matter is made up of atoms and molecules. Anolyting external forces the weight, pressure, heat, etc., causes the deformation of the mater, which in turm changes the mather's shape, dimension, ang americacion.
Solid matter is made up of atoms and molecules which zacket cinsels. The intermolecular space between the atoms s significantly less than in liquid and gas. Because of this property of solids, they recain their original shapes easily, and the atoms of molecules return to equilibrium alter removal force.
in the case of hound and gaseous matter, the atoms and moleculles are loosely packed and the deformation of this matter takes less force as compared to sods. LIQUIDS and gaseous mater do not retain their equilibrium state unless an external force is azched again. Some examples include a stretched rubber band as shown in figure 5.1, a bent metal rod and a shattered glass as shown in figure 5.2.
"The ability of a deformed body to return to its original shape and size when the deforming forces are removed is called elasticity'. When a stretched spring is released, it comes back to its original form. When a tennis racket hits a tennis ball, the shape of the ball is distorted or deformed, but it regains its original shape when it bounces off the tennis ball. Similarly, when an archer shoots an arrow, she bends the bow which comes back to its original form after the arrow is released as shown in figure 5.3.
Not all materials return to their original shapes when a deforming force acting on it is removed. Materials that do not return to their original shapes after being distorted are said to be inelastic. Examples of inelastic materials are plasticine, clay, and dough.
Most materials are elastic up to a certain limit known as the elastic limit. Beyond the elastic limit, a material will not return to its original dimensions when the deforming force is removed.
When a spring is stretched or compressed (within elastic limit), the extension or compression is directly proportional to the applied force (Figure 5.4). This relationship is known as Hooke's law which states that within elastic limits the extension (or compression) x is directly proportional to the restoring force F i.e. Fx-x or Fkx therefore k=-Fres / X
where 'k' is the ratio of restoring force to the extension and is known as the force constant or spring constant having units Nm. The negative sign shows that force is directed against displacement. This relationship is also true for a wire under tension. Provided that the limit of proportionality is not exceeded, a graph of stretching force against extension is a straight line through the origin, as shown in figure 5.4.
The gradient of the line F/x is the spring constant 'k'. Hooke's Law is obeyed up to the limit of proportionality. Beyond this point, stretching force and extension are no longer directly proportional and the graph begins to curve.
Hooke's law has many important practical applications, with one being the creation of a balance wheel, which made possible the creation of the mechanical clock, the portable timepiece. Hooke's law is also used as a fundamental principle behind spring scale. It is also used as the foundation for diving boards and car suspension systems, seismology, acoustics, molecular mechanics, and even in medical science. The spring is a marvel of human engineering and creativity, still in use in many modern-day instruments.
A balance wheel is the timekeeping device used in mechanical watches. It is a weighted wheel that rotates back and forth, being returned toward its center position by a spiral torsion spring or hairspring as shown in figure 5.5 (a). It is driven by the escapement, which transforms the rotating motion of the watch gear train into impulses delivered to the balance wheel. Each swing of the wheel (called a 'tick' or 'beat') allows the gear train to advance a set amount, moving the hands of watch forward. The combination of the mass of the balance wheel and the elasticity of the spring keep the time between each oscillation or 'tick' very constant.
A spring scale (spring balance) is a type of mechanical force measuring instrument that makes use of a spring. This device is mainly used to weigh items or objects by connecting them to a hook at its bottom as shown in figure 5.5 (b). Since by Hooke's law the force or weight that extends a spring is directly related to the distance that the spring is extended from its initial position, the spring scale converts this extension to measuring weight using an analog or digital gauge attached to the device.
A galvanometer is a device used for detecting current or voltage. It makes use of the hairspring which not only provides electrical connection to the coil and restores the pointer back but also makes the deflection proportional to the force according to Hooke's law as shown in figure 5.5 (c). And since the force is proportional to the current, it permits us to draw an analog scale under the pointer and measure the current.
What would happen to the reading if two or more spring balances are hung one below the other in series?
Stress and strain curves are measured by a stress tester, one such machine Rockwell hardness tester is shown in the figure 5.6 (a). The applied stress is increased, and the change in length is noted. The values are then plotted on a graph. A typical graph for metal is shown in the figure 5.6 (b). Here, Point A, is the limit of proportionality, the limit up to which Hooke's law is obeyed called the proportional limit. Point B, is the elastic limit, the limit up to which material shows elastic behavior also called yield strength, point C is the maximum stress a material can bear before fracture (breaking) called ultimate stress and point D, is the breaking point, where material breaks.
Kamil sits on a spring chair as shown in the figure. If Kamil's weight is 50 kg and compresses the spring by about 10 cm, when he sits on the chair, find the spring constant of this chair's spring.
Spring constant 'k' = ?
The force stretching the spring is equal to the weight of the body, given by:
W = F = mg = 50 kg x 9.8 m/s² = 490 N
From Hook's law: F = kx or k = F / x
Therefore, Putting values: k = 490 N / 0.1 m = 4,900 N/m
So, the given chair spring has a spring constant of 4,900 N/m.