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Some More Problems Solved by Drawing
Published in Ken Morling, Stéphane Danjou, Geometric and Engineering Drawing, 2022
When two or more forces act at or on a point, it is useful to be able to change these forces and show how they could be replaced with a single force that acts in the same way. This force is called the ‘resultant force’. The force that would have to be applied to stabilise the system (by acting against and cancelling out the two or more forces) is called the ‘equilibrant force’. An example is shown in Figure 12.10.
Statics
Published in Bjørn N. Sandaker, Arne P. Eggen, Mark R. Cruvellier, The Structural Basis of Architecture, 2019
Bjørn N. Sandaker, Arne P. Eggen, Mark R. Cruvellier
If two or more forces act along the same line, as they do in the well-known tug-of-war game, we say that they have the same line of action. The combined result of such forces acting on a body can be found by simple arithmetic. When acting in the same direction the resultant force will be the sum of the two forces. If they are acting in opposite directions, then one should be subtracted from the other. Graphically, the resultant force vector is found by setting the beginning of one vector after the end of another, observing their magnitude and direction. (Fig. 4.5.) The specific succession of the vectors is unimportant, and their sum – the resultant force or net force – is the vector force which may be drawn from the tail of the first vector to the tip of the last vector in the sequence. This is the principle of vector addition along a straight line.
Rigging and Material Handling Safety
Published in Frank R. Spellman, Kathern Welsh, Safe Work Practices for Wastewater Treatment Plants, 2018
Frank R. Spellman, Kathern Welsh
Frequently, two or more forces act together to produce the effect of a single force, called a resultant. This resolution of forces can be explained by either the triangle law or the parallelogram law. The triangle law provides that if two concurrent forces are laid out vectorially with the beginning of the second force at the end of the first, the vector connecting the beginning and the end of the forces represents the resultant of the two forces (see Figure 16.2A). The parallelogram law provides that if two concurrent forces are laid out vectorially, with either forces pointing toward or both away from their point of intersection, a parallelogram represents the resultant of the force. The concurrent forces must have both direction and magnitude if their resultant is to be determined (see Figure 16.2B). If the individual forces are known or if one of the individual forces and the resultant are known, the resultant force may be simply calculated by either the trigonometric method (sines, cosines, and tangents) or the graphic method (which involves laying out the known force, or forces, at an exact scale and in the exact directions in either a parallelogram or triangle and then measuring the unknown to the same scale).
The container loading problem with cargo stability: a study on support factors, mechanical equilibrium and grids
Published in Engineering Optimization, 2021
Liliane de Azevedo Oliveira, Vinícius Loti de Lima, Thiago Alves de Queiroz, Flávio Keidi Miyazawa
According to Baraff (1989), each contact point i of a given contact surface of an item k has acceleration . This acceleration should be non-negative since items cannot accelerate so as to interpenetrate each other, and it is given by where stands for the direction of the normal force and is the inertia tensor of item k, which is diagonal and calculated as Figure 3 shows an example of an item k resting on the container's floor. The forces acting on k, on the direction of the normal force, are . They lead to the resultant force and the resultant torque , respectively,
Feedback motion control of a spatial double pendulum manipulator relying on swept laser based pose estimation
Published in International Journal of Optomechatronics, 2021
The torques and are exerted by the SC winch motors. are the resultant force components in the SU plane and is the resultant torque about the axis perpendicular to the SU plane. These are composed by the combination of the thrust forces exerted by the fan actuators. The number of independent control inputs is l = 6. Since there is a dimensional subspace which is not actuated directly. Hence, the system is underactuated.
Hydrodynamic study of sperm swimming near a wall based on the immersed boundary-lattice Boltzmann method
Published in Engineering Applications of Computational Fluid Mechanics, 2020
Qiong-Yao Liu, Xiao-Ying Tang, Duan-Duan Chen, Yuan-Qing Xu, Fang-Bao Tian
The sperm head and the tail are made up of a set of nodes connected by springs in a consecutive way (Afra et al., 2018; Huang et al., 2017; Salih et al., 2019; Xu et al., 2014). Each node is governed by four force components, i.e. the stretching force , the bending force , and the external driving force . The resultant force is The stretching force follows Hooke's law in the tangential direction. It is used to maintain the original head shape and the original tail length, and it is also used to interlock the head and the tail. Which is calculated by (Tian, 2014; Wei et al., 2014) where is the extensional coefficient. For the tail, (Wei et al., 2014), and the original tail length (55μm). Similarly, for the head, and the boundary length . In addition, the elastic modulus is set to be to link the tail and the head together. The above three settings of , and can restrict the stretching rate within the range of in simulation.