English Physicist Robert Hooke (1635 – 1703) in the year 1676 put forward the relationship between the extension produced in a cable and the restoring force developed in it. An ideal spring is remarkable in the logic that it is a method where the generated force is linearly dependent on how far it is stretched; this activity is described by Hooke’s law. The law formulated on the base of this study is known as Hooke’s law.
A spring is suspended from rigid support as shown in the Figure. A weight hanger and a light pointer are attached at its lower end such that the pointer can slide over a scale graduated in millimeters.
The initial reading on the scale is noted. A slotted weight of m kg is added to the weight hanger and the pointer position is noted. The same procedure is repeated with every additional m kg weight. It will be observed that the extension of the spring is proportional to the weight. This verifies Hooke’s law.
According to Hooke’s law, within the elastic limit, the strain produced in a body is straight proportional to the pressure that produces it. This Law stated above that to extend a spring by an amount dx from its previous position, one needs a force F which is determined by F = kdx. Here k is the spring constant which is a quality of each spring.
(i.e) pressure α strain
Stress / Strain = a constant, known as modulus of elasticity.
Hooke’s Law Formula is given by: F = -kx
Its unit is Nm-2 and its dimensional formula is ML-1T-2.
Experimental verification of Hooke’s law –
Therefore, in order to verify Hooke’s Law, you must prove that the force F and the detachment at which the spring is stretched are comparative to each other and that the constant of proportionality is k.
A spring is balanced from a rigid hold as shown in Fig. A weight hook and a light cursor are attached at its inferior end such that the cursor can slide over a scale graduated in millimeters. The primary reading on the scale is noted. A slotted weight of ‘m’ gram/kg is further to the weight hook and the cursor place is noted. It will be experimental that the conservatory of the spring is comparative to the weight. This verifies Hooke’s law.
- The spring reading meter will measure in its primary face.
- Then the spring placed in the fix of the retort position and hold together strongly adequate to grasp it in position.
Example: A spring is stretched by 5 cm and has a force constant of 2 cm /dyne. Calculate the Force applied?
Given: Force constant k = 2 cm/dyne,
Extension x = 5 cm.
The force applied is given by F = – kx = – 2cm/dyne * 5 cm = – 10 cm/dyne.