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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
Diagram 3 shows three rope parts supporting the load W, which means the tension in the rope is W/3. Thus, the mechanical advantage is three-to-one. By adding a pulley to the fixed block of a gun tackle the direction of the pulling force is reversed though the mechanical advantage remains the same, Diagram 3a. This is an example of the Luff tackle.
In physics, Hooke's law is an empirical law which states that the force (F) needed to extend or compress a spring by some distance (x) scales linearly with respect to that distance—that is, F s = kx, where k is a constant factor characteristic of the spring (i.e., its stiffness), and x is small compared to the total possible deformation of the spring.
For example, a vibrating rope in 2D space is defined by a single-frequency (1D axial displacement), but a vibrating rope in 3D space is defined by two frequencies (2D axial displacement). For a given amplitude on the modal variable, each mode will store a specific amount of energy because of the sinusoidal excitation.