Force-velocity curve

Just as important as the maximum active force a muscle can exert at various lengths, is the rate at which the muscle shortens as a function of the force load, i.e., the force-velocity curve. Both the length-tension curve and the force-velocity curve vary according to the degree of activation of a muscle. The rate at which crossbridges cycle is an inverse function of the load force (Figure 4). 

Figure 4. When a muscle contracts isotonically or a constant resisting force is imposed on it during a contraction, the velocity at which it shortens quickly comes to a constant. The force-velocity curve shows the relationship between the force applied to a muscle and the steady-state velocity of shortening. As in all other muscles, the force-velocity curve of smooth muscle is a rectangular hyperbola for all positive shortening velocities. In order to compare the behavior of muscles of different lengths and diameters, it is common to normalize force and velocity by dividing each by its maximum value and expressing the result as a percentage, nd...

The mechanical behavior of the contractile apparatus of smooth muscle is also very similar to that of striated muscle. So that to the extent that the force-velocity curves reflect the interaction of mechanical force and the rate of enzymatic catalysis, the steps of the chemomechanical transduction cycles in the two muscles are apparently modulated in similar ways. Also relationships between the active isometric force and muscle length are very similar (except as noted above for shorter lengths). 

The previous linear model of the oculomotor plant is derived from a nonlinear oculomotor plant model by Hsu et al. [1976], and based on a linearization of the force-velocity curve [Bahill et al., 1980). Muscle viscosity traditionally has been modeled with a hyperbolic force-velocity relationship. Using the linear model of muscle reported by Enderle and coworkers [1991], it is possible to avoid the linearization, and derive an updated linear homeomorphic saccadic eye movement model. 

In contrast, the information ratchet model [9], on which (18) and (19) are based, is consistent with microscopic reversibility for both the chemical and the mechanical processes. The shape of the curve described by (18) is governed by both the force dependence ofr and by the term q that parameterizes the relative likelihood of a forward ATP driven step vs a backward ATP-driven step. The force velocity curve is close to hyperbolic with a=l, but with a = 0, the velocity is nearly constant up to a force of slightly more than half the stopping force and then dramatically decreases to zero at the stopping force, and with a = 0.25 (not shown) the velocity is a nearly linearly decreasing function of the applied force up to Fstaii. The thermodynamic properties such as the step ratio, stoichiometry, efficiency, and stall force are independent of t. ... 

In order to facilitate the operation of a fast Journal orbit analysis programme, it was necessary to develop oil film force equations which would give a satisfactory approximation to computed data of the type given in Figures 2a and 2b. This data is for e =0.7. At reduced eccentricity ratio the form of the force - velocity curves is essentially... 

The form of the force-velocity curves is clearly complex, and an extensive search was made for equation forms that would accurately fit this data. No solution was found which would yield satisfactory results over a wide range of eccentricity ratios. In attempting... 

Fig. 2 Typical depth indentation (1), indenter velocity (2), contact force (3) curves obtained on polyvinyl cWoride sample.

In a synchrotron, electrons are accelerated to near relativistic velocities and constrained magnetically into circular paths. When a charged particle is accelerated, it emits radiation, and when the near-relativistic electrons are forced into curved paths they emit photons over a continuous spectrum. The general shape of the spectrum is shown in Fig. 2.4. For a synchrotron with an energy of several gigaelectronvolts and a radius of some tens of meters, the energy of the emitted photons near the maximum is of the order of 1 keV (i.e., ideal for XPS). As can be seen from the universal curve, plenty of usable intensity exists down into the UV region. With suitable mono-... 

Introduction. For the problem depicted in Fig. 4.44, the heat transfer by pure forced convection would increase monotonically with Reynolds number along the curve shown. The heat transfer by pure natural convection from the same surface for various Ra is denoted by the horizontal lines in the figure. If Re is slowly increased from zero in the real problem, the measured values of Nu would at first follow the natural convection curve, since the superimposed forced convection velocities are too feeble to affect the heat transfer. If the forced convection assists the natural convection, the Nu curve in Fig. 4.44 will break upward along path A at larger Re and approach the pure forced convection curve from above. If the flows are opposed, Nu passes through a minimum along path B in Fig. 4.44 and approaches the forced convection curve from below. Mixed convection occurs when the heat transfer is significantly different from that for either pure natural convection or pure forced convection. 

Figure 11.23 Schematic representation of the fracture surfaces of isotactic PP CT specimens as a function of test velocity along with the corresponding force-displacement curves. (From Reference 62 with permission from Elsevier.)...

Figure 11.28 Force-displacement curves of (3-PP compact tension specimens having different crack lengths loaded under velocities of (a) 0.001 m and (b) 3 m at room temperature. (From Reference 63 with permission from Elsevier.)...

Comparison between predicted (Equation 18.1) and measured pressure curves exposed the so-called ejection effect early into ejection the predicted pressure is higher, later in ejection it is lower than the measured one (akin to Hill s 1938 force-velocity relation). To include the ejection effect quantitatively, the function f(t) must be modified and Equation 18.1 becomes... 

Fig. 5 (a) Force induced ring opening of gem-dihalocyclopropane (gDHC). X=F, Cl, and Br. (b) Force-distance curve measured upon extension of gDBC by single molecule AFM at a constant tip withdrawal velocity of 3 pm/s. Adapted with permission from [87], Copyright 2010 American Chemical Society... 

Fig. 4.41 Force-elongation curves of the radial and spiral threads prepared from an Argiope bruennuichii spider with a weight of 0.949 g. Stretching velocity 3.3 X10 m/s.

The force curves, i.e., loading-unloading cycles, were recorded with a velocity of 0.4 /traJs. Hysteresis in the force-distance curves is known to occur under certain conditions of scan velocity. However, hysteresis was minimal for the velocity used in the present work. Following measurement, the tip displacement versus distance curves recorded with the AFM-LPM were transformed to force versus tip—sample separation curves, following the procedure described in refs 16 and 17. 

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