What is Counterweight?

A counterweight is an equivalent counterbalancing weight that balances a load.
A counterweight is often used in traction lifts (elevators), cranes and funfair rides. In these applications, the expected load multiplied by the distance that load will be spaced from the central support (called the "tipping point") must be equal to the counterweight's mass times its distance from the tipping point in order to prevent over-balancing either side. This distance times mass is called the load moment.

Counterweights in Action

Trebuchet: There are five major components of a trebuchet: beam, counterweight, frame, guide chute, and sling. After the counterweight drops from a platform on the frame, gravity pulls the counterweight and pivots the beam. Without the counterweight, the beam could not complete the arc that allows the sling to accurately release the projectile.

Crankshaft: A counterweight is also used in many rotating systems to reduce vibrations due to imbalances in the rotating assembly. A typical example is counterweights on crankshafts in piston engines.

Elevator: In traction (non-hydraulic) elevators, a heavy counterweight counterbalances the load of the elevator car, so the motor only has to lift the difference between the car load and the counterweight load. The counterweight also increases the ascending acceleration force and decreases the descending acceleration force to reduce the amount of power needed by the motor. The elevator car and the counterweights both have rollers attached to them to prevent irregular movement and provide a smoother ride for the passengers.

Space elevator: A space elevator is a proposed structure designed to transport material from a celestial body's surface into space. Many variants have been proposed, but the concept most often refers to an elevator that reaches from the surface of the Earth to geostationary outer space, with a counterweight attached at its outer end.

By attaching a counterweight at the end, inertia ensures that the cable remains stretched taut, countering the gravitational pull on the lower sections and thereby allowing the elevator to remain in geostationary orbit.
And due to some Special properties of tungsten alloy weights
- High density up to 18.5 g/cm3.
- Up to 65% denser than Lead.
- Up to 130% denser than Steel.
- Mechanical properties to suit either dynamic or static locations.
- Weakly Ferro magnetic.
- Non-magnetic, if specifically required.
- Alternative to Lead.
- Non-Toxic.
- Corrosion resistant.
- Easily machined.
- Easily mechanically joined, brazed or shrunk fit to other materials.
Tungsten alloy is a suitable material to make counterweight. And also it can be made into different shapes, such as ball, brick, and rod to satisfy various requirements.

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Or you can see more details in http://en.wikipedia.org/wiki/Counterweight.