Lever

A lever in the physics and technology, a mechanical force transducer consisting of a rigid body, which is rotatably mounted on a pivot. The mathematical description of such a system is referred to as a lever law. This law was formulated in ancient times by Archimedes.

Differences are one-sided and two-sided lever, depending on whether the forces act only on one side or on both sides of the fishing point. Further, there are next to the straight lever also has the bent lever or bell crank as he finds in the tilt scale application.

Physical Description

The central physical quantity that is needed for the description of a lever, the torque with respect to the pivot on which the can rotate the lever.

Here, the position vector of the pivot point and the position vector is in the point at which a force acts. The distance between the fulcrum and point of application of force is called the lever arm. The amount of the torque is proportional to the lever arm. Can be practiced with a large lever arm, therefore with a small force, a large torque. This circumstance led Archimedes to remark:

"Give me a fixed point in space, and I'll turn the world upside down. "

A lever is in equilibrium when the sum of all torques applied to it is equal to zero:

If the lever is tilted by disturbance of the balance by a further torque, the same work is performed on both sides of the hinge point, in each case the road is being traveled during the tilting movement.

The calculation is simplified if one considers forces that are perpendicular to the lever. Thereby, the cross product of a normal product of the magnitude of the vectors. The result is the ratio

The two forces, and at the points and of the lever.

This is the form which leads to the known formulation:

Another quantity that can be considered is the speed at different points of the lever during the movement of the lever. Since there is a rotation movement, the web speed may vary depending on the distance from the pivotal point and of the angular speed. This consideration may, analogous to force ratio, an equation for calculating the velocity ratio can be established:

Real lever

Lever in the art are described by their three components:

• Load arm: The side on which the load to be moved is
• Power arm: The side on which rests the moving force
• Fulcrum or pivot point: The point around which can rotate the lever

With these designations is the lever rule:

In a one-sided load arm and effort arm lever fall together, as the focal point is located at one end of the lever, but both have a different length. In real levers, the effect of friction at the pivot point is also not negligible. Characterized a higher motive power is required, or the resulting force has not reached the theoretical value, since some of the work performed is converted into heat. Another technical problem is the deformation of real materials: In nature there are no " perfectly rigid " body. As a result, that the lever at the pivot point bend or break and does not transmit the required power to the load. In order to reduce these effects are balls or rollers, for example, used as a fulcrum so as to prevent too strong bending.

Real lever, as used for example in engineering, can be made of various materials. In the classical mechanical lever consist of cast iron or steel, the most heavily loaded levers are forged generally in the production. In other industrial areas and lever of other materials, such as used eg plastics.

Applications

Lever can be found in many technical and everyday things again. For rowing, the lever rule is applied by the sportsmen by a large force at the short end of a long way on the long end of the rudder cover, resulting in a high speed. Although it may seem otherwise at first glance: The rudder is a one lever. Load and force attack on the same page. The support - so pivotal point, the point at which supports the lever, located on the rudder blade. Because the motion of the boat is the real purpose, the submerged rudder blade can be regarded as a pivotal point around which the boat is moving, ie is pushed in direction of action of the attacking force. The rudder is fixed to the so-called Dolle the boat; it is only the point of the load, not the focal point of the lever. The exact location of the pivot point depends on how much the rudder is anchored relative to the boat: Supports to the rudder blade from a rock off, there is the crucial point; rowing in the air is the Dolle the pivotal point.

On playgrounds to find levers in the form of paddles. There, the rocker is moved back and forth by alternately applying a force. A nutcracker is a one double lever. Beam balances use the lever rule to compare weights. In automotive engineering rocker arm can be used to change the direction of a force. Nail tool use the law to remove with little force on a long road nails. The piano action is especially the speed ratio is important. A further application is the toggle lever, for example at the knee joint press.