10 Youngs Modulus, Study notes of Law

Download 10 Youngs Modulus and more Study notes Law in PDF only on Docsity! Exp 10-1 P Experiment 10. Young's Modulus - Is rubber more elastic than steel? The answer lies in the concept of elasticity. Objective: To determine the Young's modulus of the material of a wire. Apparatus: Yourig's -·ma~dDlus --appararns~- ·a· rrHcromerer,-·a · vernrer · caliper, a meter --- stick. Theory: If a balanced system of forces is applied to a body, the shape and/or size of the body change and the body is said to have developed strain. Due to this, internal forces are produced within the body which tend to bring the body back to its original shape and size when the external forces are withdrawn. This property of matter to develop these internal forces (of stress) is known as elasticity. - - Cylinder Mirror Scale Loadr~1 Fig. 1 Fig. 2. Schematic Diagram of Young's Modulus Apparatus If one end of a wire (Fig. 1) is fixed and a mass M is suspended from the Exp 10-2P other end of the wire, equal and opposite forces of magnitude Mg are applied to the wire by the mass M and by the support at the top. Due to this, the length of the wire increases. (There is also a slight change in other dimensions of the wire but we will not consider them.) If the increase in the length of the wire is ii l and the original length of the wire is l, then longitudinal strain or tensile strain = iil/l( Further, the internal forces over any cross\seCtiOll of the wire are equal to the external force Mg. Thus longitudinal stress or tensile stress = Mg/nr2. Here r is the radius of the wire. According to Hooke's law, within elastic limits, stress is directly proportional to strain. Thus tensile stress = Y (tensile strain), where Y is called the Young's modulus or modulus of longitudinal elasticity or stretch modulus of the material of the wire. - - 2 Thus y = Tensile stress= Mg/nr = Mgl Tensile strain iil/l nr 2 iil ( 1 ) The wire whose Young's modulus is to be determined passes over a small -cyltnder--which-is free--to · rotate about a horizontal axis (Fig. 2). When the length of the wire increases by an amount ii l, the cylinder of radius r 1 rotates through an angle 0 which is given by e = ill r1 (2) There is a small plane mirror attached to the cylinder which rotates along with the cylinder. The increase in length ill and thus angle 0 are very small and so an optical lever (an arrangement of scale, mirror and telescope shown in Figs. 2) is used to determine e and ~L. The image of a vertical scale formed by the mirror is observed through the telescope. When the mirror is in the vertical position MP (Fig. 3), the image of point N of the scale is seen through the telescope. When the cylinder and mirror rotate through an angle e and is in position M1 P 1 , the - t York College of The City University of New York Physics I Name: Experiment No. 10: Pre-Lab Questionnaire 1. Briefly describe how an optical lever works. 2. Calculate Young's modulus from the following data: Load on the Readings of the scale (cm) Change in the reading of the scale when the load is increased by M= __ gm hanger (gm) when the load is Average s increased (si) decreased ( sd) · 100 8.4 8.5 300 6.2 6.3 S4 - s1 = x1 = 500 ·· -~ ·- -3.9 --- -·- --- -·-- 4.0 s5 - s2 = x2 = 700 1.7 1.8 ss - s3 = x3 = 900 -0.5 -0.4 _ _1 lOJ) ____ -- -------- --_2.7 _ _ ----- -- --- -2.6 _______ - ---- - -- - Average x - - - Average diameter of the wire = 0.036 cm Average length of the wire = 96.7 cm Average diameter of the cylinder = 1.24 cm Average distance between the mirror and the scale = 84.6 cm - · - . . . ··-·-· ·· ... ...... ·-· · - Experiment No. 10 Name: Marks: Partner: Rem;:uks: Section: Date Submitted: Title: Objective: Theory/Formulas: - Exp 10-7D Data Sheet - Table I Readings for the determination of ~L: Change the load on the hanger in equal steps. Number of sets of readings must be even. No. Load on Positions of the cross wires (cm) Change ir:, the position of the Load Load Average cross wires when load is ' hanger increasi~9 .. .... - ,. del~reasi~9 .. .. (§) ······ changed by M -= ··-····· gm -- (gm) (Si) (Sd) - S1 =X1= 1 S5 2 -Ss S2=X2= 3 4 S7 - S3=X3= 5 6 Sa - S4=X4= 7 8 - Average x = Table II Readings for the diameter of the wire: Least count of the micrometer = ; Zero error = No. 1 2 3 4 Average -·--. One diameter Perpendicular diameter Average diameter of the wire = Diameter of the wire corrected for zero error = Radius of the wire, r = · Length of the wire (reading 1) = Length of the wire (reading 2) = Average length of the wire, L = -