Solution: (a) First, we set up the initial value problem to determine the velocity of the object. The air resistance is equivalent to the instantaneous velocity, so FR=v. The formula mdv/dt=mg−FR then gives us dv/dt=32−v and imposing the initial velocity v(0)=2 yields the init...
completely characterized in terms of the materials that the fibers are made of (i.e., of the Young's modulus of the fiber materials), of their cross sections (i.e., of the area and of the moment of inertia of the fiber cross sections), and of the distance between the nearest pivots...
According to the Second Law in Newtonian mechanics, the force acting upon a body is equal to the product of its mass and acceleration, expressed by the formula F = ma, where F is the force, m is the mass, and a — the acceleration. A force acting upon a body changes the o...
For the conventional design procedure, which is mainly based on the first order linear elastic theory, it is common to assume the effective moment of inertia for the concrete component by the empirical values or the code-specified reduction factors. Generally, it uses half of the gross moment ...
However, in this context, given the taxi drivers’ lurching driving style and heavy usage of brake pads, this means the dynamic formula will overestimate the energy recuperated back into the battery. For this reason, our kinetic model does not use a dynamic regenerative braking formula. Instead...
The work of Malenica and Molin (1995) compared the semi-analytical results of the force and moments on the structure against the approximation formulae and suggested that the FNV formulation is valid for low scattering parameter, ka, below a value of approximately ka=0.05 based on an ...
In a recent publication [15], instead of a numerical calculation approach, a parametric formula was derived analytically, e.g., for the area of a triangle and rectangle control polygon. Figure 1 shows the example of a bar with Cartesian coordinates and with a parametric of the control ...
The IMO 2nd generation intact stability criteria goes through the evaluation procedure by the formulas of Level 1 and Level 2. If the standard formula is satisfied in the Level 1, there is no need to perform the next step. If the evaluation by the formula up to Level 2 is not ...
Wells turbines always rotate in the same direction, yet they can move in a different direction from the direction of the airflow [25]. The following formula establishes a mathematical model of a wells turbine [26,27]: 𝑑𝑃=𝐶𝑎𝑘𝑡1𝑎[𝑣2𝑥+(𝑟𝜔)2]dP=Cakt1avx2+rω...
Figure 1. The structure of the ETV system. The mechanical equation of the throttle plate has the following form: 𝐽𝑒𝑡𝜔˙=𝑇𝑙−𝑇𝑓−𝑇𝑠−𝑇𝐿Jetω˙=Tl−Tf−Ts−TL (1) where, Jet is the rotational inertia of the throttle plate, 𝜔ω is the angul...