Music composed to accompany a play. The practice dates back to ritualistic Greek drama, and it is thus connected to the use of music in other kinds of ritual. Sometimes limited to the role of introduction or interlude (setting a mood or a historical period, for example), it may also accompany spoken dialogue (see melodrama). Film and television music is sometimes considered incidental music.
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Eliminating friction from a slide increases the maximum speed at which an object can move down the slide, while the acceleration of the moving object can be controlled to any degree by varying the angle of the slide. Because of this, slides are one of the most common and popular forms of entertainment. A well-polished slide can allow a human to move at a high speed with no effort, even experience near free-fall acceleration, yet arrive on the ground safely because the angle of slide can be varied along its length to end up parallel to the ground, so the forward motion of the slider can be slowly arrested by friction. The metal slide is a popular piece of playground equipment, and towering water slides employ liquid lubrication to reduce friction even further. Wheeled cars of rollercoasters roll down inclined tracks to achieve high speeds. In the sports of Luge, bobsled, sledding, and skiing, participants accelerate to extremely high speeds utilizing only the inclined plane, whether a mountain slope provided by nature, or a chute lined with near-frictionless ice.
Wedges, saws and chisels can separate thick and hard materials, such as wood, including solid stone and hard metals, with much less force, less waste of material, and more precision, than crushing. Saws have many chisel-like "teeth" along their cutting surface to transfer linear or circular motion to counteract the normal force of the surface to be cut. Crushing, the overcoming of material bonds by transferring momentum to a material through the normal force of another, harder, object was the only way to cut through a hard material before saws, and the materials to make them, were developed.
Drills produce circular holes in solids by rotating a chisel around its center, with the edge is sharpened at opposing angles on either side of the rotation axis, so as to cut in the direction of rotation. Twist drills provide one or more heliacally twisted chisels formed out of grooves cut along the side of the bit, to help evacuate cuttings from the drill hole, by using the same inclined plane principle as the archimedean screw. The water screw, though most likely preexisting Archimedes, has been used since ancient times to pump water, and is now also used to move granulated and ground materials, such as wheat, coal, and meat. Screws also join pieces of wood or metal together, by using a helical plane, usually formed by cutting a helical groove into a rod, to allow the rod force itself into the material when it is rotated.
The ancient water wheel uses inclined planes mounted around a rotating wheel to transform the momentum of moving water into a torque that can turn a shaft and do work. Sails extract the momentum of moving air to drive a vehicle, and windmills extend the principle to move a balanced set of sails around a shaft to perform work. Although known for thousands of years, these devices for extracting work from a moving fluid were always limited in efficiency by the drag-inducing vortices caused when a fluid is separated. Foils are specialized blades, shaped to allow the most efficient movement of fluid over their surfaces, to minimize the turbulence caused by these vortices. Rotating vortices dissipate the momentum of the fluid as heat, reducing the amount of energy available to do useful work.
Foils have many different designs, depending on the viscosity, velocity, and pressure of the fluid they will operate in, and their intended purpose. Aircraft wings and helicopter rotors counteract gravity by redirecting momentum generated from lateral movement, as with fixed-wing aircraft, or from rotating airfoils around a shaft, as with helicopters, so that separated air flows over the top of the foil faster than it flows over the bottom. This difference in velocity causes the pressure to increase on the bottom, generating a lifting force, through what is known as Bernoulli's Principle. The same principle in reverse allows an automotive spoiler to keep a car firmly in contact with the road.
Airplane and marine propellers use the same principle to drive vehicles though a fluid along the direction of the torque applied to the propeller shaft. Nautical propellers are often called screws. Rotating impeller blades increase the pressure difference between the inlet and outlet of a pump to force fluids through pipes. Turbines capture momentum from fast-moving fluid at high efficiency to a torque vector along the direction of the turbine's axis of rotation, while compressors use rotational motion to increase the pressure in a fast-moving fluid. Rotary fans move air, and can harness the reaction force of the moving air to drive a vehicle.
To calculate the forces on an object placed on an inclined plane, consider the three forces acting on it. Air resistance may be neglected for most calculations, except at high speeds.
We can decompose the gravitational force into two vectors, one perpendicular to the plane and one parallel to the plane. Since there is no movement perpendicular to the plane, the component of the gravitational force in this direction (mgcosθ) must be equal and opposite to normal force exerted by the plane, N. If the remaining component of the gravitational force parallel to the surface (mgsinθ) is greater than the static frictional force fs - then the body will slide down the inclined plane with acceleration (gsinθ - fk/m), where fk is the kinetic friction force - otherwise it will remain stationary.
When the slope angle (θ) is zero, sinθ is also zero so the body does not move.