THIS PRESENTATION IS BASED ON ELASTICITY THROUGH THIS

THIS PRESENTATION IS BASED ON ELASTICITY. THROUGH THIS PRESENTATION WE WILL COME TO KNOW ABOUT: ELASTICITY IN SOLIDS. HOOKE’S LAW. YOUNG’S MODULUS. BULK’S MODULUS OF RIGIDITY. COMPRESSIBILITY. ELASTIC FATIGUE. APPLICATIONS OF ELASTICITY.

ELASTICITY

ELASTICITY IN SOLIDS WHEN AN EXTERNAL FORCE IS APPLIED ON A BODY THEN A SHAPE AND SIZE TAKES PLACE AS THE FORCE IS REMOVED BODY RETURNS TOWARDS ITS ORIGINAL STATE. THIS PROPERTY OF BODY IS CALLED ELASTICITY. AND SUCH BODIES ARE ELASTIC BODIES. THE EXTERNAL FORCE APPLIED ON THE BODY TO CHANGE IS SHAPE AND SIZE IS CALLED AS DEFORMING FORCE AND THE FORCE WHICH OPPOSES THE DEFORMING FORCE TO RETAIN ORIGINAL CONFIGURATION IS CALLED AS RESTORING FORCE. FOR ELASTIC BODIES RESTORING FORCE IS EQUAL TO DEFORMING FORCE. THEREFORE ELASTICITY MAY BE DEFINED AS THAT PROPERTY OF THE MATERIAL OF THE BODY BY VIRTUE OF WHICH THE BODY OPPOSES ANY CHANGE IN ITS SHAPE OR SIZE WHEN DEFORMING FORCES ARE APPLIED TOIT , RECOVERS ITS ORIGINAL STATE AS SOON AS THE DEFORMING FORCES ARE REMOVED.

CAUSE OF ELASTICITY THE MOLECULES OF AN ELASTIC BODIES ARE CONSIDERED TO BE A JOINT THROUGH SMALL SPRINGS KNOWN AS MOLECULAR SPRING. AS DEFORMING FORCE IS APPLIED THE MOLECULAR SPRING GETS ELONGATED OR COMPRESSED. DUE TO INTERNAL SPRING FORCES EACH SPRING OPPOSSES THE DEFORMING FORCE. HENCE AS THE FORCE SI REMOVED THE MOLECULAR SPRINGS RETURN TO THEIR ORIGINAL SHAPE AND SIZE OF THE MOLECULES.

LIMIT OF ELASTICITY THE MAXIUM DEFORMING FORCE UPTO WHICH A BODY RETAINS ITS PROPERTY OF ELASTICITY IS CALLED AS “LIMIT OF ELASTICITY” OF THE MATERIAL OF THE BODY.

STRESS THE INTERNAL RESTORING FORCE ACTING PER UNIT AREA OF CROSS SECTION OF THE DEFORMED BODY IS CALLED ‘STRESS’. STRESS=F/A THE SI UNIT OF STRESS IS Nm-2 OR Pa. DIMENSIONS [M L-1 T-2]. THE STRESS DEVELOPED IN ABODY DEPENDS UPON HOW THE EXTERNAL FORCES ARE APPLIED OVER IT. ON THIS BASIS THERE ARE THREE TYPES OS STRESS: LONGITUDINAL STRESS, NORMAL STRESS AND TANGENTIAL STRESS.

STRAIN THE CHANGE OCCURRED IN THE UNIT SIZE OF THE BODY IS CALLED ‘STRAIN’. FOR EXAMPLE , WHEN THE LENGTH OF A SUSPENDED WIRE INCREASES UNDER AN APPLIED LOAD, THE RATIO OF THE INCREASE IN LENGTH TO THE ORIGINAL LENGTH IS CALLED THE ‘STRAIN’. SINCE STRAIN IS A RATIO, IT HAS NO UNIT. DEPENDING UPON THE WAY THE DEFORMING FORCES ARE APPLIED TO A BODY , THERE ARE THREE TYPES OF STRAIN; LONGITUDINAL STRAIN, VOLUMETRIC STRAIN AND SHEARING STRAIN.

HOOKE’S LAW HOOKE IN 1679, SHOWED EXPERIMENTALLY THAT IF STRAIN IS SMALL, THEN THE STRESS PRODUCED IN A BODY IS PROPROTIONAL TO THE STRAIN. THE RATIO OF STRESS TO STRAIN IS CONSTANT FOR A MATERIAL OF THE GIVEN BODY AND IS CALLED ‘MODULUS OF ELASTICITY’. E THUS, E=STRESS/STRAIN

YOUNG’S MODULUS WHEN STRAIN IS SMALL, THE RATIO OF THE LONGITUDINAL STRESS TO THE CORRESPONDING LOGITUDINAL STRAIN IS CALLEDE THE YOUNG’S MODULUS OF THE MATERIAL OF THE BODY. IT IS DENOTED BY ‘Y’. LET THERE BE AWIRE OF LENGTH L AND RADIUS R. ITS ONE END IS IS CLAMPED TO A RIGID SUPPORT AND A WEIGHT Mg IS APPLIED AT THE OTHER END. SUPPOSE , WITHIN THE ELASTIC LIMIT , ITS INCREASES BY L. THEN SI UNIT=N/m -2 DIMENSION= [M L-1 T -2 ] LONGITUDINAL STRESS=FORCE /AREA =Mg / PR 2 LONGITUDINAL STRAIN=l / L HENCE, YOUNG’S MODULUS OF THE MATERIAL OF THE BODY IS : Y= LONGITUDINAL STRESS/ LONGITUDINAL STRAIN = Mg /PR 2 / l/ L =Mg L /P R 2 l P

STEEL IS MORE ELASTIC THAN RUBBER ELASTICITY IS THE PROPERTY OF THE BODY BY VIRTUE OF WHICH THE BODY OPPOSES ANY CHANGE IN ITS SIZE OR SHAPE CAUSED BY AN EXTERNAL FORCE. CLEARLY, GREATER IS THE FORCE REQUIRED TO PRODUCE A GIVEN CHANGE IN SIZE OR SHAPE OF ABODY, THE MORE ELASTIC THE BODY IS SAID TO BE. IF WE YAKE STEEL AND RUBER WIRES OF EQUAL LENGTHS AND AREAS OF CROSS-SECTION, A LARGER FORCE WOULD HAVE TO BE APPLIED TO THE STEEL WIRE IN ORDER TO PRODUCE EQUAL EXTENSIONS IN THEIR LENGTHS.

PROOF: SUPPOSE TWO WIRES OF SAME LENGTH L AND SAME RADIUS R , ONE OF THE STEEL AND THE OTHER OF THE RUBBER ARE SUSPENDED GROM RIGID SUPPORT. SUPPOSE, ON APPLYING EQUAL WEIGHTS Mg, Mg TO THEIR LOWER ENDS, THEIR LENGTH INCREASES BY LS AND LR RESPECTIVELY. IF YS AND YR ARE THE YOUNG’S MODULI OF STEEL AND RUBBER RESPECTIVELY, THEN. YS=Mg L / PR 2 LS AND , YR= Mg L / PR 2 LR YS / Y R = L S / L R YS > Y R THUS, STEEL IS MORE ELASTIC THAN RUBBER.

BULK’S MODULUS WHEN STRAIN IS SAMLL , THE RATIO OF THE NORNAL STRESS TO THE VOLUME STRAIN IS CALLED THE ‘BULK’S MODULUS’ OF THE MATERIAL OF THE BODY. IT IS DENOTED BY B. THE BULK MODULUS OF THE BODY IS GIVEN BY: B=NORMAL STRESS/VOL. STRAIN =p/-v/V =-Pv/V. SI UNIT IS Nm-2 DIMENSION [M L-1 T -2 ]

COMPRESSIBILITY THE RECIPROCAL OF BULK MODULUS OF THE MATERIAL OF A BODY IS CALLLED THE COMPRESSIBILITY OF THAT MATERIAL.

MODULUS OF RIGIDITY WITHIN THE LIMIT OF ELASTICITY THE RATIO OF TANGENTIAL STRESS TO THE SHEARING STRAIN IS CALLED MODULUS OS RIGIDITY ie, MODULUS OF RIGIDITY = TANGENTIAL STESS SHEARING STRAIN h = SHEARING STRESS SHEAR h= F/A q SI UNIT IS Nm-2 DIMENSION [M L-1 T -2 ]

ELASTIC FATIGUE THE PROPERTY OF AN ELASTIC BODY DUE TO WHICH ITS ELASTIC BEHAVIOUR BECOMES LESS AND LESS INDER THE ACTION OF REAPETED ALTERNATING DEFORMING FORCE IS CALLED AS ELASTIC FATIGUE.

APPLICATIONS OF ELASTICITY 1. THE MAXIMUM HEIGHT OF THE MOUNTAIN CAN BE ESTIMATED BY ELASTIC BEHAVIOUR OF EARTH. 2. THE ROPES USED IN THE CRANE ARE DESIGNED TO LIFT HEAVY LOAD WHOSE SELECTION IS MADE FROM THE KNOWLEDGE OF ELASTIC LIMIT OF THE MATERIAL. 3. BRIDGES ARE DESINED IN SUCH A WAY THAT THEY DO NOT BEND OR BREAK UNDER THE LOAD OF HEAVY TRAFFIC.

PRESENTED BY CHITRA JOSHI PGT PHYSICS KVOFD RAIPUR DEHRADUN