When an object's motion repeats with a given cycle, it is said to be in periodic motion.
Oscillation is another term for this kind of motion. Simple examples include the rotation of springs and pendulums, but oscillations may also occur in a variety of other contexts. The observer has a steady equilibrium position, which is an essential aspect of periodic motion. There is also a restoring force aimed at that location. Spring is characterised by the use of force.
Spring Force
There is a spot for the springs where they are at rest.
As they are strained or squeezed, though, a restoring force is created that often points in the direction of equilibrium. Pendulums are secure when hanging straight down. As a pendulum is moved out from its equilibrium point, it bounces back and forth while friction force and momentum work on it.
Hooke's theorem, F = -kx, applies to spring scales. Hooke's law is extremely broad. For very small displacements, almost any entity that can be distorted pushes or pulls with a restoring force equal to the displacement from equilibrium towards the equilibrium state. In addition, the spring force formula is also called Hooke’s law formula. The Hooke’s law equation is also derived as a spring constant equation.
Spring is a commonly used tool, and their inertia is easily overlooked, resulting in a mass of negligible mass. When springs are stressed, they will undergo displacement, and when they are compacted, they will become compressed. And it reaches its equilibrium point. As a result, when a spring compresses or stretches a body, it exerts an equivalent and opposite energy.
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The Spring Force Formula
Simple Harmonic Motion (SHM) is a form of periodic motion. The restoring force Fx is proportional to the displacement x in SHM. The displacement and the restoring power are still in opposition. The spring force equation can be constructed by using a proportionality constant, k. The spring force formula is also called as spring constant formula.
The spring force equation is written as follow,
\[F_{x} = k (x-x_{0})\]
Hooke's Law is the relationship with springs, where k is the spring constant.
Newton per metre is the SI unit of k.
The another form of spring constant equation,
\[F_{x} = -kx\]
Where,
x : The displacement of the spring from its initial position.
\[x_{0}\]: Equilibrium position
k : Spring constant
\[F_{x} \]: The spring force
Note: The negative sign indicates that the spring force visualised is a restoring force that works in the opposite direction.
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Spring Force Solved Examples
Ex.1. A spring has a length of 14 cm/s. If it is loaded with 4 kg, it gets stretched by 28 cm/s. Calculate the spring constant (k).
Answer:
Given,
(Mass) m = 4 kg
(initial length) xo = 14 cm
(displacement) x = 28 cm
Final displacement = x – xo = 28 cm – 14 cm = 14 cm = 0.14 m
The spring force is articulated as,
F = ma
F = 4 kg × 0.14 m
F = 0.56 N
The spring constant equation is,
\[F_{x} = k (x-x_{0})\]
Rearrange the formula of spring force, we get
K = \[-\frac{F_{x}}{(x-x_{0})}\]
K = \[-\frac{0.56}{(28-14)}\]
K = \[-\frac{0.56}{(0.14)}\]
k = - 4 N/m
Thus, the spring constant is -4 N/m.
Ex.2. If a body is stretched by 6m with force 120 N. Calculate its spring constant.
Answer:
Given,
(Displacement) x = 6m
(force) F = 120 N
The spring force constant formula is articulated as,
k = \[-\frac{F_{x}}{(x)}\]
k = \[-\frac{120}{(6)}\]
k = -20 N/m
Thus, the spring constant is -20 N/m.
FAQs on Spring Force Formula
1. Why is spring force negative?
The force exerted by a spring is known as a restoring force, and it often serves to get the spring back to equilibrium. The negative sign on the spring's power in Hooke's law indicates that the spring's force opposes the spring's displacement.
2. Can work done by a spring be negative?
No, when you stretch or compress a spring, the work done by the spring force is negative, but when you release the stretched/compressed spring, the work done by the spring force is positive.
3. Who discovered the spring force?
Robert Hooke.
Hooke's law, which says that the force exerted by a spring is proportional to its extension, was proposed by British physicist Robert Hooke in 1676.
