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Experiment 3...

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BASIC PHYSICS LAB MANUALS FOR

Undergraduate Classes

DEPARTMENT OF PHYSICS UNIVERSITY OF ENGINEERING AND TECHNOLOGY, LAHORE, PAKISTAN

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EXPERIMENT # 3 To determine the modulus of rigidity of the material of a wire by Maxwell’ needle. Apparatus:

Maxwell’s needle, Copper wire, Support with torsion head, Stop watch, Screw gauge, Meter rod, Telescope

Related Concept:

Young’s Modulus, Bulk Modulus, Shear Modulus, Tension, stress, Strain

H

S

H

(a)

S

(b)

Figure 1: Maxwell Needle (a) Solid Cylinder at Outer ends (b) Hollow Cylinder at Outer ends

Observations: Length of the suspension wire =

l =…….cm

Total length of needle (brass tube)

= 2a =…….cm

Half length of needle

= a =…….cm

Average mass of a solid cylinder

= m1 =…….gm

Average mass of a hollow cylinder

= m2 =…….gm

Diameter of the wire

= (1) =…….cm. (2) =……..cm 2

Mean diameter of the wire

= D =………….cm

Mean radius of the wire

= r = D/2=………..cm

Arrangement

Solid Cylinders outside

1 Sec.

Ti me for 20 vibration

Time Period

2 Sec.

Sec.

Mean Sec.

T1 =…………………. T2 =………………….

Hollow Cylinder outside Calculations:

=………..dynes/cm2 Correct value of η

=……….. dynes/cm2 Procedure:-

1. Suspend the Maxwell’s needle (hollow brass tube) horizontally from a rigid support by means of a long wire as long as possible free of kinks 2. Put the solid cylinders S-S on the outside and check that the Maxwell’s needle is horizontal. Press one end of the needle slightly backwards to make it vibrate in a horizontal plane. Pause for some time for the motion to become steady (i.e. pure rotational). 3. Find time for 20 vibrations and repeat it twice. Work out the time period T1. 4. Proceed in the same manner by putting the hollow cylinders H-H now on the outside and work out the time period T2. 5. Measure the length of the tube ‘a’ and that of the wire ‘l’ with the help of meter rod. 6. Measure the diameter of the wire with the help of the screw gauge at about different places. 3

7. Determine the average masses m1 and m2 of the solid and hollow cylinders by using weigh balance 8. Measure the diameter of the solid and hollow cylinders using vernier caliper. 9. Make a record of your observations as shown. Evaluate modulus of rigidity by the relation.

Precautions: 1. The experimental wire should be free of kinks. 2. The Maxwell needle should vibrate in a horizontal plane. 3. The amplitude of torsional vibration should be small to keep the wire within elastic limit under the twisting couple. 4. The needle should be protected from air draughts during actual performance of the experiment. 5. The vibrations should be counted with reference to the movement of the image in the same direction (i.e. from left to right) only. 6. The diameter of the wire should be measured at different point extended along entire length of the wire.

Theory This is particularly convenient oscillator used for measuring the modulus of rigidity of wires. It consists of tube into which four equal short pieces can be inserted. Each of short piece is onefourth of total length of the long tube. Two of short pieces of are hollow and two are solid. By placing the tubes as shown in figure 1a and figure 1b, the moment of inertia can have two values given to it, I1 and I2 of which I1 is considerably larger. To express the change in moment of inertia or I1-I2, let a be the half length of long tube, m1 the mass of the each of the two short tubes that are filled with solid material just like lead etc, and m2 the mass of each of the empty short tubes.

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Then the system is changed by shifting two masses each equal to m 1-m2, so that the system of the center of gravity of each from the axis changes from 3/4 a to 1/4 a.

Tension In physics, tension is the pulling force exerted by a string, cable, chain, or similar solid object on another object. It results from the net electrostatic attraction between the particles in a solid when it is deformed so that the particles are further apart from each other than when at equilibrium, where this force is balanced by repulsion due to electron shells; as such, it is the pull exerted by a solid trying to restore its original, more compressed shape. Tension is the opposite of compression. Slackening is the reduction of tension. As tension is the magnitude of a force, it is measured in newtons (or sometimes pounds-force) and is always measured parallel to the string on which it applies.

Young’s Modulus Young's modulus, also known as the tensile modulus or elastic modulus, is a measure of the stiffness of an elastic material and is a quantity used to characterize materials. It is defined as the

ratio of the stress along an axis over the strain along that axis in the range of stress in which Hooke's law holds. In solid mechanics, the slope of the stress-strain curve at any point is called the tangent modulus. The tangent modulus of the initial, linear portion of a stress-strain curve is

called Young's modulus. It can be experimentally determined from the slope of a stressstrain curve created during tensile tests conducted on a sample of the material. In anisotropic materials, Young's modulus may have different values depending on the direction of the applied force with respect to the material's structure. Bulk Modulus The bulk modulus describes the material's response to uniform pressure (like the pressure at the bottom of the ocean or a deep swimming pool). Shear’s Modulus The shear modulus is concerned with the deformation of a solid when it experiences a force parallel to one of its surfaces while its opposite face experiences an opposing force (such as friction). In the case of an object that's shaped like a rectangular prism, it will deform into a parallelepiped. Anisotropic materials such as wood, paper and also essentially all single crystals exhibit differing material response to stress or strain when tested in different directions. In this 5

case one may need to use the full tensor-expression of the elastic constants, rather than a single scalar value. One possible definition of a fluid is material with zero shear modulus. Shear Modulus of Metals The shear modulus of metals is usually observed to decrease with increasing temperature. At high pressures, the shear modulus also appears to increase with the applied pressure. Correlations between the melting temperature, vacancy formation energy, and the shear modulus have been observed in many metals.http://en.wikipedia.org/wiki/Shear_modulus - cite_note-March-9 Several models exist that attempt to predict the shear modulus of metals (and possibly that of alloys). Shear modulus models that have been used in plastic flow computations include: 1. The MTS shear modulus model developed by and used in conjunction with the Mechanical Threshold Stress (MTS) plastic flow stress model. 2. The Steinberg-Cochran-Guinan (SCG) shear modulus model developed byhttp://en.wikipedia.org/wiki/Shear_modulus - cite_note-Guinan74-13 and used in conjunction with the Steinberg-Cochran-Guinan-Lund (SCGL) flow stress model. 3. The Nadal and LePoac (NP) shear modulus model that uses Lindemann theory to determine the temperature dependence and the SCG model for pressure dependence of the shear modulus.

Applications Material scientists and applied physicists use this concept in special ways. Understanding the modulus of rigidity will help select the correct material to use for construction under many circumstances. The smaller the force is, the easier the material will bend. It is calculated and publicly recorded for most materials. A rod made of gold will bend more easily than one of the same thickness made of steel, for example, and the shearing modulus displays this clearly for most comparisons.

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