Modulus of rigidity of a given wire by oscillating method
- 1. GROUP-B AREEBA FATHA ALI 12 ANEESA ARIF 14 HAMEEZA SAEED 24 UMM-E-HANI 26 TANIA CH 02 SAFFA MARYAM 03 FAREEHA SHABBIR 20 SEHRISH SARWAR 21
- 3. PROJECT TOPIC Determination of modulus of rigidity of a material of a given wire by oscillating method
- 4. PURPOSE OF PRCTICAL To find the MODOLUS OF RIGIDITY OF WIRE when a heavy body is supported by it and execute torsional head.
- 5. APPARATUS • Solid Cylindrical Rod • Suspension Wire • Tortion Head • Stop Watch • Vernier Callipers • Screw Guage • Mass Balance • Meter Rod • Knitting Needle • Stand
- 6. THEORY MODULUS OF RIGIDTY: Within the elastic limit, the ratio of shearing stress to shearing strain is called MODOLUS OF RIGIDITY. • Unit of modulus of rigidity is n/𝐦 𝟐 • FORMULA is Y= 𝑭/𝑨 𝒕𝒂𝒏Ө
- 7. THEORY • STRESS: THE FORCE APPLIED ON THE UNIT AREA TO PRODUCE ANY CHANGE IN THE SHAPE, LENGTH AND SHAPE OF THE BODY STRESS = 𝑭𝑶𝑹𝑪𝑬 (𝑭) 𝑨𝑹𝑬𝑨(𝑨) UNIT: N𝒎−𝟐 • STRAIN: STRAIN IS THE MEASURE OF THE DEFORMATION OF THE SOLID WHEN STRESS IS APPLIED TO IT IN CASE OF DEFORMATION IN ONE DIMENSION STRAIN IS DEFINED AS A FRACTIONAL CHANGE IN LENGTH STRAIN (Ɛ) =∆𝑙/𝑙 UNIT UNITLESS
- 8. THEORY SHEARSTRESS: When two equal and opposite forces are applied tangentially to the cross section of the body .The stress induced is known as SHEAR STRESS. SHEARSTRAIN: SHEAR STRAIN is defined as the strain accompanying a shearing action.It is the angle in radian measure through which the body gets distorted when subjected to an external shearing action.
- 9. PROCEDURE We perform following steps in doing this EXPERIMENT ….. 1. Measure the MASSof Cylindricalrod by using digital mass balance. 2. Measure the mean DIAMETER of Suspension wire by using Screw Gauge. DIAMETER (𝒅)
- 10. 3.Find the RADIUS of the wire 𝒓 = 𝒅/𝟐 4.FIND THE Measure the DIAMETER of Cylindrical Rod by using Vernier Caliper diameter(d) 5.Find the RADIUS of the cylindrical rod r=d/2
- 11. 6.Find the length of SUSPENSION WIRE and length of rod (l) by using METER ROD 7. Calculate the time for 10 vibrations a) t1 for first time b) t2 for second time c) t = 𝑡1+𝑡2 2 8. Calculate TIME PERIOD as T=t/10
- 12. DIAGRAM
- 13. • Calculate modulus of rigidity by using this formula.…. η= 2∏mL(3R2+ 4L2)/3r4T2 UNIT: dynes/cm 𝟐 Sr. No Vibrations Time fore 10 vibrations (s) Time period T=t/10 (s) 1 10 16.50 1.650 2 10 16.53 1.653 3 10 16.38 1.638
- 14. OBSERVATIONS • LENGTH OF ROD = L = 25.5 cm • MASS OF ROD = m =587.3 cm • MEAN DIAMETER OFD WIRE = d = 0.427 mm = 0.0427 cm • MEAN RADIUS OF WIRE = 0.2135 cm • LENGTH OF WIRE = 59.5 cm • MEAN DIAMETER OF ROD = D= 19.006 mm = 1.9006 cm • MEAN RADIUS OF ROD = R =0.9503 cm
- 15. RESULT • The MODULUS OF RIGIDITY of wire calculated by using solid cylindrical rod is 1.48 × 1014 dynes/𝑐𝑚2