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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.
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.
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 =).
a simple massless force, [citation needed] an oscillator, [citation needed] or; an inertial force (mass and a massless force). [citation needed] Numerous historical reviews of the moving load problem exist. [1] [2] Several publications deal with similar problems. [3] The fundamental monograph is devoted to massless loads. [4]
The rod or cord is massless, inextensible and always remains under tension. The bob is a point mass. The motion occurs in two dimensions. The motion does not lose energy to external friction or air resistance. The gravitational field is uniform. The support is immobile. The differential equation which governs the motion of a simple pendulum is
In an ideal system, the massless and frictionless pulleys do not dissipate energy and allow for a change of direction of a rope that does not stretch or wear. In this case, a force balance on a free body that includes the load, W, and n supporting sections of a rope with tension T, yields: =
In the Lagrangian, the position coordinates and velocity components are all independent variables, and derivatives of the Lagrangian are taken with respect to these separately according to the usual differentiation rules (e.g. the partial derivative of L with respect to the z velocity component of particle 2, defined by v z,2 = dz 2 /dt, is ...
The angular deficit δ is linearly related to the string tension (= mass per unit length), i.e. the larger the tension, the steeper the cone. Therefore, δ reaches 2π for a certain critical value of the tension, and the cone degenerates to a cylinder. (In visualizing this setup one has to think of a string with a finite thickness.)