the concepts of fracture and elasticity

static equilibrium

Chapter 9 introduces the topic of static equilibrium as well as the concepts of fracture and elasticity. The chapter begins by highlighting the fact that in cases where the centre of mass of an object or system of objects is moving at a constant velocity or is at rest, the net torque, net force, linear and angular acceleration are at zero. The main focus of the chapter is however objects at rest, with the term statics referring to the calculation of forces acting within or on an object in equilibrium. The chapter poses that for an object to be in equilibrium, the sum of the forces acting on it must be zero, giving the example of a book on a table, whereby, the upward force is equal to the force of gravity, meaning the net result of the action of the two forces is equilibrium.

The first condition of equilibrium

The first condition of equilibrium is therefore represented as ∑Fx =0, ∑Fy = 0 and ∑Fz= 0, in cases where the forces are acting along more than one plane. The second condition similar to the first one, stipulates that the sum of all torques acting on the object must also be zero, such that ∑τ = 0. The chapter then proceeds to provide examples of how these two conditions can be used to make calculations on the forces acting on objects that are in equilibrium. Further, the chapter also highlights how various forces exerted by the body muscles act to sustain balance and body posture still based on the two conditions of equilibrium.

The chapter then proceeds to argue that in cases where objects in equilibrium are not disturbed, they remain static, before introducing the concepts of stable, unstable and neutral equilibrium. In the first case, the application of a force only displaces the object before it returns to its original position. In the second scenario, the object moves farther away from its original position and in the third case, the object remains in its new position. The chapter further elaborates that objects in stable equilibrium have their centre of gravity (CG) below the point of support, while objects in unstable equilibrium have the CG above the point of support, meaning it could shift with the exertion of torque. Stability in objects with an unstable equilibrium, comes when a vertical line that passes through the centre of gravity falls within its base of support, such that the wider the base, the more stable an object is.

The next concept introduced in the chapter is that of Hooke’s law, which argues that the change in length of an object is proportional to the amount of force applied, represented as F = kΔL, until the object reaches the elastic limit, and the relationship between F and ΔL ceases to be proportional. The maximum force that an object can withstand before breaking is known as the ultimate strength. Young’s modulus, which refers to the property of the material with which an object is made also determines the elasticity and ultimate strength of an object and is an important factor when it comes to calculations of forces that result in the elongation of an object, as given by the equation ΔL = 1/E(F/A)L0, where E is Young’s modulus (elastic modulus) and L0 refers to the initial length. Further, simplification of the equation shows that E = stress/strain.

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