Physics
Spring Force
Spring force is the restoring force exerted by a compressed or stretched spring, seeking to return to its equilibrium position. It follows Hooke's Law, which states that the force is directly proportional to the displacement from equilibrium. This force is a fundamental concept in physics and is used to describe the behavior of springs in various mechanical systems.
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5 Key excerpts on "Spring Force"
eBook - PDF- Raymond Serway, Chris Vuille(Authors)
- 2017(Publication Date)
- Cengage Learning EMEA(Publisher)
WCN 02-300 5.5 | Spring Potential Energy 137 Unless otherwise noted, all content on this page is © Cengage Learning. 5.5 Spring Potential Energy Springs are important elements in modern technology. They are found in machines of all kinds, in watches, toys, cars, and trains. Springs will be introduced here, then studied in more detail in Topic 13. Work done by an applied force in stretching or compressing a spring can be recov- ered by removing the applied force, so like gravity, the Spring Force is conservative, as long as losses through internal friction of the spring can be neglected. That means a potential energy function can be found and used in the work–energy theorem. Figure 5.21a shows a spring in its equilibrium position, where the spring is nei- ther compressed nor stretched. Pushing a block against the spring as in Figure 5.21b compresses it a distance x. Although x appears to be merely a coordinate, for springs it also represents a displacement from the equilibrium position, which for our pur- poses will always be taken to be at x 5 0. Experimentally, it turns out that doubling a given displacement requires twice the force, and tripling it takes three times the force. This means the force exerted by the spring, F s , must be proportional to the displacement x, or F s 5 2kx [5.16] where k is a constant of proportionality, the spring constant, carrying units of new- tons per meter. Equation 5.16 is called Hooke’s law, after Sir Robert Hooke, who discovered the relationship. The force F s is often called a restoring force because the spring always exerts a force in a direction opposite the displacement of its end, tending to restore whatever is attached to the spring to its original position. For positive values of x, the force is negative, pointing back towards equilibrium at x 5 0, and for negative x, the force is positive, again pointing towards x 5 0.
- David Halliday, Robert Resnick, Jearl Walker(Authors)
- 2023(Publication Date)
- Wiley(Publisher)
The constant k is called the spring constant (or force constant) and is a measure of the stiffness of the spring. The larger k is, the stiffer the spring; that is, the larger k is, the stronger the spring’s pull or push for a given displacement. The SI unit for k is the newton per meter. In Fig. 7.4.1 an x axis has been placed parallel to the length of the spring, with the origin (x = 0) at the position of the free end when the spring is in its relaxed state. For this common arrangement, we can write Eq. 7.4.1 as F x = −kx (Hooke’s law), (7.4.2) where we have changed the subscript. If x is positive (the spring is stretched toward the right on the x axis), then F x is negative (it is a pull toward the left). If x is negative (the spring is compressed toward the left), then F x is positive (it is a push toward the right). Note that a Spring Force is a variable force because it is a function of x, the position of the free end. Thus F x can be symbolized as F(x). Also note that Hooke’s law is a linear relationship between F x and x. The Work Done by a Spring Force To find the work done by the Spring Force as the block in Fig. 7.4.1a moves, let us make two simplifying assumptions about the spring. (1) It is massless; that is, its mass is negligible relative to the block’s mass. (2) It is an ideal spring; that is, it obeys Hooke’s law exactly. Let us also assume that the contact between the block and the floor is frictionless and that the block is particle-like. We give the block a rightward jerk to get it moving and then leave it alone. As the block moves rightward, the Spring Force F x does work on the block, decreasing the kinetic energy and slowing the block. However, we cannot find this work by using Eq. 7.2.5 (W = Fd cos ϕ) because there is no one value of F to plug into that equation—the value of F increases as the block stretches the spring.
eBook - PDF- Joaquim A. Batlle, Ana Barjau Condomines(Authors)
- 2022(Publication Date)
- Cambridge University Press(Publisher)
Springs may introduce either an attrac- tion or a repulsion between their endpoints. The most usual case is the linear spring, where the force change associated with a change of spring length is proportional to that length change through a constant parameter called the spring constant k: k Δ attraction repulsion ð Þ force between the spring ends increase decrease ð Þ of spring length : (1.12) Springs constants are always positive. However, the term spring may be used in a more general sense for any physical phenomenon whose net force is a function of ρ (in this context, the gravitational force can be seen as a spring). In that case, we will talk of equivalent spring, and the constant may be negative. A real spring (not an equivalent one) has a nonzero slack length ρ slack (length for which the force between the spring endpoints is zero). From that state, the spring will generate an attraction force if the length is increased Δρ ¼ ρ ρ slack > 0 ð Þ and a repulsion force if it is decreased Δρ < 0 ð Þ. The force associated with a spring within a mechanical system may evolve from attraction to repulsion with time. When solving the system dynamics, the Spring Force is drawn either as an attraction or a repulsion, and its value is formulated accordingly (Fig. 1.12). If the Spring Force is formulated from a nonzero-tension state (a state where its length ρ 0 is higher or lower than ρ slack , and the Spring Force is F 0 ), the choice of its description as an attraction or a repulsion is made according to the nature of the initial force F 0 : 9 The origin and the “constancy” of the fundamental constants are subjects still under discussion nowadays. Some scientists relate them to our limitations when it comes to measuring the external objective world, some others claim they might be slowly changing. . . 10 This drawback is solved within Einstein’s Theory of General Relativity. 18 Particle Dynamics
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Academic Studio(Publisher)
Forces which do not act uniformly on all parts of a body will also cause mechanical stresses, a technical term for influences which cause deformation of matter. While mechanical stress can remain embedded in a solid object, gradually deforming it, mechanical stress in a fluid determines changes in its pressure and volume. Philosophers in antiquity used the concept of force in the study of stationary and moving objects and simple machines, but thinkers such as Aristotle and Archimedes retained fundamental errors in understanding force. In part this was due to an incomplete understanding of the sometimes non-obvious force of friction, and a consequently inadequate view of the nature of natural motion. A fundamental error was the belief that a force is required to maintain motion, even at a constant velocity. Most of the previous misunderstandings about motion and force were eventually corrected by Sir Isaac Newton; with his mathematical insight, he formulated laws of motion that remained unchanged for nearly three hundred years. By the early 20th century, Einstein developed a theory of relativity that correctly predicted the action of forces on objects with increasing momenta near the speed of light, and also provided insight into the forces produced by gravitation and inertia. With modern insights into quantum mechanics and technology that can accelerate particles close to the speed of light, particle physics has devised a Standard Model to describe forces between particles smaller than atoms. The Standard Model predicts that exchanged particles called gauge bosons are the fundamental means by which forces are emitted and absorbed. Only four main interactions are known: in order of decreasing strength, they are: strong, electromagnetic, weak, and gravitational. High-energy particle physics observations made during the 1970s and 1980s confirmed that the weak and electromagnetic forces are expressions of a more fundamental electroweak interaction.
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
________________________ WORLD TECHNOLOGIES ________________________ Chapter- 6 Force Forces are also described as a push or pull on an object. They can be due to phenomena such as gravity, magnetism, or anything else that might cause a mass to accelerate. In physics, a force is any influence that causes a free body to undergo an acceleration. Force can also be described by intuitive concepts such as a push or pull that can cause an object with mass to change its velocity (which includes to begin moving from a state of rest), i.e., to accelerate, or which can cause a flexible object to deform. A force has both magnitude and direction, making it a vector quantity. Newton's second law, F=ma, can be formulated to state that an object with a constant mass will accelerate in proportion to the net force acting upon and in inverse proportion to its mass, an approximation which breaks down near the speed of light. Newton's original formulation is exact, and does not break down: this version states that the net force acting upon an object is equal to the rate at which its momentum changes. Related concepts to accelerating forces include thrust, increasing the velocity of the object, drag, decreasing the velocity of any object, and torque, causing changes in rotational speed about an axis. Forces which do not act uniformly on all parts of a body ________________________ WORLD TECHNOLOGIES ________________________ will also cause mechanical stresses, a technical term for influences which cause deformation of matter. While mechanical stress can remain embedded in a solid object, gradually deforming it, mechanical stress in a fluid determines changes in its pressure and volume.
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