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### 124_lab_elasticity

Course: PHYSICS 124, Fall 2009
School: Rutgers
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Word Count: 610

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In ELASTICITY this workshop you will explore the elastic response of a thin wire to an applied tension. The aim is to obtain a rough understanding of the size of the forces necessary to measurably deform the wire (Young's modulus). While large forces can permanently deform or break a solid, deformations caused by small forces are proportional to the applied force and disappear if...

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In ELASTICITY this workshop you will explore the elastic response of a thin wire to an applied tension. The aim is to obtain a rough understanding of the size of the forces necessary to measurably deform the wire (Young's modulus). While large forces can permanently deform or break a solid, deformations caused by small forces are proportional to the applied force and disappear if the force is removed. This phenomenon (reversible deformation proportional to the applied force) is called elasticity. In this regime "stress" is linearly proportional to the "strain" that it produces. The tension T in the wire (caused by the applied force, the added weights), divided by the wire's cross sectional area A, is called the tensile stress = T . A The tensile strain is defined as the change in length per unit length: = l l . In the elastic regime, the required stress is proportional to the strain it causes: = Y where the proportionality constant Y is called Young's Modulus; it depends only on the material of the solid, and not on its geometry (e.g., its length or cross sectional area). Note that, since the strain is dimensionless, Y has the same units as the stress, i.e., Newtons per square meter, called Pascals (Pa), the SI unit. Procedure The apparatus consists of a long wire suspended from the ceiling, at the lower end of which is a mass hanger to which additional masses can be added. You also have a ruler to measure the height of the mass hanger (relative to the reference point, either the table or the thin copper wire attached to the stand). You should be able to measure the position to a precision of 0.5 millimeters. To do this consistently as you change the masses, you MUST keep the ruler in the same position and keep the mass hanger at the same angle relative to the (To ruler. see why, note the measured position on the ruler if you move it around the bottom of the mass hanger or rotate the mass hanger.) You will be given the length l of the wire; its diameter d is 0.8 mm. Calculate its cross sectional area A assuming a circular cross section. Take measurements with at least four different masses M, and record in the table the resulting height h and the change l relative to the reference point. Include a repeat measurement, where you check a previous measurement. Do not include the mass of the hanger in the value of M used in calculating the tension; its effect is already included in the initial height. FOR YOUR SAFETY do not exceed 10 kg mass to avoid breaking the wire. Also, do not swing the mass. Names _______________ _______________ _______________ Section_______ Wire parameters: l=__________ m d=___________m A=__________m2 Initial height h relative to reference point: ________________m Tension T (N) (M g) Stress (N/m2) Displacement h(m) l (m) Strain Y (N/m2) Are all values of Y the same? Should they be? Calcula...

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