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The horizontal axis of a spring force-displacement graph will contain displacement (in m) and force (in N) on it. The graph’s area is equal to Fs. The amount of time spent working on the item is reflected in this value. With the use of a spring force-displacement graph, we can
- Read forces directly from the graph
- Read displacements with the help of the graph
- Calculate the force’s output by tracing the graph’s x-axis
The increase in kinetic or potential energy that the item experiences as a result of the force being applied is what we mean by this.
What is Spring Force?
In terms of springs, there is a resting position. However, a restoring force always points in the direction of the equilibrium position, whether they are stretched or compressed. When hung straight down, pendulums remain steady. When tension and gravity work on a pendulum that has been yanked out of balance, it swings back and forth.
The inertia of springs, which are common tools, is commonly overlooked because of their small mass. A spring is displaced when stretched and compressed when compacted. That’s when things settle down. If you compress or stretch your body, a spring will produce both an equal and opposite force.
You may hang an item the mass of m from the opposite end of the spring, as long as the spring is permitted to hang down vertically. The item will be subjected to two forces in this situation. The spring’s restoring force, which is oriented upward, will constitute one of the forces. The downward-directed force of gravity will be the opposing force on the mass. If the mass does not move, it will remain at rest at a place where the net force is zero.
Significance of Hooke’s Law
According to Hooke’s Law, the force required to extend or compress a spring by a given distance is inversely related to the distance travelled. It is named after British scientist Robert Hooke, who in the 17th century endeavoured to show the connection between the forces applied to a spring and the spring’s elasticity. Hooke presented the law in the year 1660, and the solution was published in 1678 under the title ut tension, sic vis, which means that ‘the extension is proportional to force’.
Mathematically, this translates to F is equal to -kX, where F refers to force acting on the spring (sometimes as stress or strain), X refers to the spring’s displacement, where the negative number reflects the spring’s displacement once it gets stretched, and k is the constant for spring force, which indicates how tight it is.
One of the earliest traditional attempts to explain how an item or substance might return to its previous form after being stretched or compressed was Hooke’s Law. After being distorted, something’s capacity to be back to its regular form is commonly known as restoring force. According to Hooke’s Law, the value of stretch that is experienced is often proportional to this restoring force.
Additionally, Hooke’s Law applies to many other circumstances when one elastic body is distorted, such as when a spring is deformed. For example, you might use a rubber band to tug a balloon and inflate it to see how much wind power is required to bend and wobble a tall structure.
Analysing Spring Force Versus Displacement Graph
The work done on the spring is represented by the area under the force on the spring versus the displacement curve. It is a graph that shows how much force may be exerted on a spring, based on its displacement. One can also read displacements directly from the graph. Until the spring returns to its original length, elastic potential energy is stored in the spring as a result of the effort directed at it. Consequently, the area is equal to the work done and the area under a curve, both of which are proportional.
However, even if the spring force is negative, the elastic potential energy U can’t be negative since it has a positive sign. Because of this, the spring has positive potential energy when it is extended or compressed.
Practical Applications
The construction of a balancing wheel, which allowed for the clock that is mechanical in nature, the space-saving timepiece, the scale of spring, and also the manometer, was one of the numerous practical implementations of this equation. For this reason, many disciplines of engineering and science are also beholden to Hooke’s Law for his discovery of this rule. Seismology, acoustics, and molecular mechanics are a few examples.
Conclusion
The spring force versus displacement graph serves many purposes. It helps us to read forces directly from the graph and then use the area under the graph to find the work done by the force. According to Hooke’s Law, the force required to extend or compress a spring by a given distance is inversely related to the distance travelled. Mathematically, this translates to F is equal to -kX, where F refers to force acting on the spring (sometimes as stress or strain), X refers to the spring’s displacement, where the negative number reflects the spring’s displacement once it gets stretched, and k is the constant for spring force.
