Mechanical Advantage
The simple machine called a wheel and axle refers to the assembly formed by two disks, or cylinders, of different diameters mounted so they rotate together around the same axis. Forces applied to the edges of the two disks, or cylinders, provide mechanical advantage. When used as the wheel of a cart the smaller cylinder is the axle of the wheel, but when used in a windlass, winch, and other similar applications (see medieval mining lift to left) the smaller cylinder may be separate from the axle mounted in the bearings.
Assuming the wheel and axle does not dissipate or store energy, the power generated by forces applied to the wheel must equal the power out at the axle. As the wheel and axle system rotates around its bearings, points on the circumference, or edge, of the wheel move faster than points on the circumference, or edge, of the axle. Therefore a force applied to the edge of the wheel must be less than the force applied to the edge of the axle, because power is the product of force and velocity.
Let a and b be the distances from the center of the bearing to the edges of the wheel A and the axle B. If the input force FA is applied to the edge of the wheel A and the force FB at the edge of the axle B is the output, then the ratio of the velocities of points A and B is given by a/b, so the ratio of the output force to the input force, or mechanical advantage, is given by
The mechanical advantage of a simple machine like the wheel and axle is computed as the ratio of the resistance to the effort. The larger the ratio the greater the multiplication of force (torque) created or distance achieved. By varying the radii of the axle and/or wheel, any amount of mechanical advantage may be gained. In this manner, the size of the wheel may be increased to an inconvenient extent. In this case a system or combination of wheels (often toothed, that is, gears) are used. As a wheel and axle is a type of lever, a system of wheels and axles is like a compound lever.
Read more about this topic: Wheel And Axle
Famous quotes containing the words mechanical and/or advantage:
“A man should have a farm or a mechanical craft for his culture. We must have a basis for our higher accomplishments, our delicate entertainments of poetry and philosophy, in the work of our hands.”
—Ralph Waldo Emerson (1803–1882)
“Every nation ... have their refinements and grossiertes.... There is a balance ... of good and bad every where; and nothing but the knowing it is so can emancipate one half of the world from the prepossessions which it holds against the other—that [was] the advantage of travel ... it taught us mutual toleration; and mutual toleration ... taught us mutual love.”
—Laurence Sterne (1713–1768)