A mass of 4kg rests on a smooth plane inclined at 30 degrees to the horizontal. It is held in equilibrium by a light elastic string attached to the mass and to a point on the plane. Find the extension of the string if it is known that a force of 49 N would double the natural length of 1.25m
An inclined plane is a simple machine consisting of a sloping surface, whose purpose is to reduce the force that must be applied to raise a load. 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. 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. 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. If friction is ignored, the work done using the inclined plane will be exactly equal to the work done in lifting the body directly. In any real system some work is done to overcome friction between the plane and the load. 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. 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 inclined plane has been modified in many ways. 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 chisel, carpenter's plane, auger bit, and ax are some of the many tools based on this principle. 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.coscha wrote:A mass of 4kg rests on a smooth plane inclined at 30 degrees to the horizontal. It is held in equilibrium by a light elastic string attached to the mass and to a point on the plane. Find the extension of the string if it is known that a force of 49 N would double the natural length of 1.25m
In the given question, (see attachment as well) they want us find the extension of the string resulted by the 2 g newton force, if it is known that a force of 49 N would double the natural length of 1.25 m. In simple words, a force of 49 N causes an extension of 1.25 m in the string. Hence, 1 N would cause an extension of 1.25/49 m in the string or 19.6 N (f = m g sin θ = 4 g sin 30° = 4 g × ½ = 2 g, and 2 g = 2 × 9.8 N) would cause an extension of 19.6 (1.25/49) m = 0.5 m in the string.
