined Plane
Inclined Plane is the most fundamental forms of mechanical devices used in physics. In order to get around physical obstacles and simplify tasks, inclined planes have been used for centuries in both ancient and recent construction projects. A flat surface that is angled with respect to the horizontal plane is the fundamental component of an inclined plane. It is a basic mechanism that works by extending the force over a greater distance in order to decrease the force required to move an object vertically.
In this article, we will learn in detail about inclined plane, the mechanics behind it, the resolution of forces into horizontal perpendicular component acting on inclined plane and solve examples based on it.