Hooke’s Law: History, Formulas, Sounds, and Example Problems

Hooke’s Law – If we learn about physics, of course we will find various kinds of laws that apply. Just as when we are studying the elasticity of an object, of course we will find about Hooke’s law. This is one of the laws in physics that often appears in daily questions, tests or national exams.

Therefore, it is important for you, especially those who are still in high school, to learn about hooke’s law in depth. So, in this article, we will discuss Hooke’s law more fully and with a simple discussion that is easy to understand.

What is Hooke’s Law?

Hooke’s law is a law or provision regarding forces in the field of physics that occur due to the elastic properties of a pear or spring. According to Robert Hooke, a scientist who discovered Hooke’s Law, objects are divided into two types, namely plastic objects and elastic objects. Where a plastic object is an object that changes when subjected to a force and the object cannot return to its original shape after the applied force is gone. Meanwhile, elastic objects are objects that change when subjected to a force and the object can return to its original shape when the force is removed. For example, bows, peers, rubber bands, and catapults.

Robert Hooke conducted an experiment to observe the relationship between the changes that occur between elastic objects and the force exerted on them. From these experiments, Hooke found a law about the relationship between force and changes in spring force which is now known as Hooke’s law. The magnitude of the hook force will be proportionally proportional to the distance the spring travels in its initial position. If explained through a mathematical formula, it can be described as follows:

F = -kx

Information:

F is the force or units of newtons
k is the spring constant or newtons per meter
x is the distance the spring travels from its normal position or units of meters

The ability of an object to return to its original shape when an external force is removed. If a force is applied to an elastic object, the shape of the object will change. For rubber and springs, what is meant by a change in shape is the increase in length of the two objects. Objects that are elastic also have a limit of elasticity. There are two kinds of objects, namely elastic objects and inelastic objects or often called plastic.

History of Hooke’s Law

Robert Hooke is a scientist who was born in Freshwater, Isle of Wight, England on July 18, 1635. He was an inventor, mathematician and chemist, philosopher, and architect. Hooke was a pastor’s son. Where his father named John Hooke who works as a curator at the All Saints Church museum. When he was small, Hooke often studied with his father, because his parents were poor, so Hooke was not free to choose where he studied. Finally, Hooke became interested in art and then he was sent to London to begin studying with a painter named Peter Lely.

Hooke then changed his interest and decided to enroll at Westminster school to study classics as well as mathematics. Then, he studied at Robert Boyle University because of a recommendation from a Chemistry Professor named Thomas Willis who tutored Hooke. At that time, Thomas Willis had just come from Oxford and was looking for an assistant who he wanted to make as a partner to help in making air pumps. At the time, it had taken Robert Hooke at Boyle two decades to make any quite remarkable advances in mechanics.

Then in 1662, Hooke was accepted as a member of the Curator of the Royal Society whose main task was to propose and also make various kinds of experiments to be submitted at the group’s weekly meeting. Two years later, Hooke won a position as professor of geometry at Gresham College. He replaced the position of Isaac Borrow who had previously appeared in that position. In the midst of his busy life as Curator of the Royal Society in 1665, Hooke managed to publish a book entitled Micrographia. The book is a book in biology which is the only book made by him. But it also contains a number of beautiful and unusual things from someone who has drawing skills.

Hooke’s expertise as a versatile scientist was displayed in 1666, during the great fire in the City of London. Hooke, who has the ability to draw like an architect, makes master plans and plans for rebuilding buildings that have been damaged by fire. After that, the City Council finally chose Hooke to become the city’s development planner under the auspices of Sir Christopher Wren. It was he who became a close friend of Hooke and discovered the important role of oxygen in the respiratory system.

Hooke’s law that was found has a formula with a sign (-) reveals that the direction of F is opposite to the direction of change in the length of x. According to Hooke, in the presence of x which is measured using the balance position of the spring, the sign (-) will indicate that the spring is stretched (L> 0). Vice versa, when pressing the spring (L<0), the spring force is in the positive L direction while k is referred to as the spring constant having a dimension of length or force.

Robert Hooke himself has considerable attention in scientific fields, ranging from astronomy to geology, the law of conservation or elasticity which still bears his name. Hooke made several significant contributions toward explaining the motion of the planets by suggesting that the orbits of the planets were caused by a combination of inertia descending in a straight line and the gravitational pull of the sun. Robert Hooke can also be said to have an unhappy life. Where he is easily offended, especially when he is suspicious of someone who is thought to be stealing his idea. He was also often sick and unable to sleep, in fact he only slept for three to four hours. Hooke also suffered from chronic illnesses, namely his feet were inflamed and he became blind in 1702 and exactly one year later, Robert Hooke died.

Hooke’s Law formula

The increase in length that appears will be directly proportional to the applied tensile force. This was first investigated in the 17th century by an architect from England named Robert Hooke. At that time, Hooke observed the relationship between the tensile force exerted on a spring and the increase in length of the spring. Hooke found that the increase in length of a spring occurs in direct proportion to the applied force. In addition, Hooke also found that the increase in length of the spring is very dependent on the characteristics of the spring itself.

A spring that stretches more easily, such as a rubber band, will experience a greater increase in length even though the force exerted is relatively small. Vice versa, a spring that is difficult to stretch, like a steel spring, will experience a relatively small increase in length, even though it is given a large enough force. The characteristics that exist in each of these springs are expressed by the force constant of the spring itself. Springs that stretch easily, such as rubber bands, have a smaller force constant. Vice versa, a spring that is difficult to stretch will have a greater power constant.

In general, what Hooke discovered can be stated as follows:

F = k. x

Information:

F is the force applied to the spring (N)
k is the setting of the spring force (N/m)
x is the increase in the length of the spring (m)

Spring Potential Energy

The amount of potential energy that is in a spring can be calculated from the graph of the relationship that works on the spring with the increase in the length of the spring itself: Here is the formula:

Ep = ½ F . x
= ½ (k . x) . x
Description:
Ep = spring potential energy (joules)
k = spring force constant (N/m)
x = spring extension (m)

Elasticity Modulus

Modulus of Elasticity is a comparison between strain and stress. This modulus is known as Young’s modulus.

a. Voltage or Stress

Stress is the force per unit cross-sectional area. Where the unit of stress is N/m2.

b. Strain or Strain

Stretch is the comparison between the increase in length in a rod compared to the beginning if the rod is subjected to force.

Hooke’s Law sounds

After discussing a little description of Hooke’s law and also various things related to elasticity in an object. Now, we will discuss about the sound of Hooke’s law. So, according to Hooke’s law, the greater the force exerted on an object, the longer the spring will be.

The following is Hooke’s law:

“If the tensile force exerted on a spring does not exceed the elastic limit of the material, the increase in spring length is directly proportional or proportional to the tensile force.”

After reading Hooke’s law above, do you understand more? So, we can conclude that the purpose of Hooke’s law is that when the force we apply exceeds the elastic limit, the object cannot return to its original shape.

Hooke’s Law Application

In everyday life, we will often encounter objects related to Hooke’s law. The application of Hooke’s law will be closely related to objects that have a working principle by using an elastic spring.

There are various examples of applications related to Hooke’s law, including:

1. A microscope that has the function of seeing various kinds of objects that have small properties or micro-organisms that are very small and cannot be seen using only the naked eye.
2. A clock that uses a peer to set the time.
3. Swings that have spring properties.
4. A gauze clock or chronometer used to determine the direction or position line of a ship in the middle of the sea.
5. An instrument for measuring the acceleration of gravity of the earth.
6. Connection of a gear stick to a vehicle such as a car or motorcycle.
7. Tools such as telescopes are useful for being able to see objects that are far away so that they look closer.

So, basically the idea of ​​Hooke’s law will have a positive impact on ourselves.

Hooke’s Law Magnitude

Hooke’s law also has a quantity that you can learn, including:

1. Voltage

Tension is a condition of an object that experiences an increase in length when an object is given a force at one end, while the other end is held. The following is the voltage formula:

σ = F/A

F is the force (N)
A is the cross-sectional area (m2)
σ is the stress (N/m2 or pa)

2. Stretching

Stretch is a comparison between the increase in the length of the wire in x meters and the normal length of the wire in x meters. The appearance of a stretch because there is a force given to the object or wire that is removed. So that the wire will return to its original shape.

The following is the strain formula:

e = ΔL/ Lo

e is the stretch
AL is the increase in length (m)
Lo is the initial length (m)

3. Modulus of Elasticity

The modulus of elasticity is the ratio between the stress and strain experienced by a material. It is formulated by:

E = p/e

E is the elastic modulus (N/m)
σ is the stress (N/m2 or Pa)
e is the strain

4. Compression

Compression is a condition that is almost the same as strain. The difference is only in the direction of movement of the object’s molecules after being given a certain force. When compressed, the object’s molecules will be pushed inwards.

5. Relationship Between Tensile Force and Modulus of Elasticity

If written mathematically, the relationship between tensile force and elastic modulus is as follows:

Information:
F = Force (N)
E = Modulus of elasticity (N/m)
e = Strain
σ = Stress (N/ m2 or Pa)
A = Cross-sectional area (m2)
E = Modulus of elasticity (N/m)
ΔL = Length gain (m)
Lo = initial length (m)

6. Exemption Law

Hooke’s law states that if the tensile force does not exceed the elastic limit of the spring, then the length of the spring will be proportional to the tensile force. If written mathematically, it would be like this:

Information:
F = external force exerted (N)
k = spring constant (N/m)
Δx = addition of spring length from its normal position (m)

Hooke’s Law for Spring Arrays

a. Series order

If two springs that have the same spring constant are in series, then the length of the spring is 2 times. Therefore, the spring equation is as follows:

Note:
Ks = spring equation
k = spring constant (N/m)

While the equation for n springs whose settings are also arranged in series, will be written like this:

Description:
n = Number of springs

b. Parallel Arrangement

If the springs are arranged in parallel, the length of the spring remains as it was at the beginning, while the cross-sectional area is doubled from the beginning if the spring is composed of two pieces. For spring equations arranged in parallel are:

Note:
Kp = Equation of a parallel arrangement of springs
k = Spring constant (N/m)

While the equation of n springs with the same settings and arranged in a parallel system, it will produce a stronger spring. Because the settings become larger. The spring equation can be written as follows:

Description:
n = Number of springs

Example of Hooke’s Law Problem

A spring has an increase in length of 0.25 m after a force is applied. If the spring reads 400 N/m. How much force is exerted on the spring?

known :
x = 0,25 m
k = 400 N/m