![]() The coefficient of friction between the box and the inclined plane is 0.3.Ī) Draw a Free Body Diagram including all forces acting on the particle with their labels.ī) Find the magnitude of the tension T in the string.Ĭ) Find the magnitude of the force of friction acting on the particle. The string makes an angle of 25 ° with the inclined plane. A string is used to keep the box in equilibrium. |N| = 50 cos (30) = 25 √3 ≈ 43.3 N Problem 3Ī box of mass M = 10 Kg rests on a 35° inclined plane with the horizontal. The F a + W + N + F s = 0 in components form: The components form of all forces (vectors) acting on the box are: The box is at rest, hence its acceleration is equal to 0, therefore the sum of all forces acting on the box is equal to its mass times its acceleration which is zero. In the diagram below, W is the weight of the box, N the normal force exerted by the inclined plane on the box, F a is the force applied to have the box in equilibrium and F s the force of friction opposite F a. A force F a of magnitude 30 N acts on the particle in the direction parallel and up the inclined plane.Ī) Draw a Free Body Diagram including the particle, the inclined plane and all forces acting on the particle with their labels.ī) Find the force of friction acting on the particle.Ĭ) Find the normal force exerted by the inclined on the particle. ![]() |N| = |W| cos (27°) = 2 × 10 cos (27°) ≈ 17.8 N Problem 2 A particle of mass 5 Kg rests on a 30° inclined plane with the horizontal. Y-components are equal : - |W| cos (27°) + |N|= 0 X-components are equal : |W| sin (27°) + 0 = M |a| (|W| sin (27°), - |W| cos (27°)) + (0, |N|) = M (|a|, 0)įor two vectors to be equal, their components must be equal. In components form, the above equation becomes Use Newton's second law to write that the sum of all forces on the box is equal to the mass times the acceleration (vector equation) W = (Wx, Wy) = (|W| cos (27°), - |W| sin (27°))Ī = (a x, a y) = (|a|, 0), box moving down the inclined plane in the direction of positive x hence a y = 0. Use system of axes x-y as shown to write all forces in their Two forces act on the box: the weight W of the box and N the force normal to and exerted by the inclined plane on the box (blue point) ![]() All rights reserved.How to solve the house problem of the box on the inclined plane and label all forces acting on the box.ī) Determine the acceleration a of the box down the plane.Ĭ) Determine the magnitude of the force exerted by the inclined plane on the box. Copyright © 2022, Columbia University Press. The Columbia Electronic Encyclopedia, 6th ed. Switchbacks on mountain roads are inclined planes that reduce the effort of an automobile engine but increase the distance a car must travel to ascend the mountain. The chisel, carpenter's plane, auger bit, and ax are some of the many tools based on this principle. The screw and wedge are applications of the principle of the inclined plane but do not require that the load be moved vertically for their successful operation. The inclined plane has been modified in many ways. An inclined plane whose sloping length is 5 m and whose vertical rise is 1 m has a mechanical advantage of 5 a 300-newton load can be moved up such a plane by a 60-newton force. The actual mechanical advantage of an inclined plane is the ratio of the load lifted to the force applied ideally it is equal to the ratio of the length of the sloping plane to its vertical rise. In any real system some work is done to overcome friction between the plane and the load. If friction is ignored, the work done using the inclined plane will be exactly equal to the work done in lifting the body directly. By means of an inclined plane a force smaller than the weight of the body can be exerted over a distance greater than the direct vertical distance, doing work equal to the product of the force and the distance through which it acts. The amount of work done (i.e., energy expended) in raising the body is equal to its weight times the distance through which it is raised. To raise a body vertically a force must be applied that is equal to the weight of the body, i.e., the product of its mass and the acceleration of gravity. Inclined plane, simple machine, consisting of a sloping surface, whose purpose is to reduce the force that must be applied to raise a load.
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