Osm Physics by Ashish

Elastic Properties of Matter | Physics Notes Elastic Properties of Matter 17. Bending of Beams and Structural Applications When a beam is supported at its two ends and loaded at the middle, it bends under the action of the applied load. During bending, the longitudinal layers of the beam undergo extension or compression. For a simply supported beam subjected to a downward central load, the upper layers are compressed, whereas the lower layers are stretched. Between these two regions lies a neutral surface , where the longitudinal strain and bending stress are zero. According to the theory of simple bending, the magnitude of longitudinal bending stress at a distance \(y\) from the neutral axis is \[ \boxed{\sigma_b=\frac{M_b y}{I_A}} \] where \(\sigma_b\) = longitudinal bending stress, \(M_b\) = bending moment at the section, \(y\) = perpendicular distance from the neutral axis, \(I_A\) = second moment of area of the cross-section about the neutral...

Elastic Constants by Searle's Dynamical Method 1. Aim To determine Young's modulus \(Y\), modulus of rigidity \(n\), and Poisson's ratio \(\sigma\) of the material of a given wire by Searle's dynamical method using the time periods of oscillation. 2. Apparatus Required Searle's dynamical apparatus, two identical cylindrical bars, experimental wire, rigid supporting stand, stopwatch, screw gauge, vernier calipers, metre scale and physical balance. 3. Theory When an elastic body is deformed within its elastic limit, restoring forces or couples are developed. These restoring actions tend to bring the body back to its original configuration. Searle's dynamical method determines the elastic constants of a wire by observing two independent modes of oscillation of an arrangement containing the wire and two identical bars. The first mode is associated with flexural deformation, while the second mode involves torsional deformation. Th...

Experiment: Non-Uniform Bending of a Beam Study of Bending of a Beam and Determination of Young's Modulus Method: Non-Uniform Bending (Central Loading Method) 1. Aim To study the non-uniform bending of a rectangular beam supported on two knife edges and to determine Young's modulus of the material by applying a load at the centre of the beam. 2. Apparatus Required Rectangular beam (metallic or wooden), two knife-edge supports, weight hanger, slotted weights, travelling microscope, metre scale, Vernier calipers and screw gauge. 3. Theory When a rectangular beam is supported horizontally on two knife edges and a load is applied at its midpoint, the beam bends downward. The bending moment varies along the length of the beam; therefore, this type of bending is called non-uniform bending . For a simply supported beam carrying a central load, the depression at the midpoint is given by \[ y=\frac{Wl^3}{48YI} ...

Elasticity 1. Elasticity When an external force acts on a solid body, its dimensions or shape may change. This change is called deformation . Depending on the direction and nature of the applied force, deformation may involve a change in length, volume, shape, or a combination of these. For example: A wire undergoes elongation when a tensile force acts along its length. A solid body undergoes a change in volume when subjected to uniform external pressure. A block undergoes a change in shape when a tangential force acts on its surface. In crystalline solids, deformation generally involves changes in interatomic distances and bond angles. In rubber and other polymers, deformation may also involve the uncoiling, orientation, and stretching of polymer chains. Elasticity: Elasticity is the property of a material by virtue of which it tends to regain its original shape and dimensions after the removal of the external deforming force, provided that th...

Consider a closed thermodynamic system \(A\) consisting of a gas enclosed in a cylinder fitted with a frictionless movable piston. The system is in thermal contact with a large heat reservoir maintained at temperature \(T_0\). The external pressure \(P_0\) remains constant. When the system absorbs heat from the reservoir, the gas may expand and perform pressure–volume work against the surroundings. Suppose the system absorbs heat \(Q\) and undergoes a change in volume \(\Delta V\). The work done by the gas against the constant external pressure is \[ \Delta W=P_0\Delta V. \] From the first law of thermodynamics, \[ \Delta U=Q-\Delta W. \] Therefore, \[ Q=\Delta U+P_0\Delta V. \] Since \(P_0\) is constant, \[ Q=\Delta(U+P_0V). \] A thermodynamic state function called enthalpy is defined as \[ \boxed{H=U+PV} \tag{1} \] For initial and final equilibrium states at the same constant pressure \(P=P_0\), and when only pressure–volu...

Consider a closed thermodynamic system \(A\) in thermal contact with a large heat reservoir \(A'\) maintained at a constant temperature \(T_0\). The system is enclosed within rigid walls, so its volume remains constant. Only heat is exchanged between the system and the reservoir, and no external work is performed. Let the system absorb an amount of heat \(Q\) from the reservoir. Since the reservoir loses the same amount of heat, its entropy change is \[ \boxed{ \Delta S'=-\frac{Q}{T_0} } \tag{1} \] From the first law of thermodynamics, \[ \Delta U=Q-W. \] At constant volume, assuming only pressure–volume work, \[ W=\int P_{\mathrm{ext}}\,dV=0. \] Therefore, \[ \boxed{Q=\Delta U} \tag{2} \] Substituting equation (2) into equation (1), \[ \boxed{ \Delta S'=-\frac{\Delta U}{T_0} } \tag{3} \] The combined system consisting of \(A\) and the heat reservoir \(A'\) is thermally isolated from the surroundings. Henc...