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Fundamental Concepts
Published in Irving Granet, Jorge Luis Alvarado, Maurice Bluestein, Thermodynamics and Heat Power, 2020
Irving Granet, Jorge Luis Alvarado, Maurice Bluestein
In physics, when studying the motion of a rigid body (i.e., a body that is not deformed or only slightly deformed by the forces acting on it), extensive use is made of free-body diagrams. Briefly, a free-body diagram is an outline of a body (or a portion of a body) showing all the external forces acting on it. A free-body diagram is one example of the concept of a system. As a general concept applicable to all situations, we can define a system as a grouping of matter taken in any convenient or arbitrary manner. We can consider a fixed amount of mass and follow it as it changes shape, volume, or position. In such a system, the mass will have a boundary that prevents any portion of mass from entering or leaving it; and this is called a closed system. However, it still permits energy (i.e., heat and/or work) to cross the specified or denoted boundary. Figure 1.1 shows a piston-cylinder device, which is an example of a closed system. As Figure 1.1 shows, energy in the form of heat (Q) or work (W) can cross its boundary; however, the mass (m) inside the system remains constant and cannot move across the boundary. Another example of a closed system is a closed container with fluid inside or a pressure vessel used to store air at high pressure.
Body Structures
Published in Rob Whitehead, Structures by Design, 2019
Free-body diagrams can evaluate or calculate forces. We will return to this tool often because it presents useful mathematical and geometric information. In this case, we can draw a free-body diagram to find the unknown forces acting within the supporting angled leg. From basic statics (and vector mechanics) we know that angled force vectors can be drawn as the hypotenuse of a force triangle that has both horizontal (H) and vertical (V) force components. In our scenario, we know the vertical force component (V) is one-half of the overall downward force (weight), assuming each leg provided equal support. If we also know the angle of the leg then we can draw the remaining portions of the triangle and solve for the hypotenuse (i.e., the resultant force) using trigonometry or a graphic method.
Free body diagrams
Published in Paul Grimshaw, Michael Cole, Adrian Burden, Neil Fowler, Instant Notes in Sport and Exercise Biomechanics, 2019
Free body diagrams are pictures (diagrams) of forces acting on a body. They allow us to be able to analyse the effect of all the external forces acting on a body more easily (i.e. the effect of the net force). As we have seen within human movement, there are a number of different types of forces that can act on a body: i) gravitational force (weight); ii) frictional force; iii) normal reaction forces; iv) applied contact forces; v) tensile, shear and compressive forces; vi) muscle and joint forces; and vii) centripetal, tangential and centrifugal forces. In human movement, it is often the case that several forces will act on the body simultaneously. As we have seen earlier, force is a vector quantity and thus a force can be expressed or represented by lines with both magnitude and direction. The net effect of these forces (the resultant) acting on a body can be determined through representing all the forces acting on a body using a free body diagram.
Visualising mechanics: washing machine dynamics
Published in International Journal of Mathematical Education in Science and Technology, 2021
Note IG is the mass moment of inertia of the washing load and Rdrum and Rwash are the drum radius and washing load radius, respectively. The washing is characterized as a sphere. The point of the free body diagram and the mass acceleration diagram, is they represent the left-hand and right-hand side of the equations of motion, as determined by Newton’s 2nd law for a translating and rotating body. Applying Newton’s 2nd law together with the assumption that the radius of the washing is small compared to the radius of the drum, so the washing is approximated to be a point mass making the mass moment of inertia zero. Applying Newton’s 2nd law in the normal and tangential direction gives the following equations of motion.