IIT JEE and NEET Physics @ Venkats Academy IIT-JEE and NEET Physics

Breaking stress is the maximum stress that the body can withstand before it finally breaks. It is defined as the ratio of braking force per unit area. It depends on the nature of the material but it is independent of the physical dimensions of the body like area and the length of the body.

Braking force can be defined as breaking stress multiplied with area. The braking force depends not only on the nature of the material but also on the area of the cross-section of the material.

So if you cut your wire to half of its original length, it is breaking stress remain same and even the braking force also remains the same.

If you cut the wire to half of its thickness, the breaking stress of the wire remains same but the braking force will be reduced to half.

It is quite possible that a very long wire due to its own weight can get the braking force and break. This particular Length is called braking length. While writing a equation for this, in the place of the weight we have to write mass of the body multiplied by the acceleration due to gravity. Basing on this concept we can read the equation further braking length of a wire as shown in the diagram below.

We can also calculate the increase in the length of the wire due to its own weight when the wire is not breaking. While solving this problem we shall consider that the entire mass of the wire is concentrated at the centre of the mass of the body and hence while calculating the length that we have to take only half of the length of the wire.The derivation for this is also shown in the above diagram.

Elastic fatigue is the phenomenon of the temporary loss of the elastic property due to the continuous application of the force on a body.Basing on this property by applying a force on a wire continuously at a particular point we can actually break it without cutting it.

Problem and solution

The length of a metal wire at tention T1 is L1 and its length is L2 for a tension T2. Find the original length of the wire when no forces applied on it?

As the given lengths of the wire when a particular forces applied, we can consider L1 as original length plus some extra length. The same can be applied in the 2^nd case also in the problem can be solved as shown below.

Loaded spring in simple harmonic motion

Waves and Oscillations

Damped Oscillations and Forced Oscillations

Mechanical Properties of Solids and Young's Modulus

Problems and Solutions on Young's Modulus of a wire

Rigidity Modulus and Bulk Modulus

Behavior of a Wire under Increasing Load

We want to study how a wire behaves when we apply the force continuously on the body. By increasing the stress on the body continuously the corresponding strain is noted down and a graph is drawn between the stress and strain as shown. Here the stress is taken and y-axis and the strain is taken on x-axis.

When we do not apply any force on the body there is no stress and hence there is no strain. With the increase of the stress the strain also increases proportionately up to certain extent and the point up to where it happens is called as elastic limit. Many times this limit is also called as proportionality limit, it meant to say that for many bodies proportionality limit and the elastic limit coincides with each other.

When the stress is applied about this point the stress is not exactly directly proportional to strain but the particle will still have elastic nature. That means if you revert back the stress that we have applied strain also comes back and the graph retraces back to the origin.

Once if this elastic limit is crossed ,with respect to the increase of the stress the strain also increases but the proportionality is no more there. From this point we cannot retrace the graph which mean to say that when you decrease the stress strain is not going to completely disappear rather a small portion of the strain will exists forever. This kind of the arrangement is called permanent set. We can calculate the value of the permanent set has the product of the original length of the wire and the shift of the graph. This point is generally called as yielding point.

If the force is applied beyond the yielding point there will be a increase of the strain even when the stress is not increases significantly and the wire start becoming thin. This can happen up to some extend and finally at a particular point the wire will break .This point where the wire breaks is called as breaking point.

If there is a good gap between the yielding point and breaking point, that kind of the material is called ductile materials and there are very much useful in making thin and long wires. Gold and copper are simple examples of this kind of the materials.

If there is no big gap between yielding point and the breaking point they cannot be molded into wires and this kind of the material is called as brittle materials. Glasses a typical example of a brittle material.