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where is the applied tension on the line, is the resulting force exerted at the other side of the capstan, is the coefficient of friction between the rope and capstan materials, and is the total angle swept by all turns of the rope, measured in radians (i.e., with one full turn the angle =).
Tension is the pulling or stretching force transmitted axially along an object such as a string, rope, chain, rod, truss member, or other object, so as to stretch or pull apart the object. In terms of force, it is the opposite of compression. Tension might also be described as the action-reaction pair of forces acting at each end of an object.
The equation used to model belt friction is, assuming the belt has no mass and its material is a fixed composition: [2] = where is the tension of the pulling side, is the tension of the resisting side, is the static friction coefficient, which has no units, and is the angle, in radians, formed by the first and last spots the belt touches the pulley, with the vertex at the center of the pulley.
B: A closed loop [2] C: Turn or single turn [3] D: Round turn [4] E: Two round turns [5] A turn is one round of rope on a pin or cleat, or one round of a coil. [6] Turns can be made around various objects, through rings, or around the standing part of the rope itself or another rope. A turn also denotes a component of a knot.
The rope is threaded through the pulleys to provide mechanical advantage that amplifies the force applied to the rope. [4] Hero of Alexandria described cranes formed from assemblies of pulleys in the first century. Illustrated versions of Hero's Mechanica (a book on raising heavy weights) show early block and tackle systems. [5]
Unless the dog is engaged, the gear will simply freewheel on the shaft. This word usage is a metaphor derived from the idea of a dog (animal) biting and holding on, the "dog" name derived from the basic idea of how a dog jaw locks on, by the movement of the jaw, or by the presence of many teeth. In engineering the "dog" device has some special ...
An equation for the acceleration can be derived by analyzing forces. Assuming a massless, inextensible string and an ideal massless pulley, the only forces to consider are: tension force (T), and the weight of the two masses (W 1 and W 2). To find an acceleration, consider the forces affecting each individual mass.
An ant starts to crawl along a taut rubber rope 1 km long at a speed of 1 cm per second (relative to the rubber it is crawling on). At the same time, the rope starts to stretch uniformly at a constant rate of 1 km per second, so that after 1 second it is 2 km long, after 2 seconds it is 3 km long, etc.