Young's Modulus-Uniform Bending experiment

Aim

To find the Young's modulus of the given material bar by uniform bending using pin and microscope method.

Apparatus

Pin and Microscope arrangement, Scale ,Vernier calipers, Screw gauge, Weight hanger, Material bar or rod.

Uniform Bending Using Pin and Microscope Method

In uniform Bending , the Young’s modulus of the material of the bar is given by

(1)

Where,

m - Mass at each end of the bar.

p - Distance between the point of suspension of the mass and nearer knife edge.

g - Acceleration due to gravity.

l is the length of the bar between the knife edges.

e - Elevation of the midpoint of the bar for a mass m at each end.

I - Geometrical moment of inertia.

For a bar of rectangular cross section,
(2)
Where b is the breadth and d is the thickness of the bar.

Substituting (2) in equation (1)

(3)

From graph, can be calculated.

Applications

1. Thin film applications.

2. It helps to predict the directional and orientation properties of metals and has application in ceramics.

3. Measurement of soft tissues -early detection, elasticity imaging, etc.

Procedure for Simulation

1. Select the environment and material for doing experiment.
2. Adjust length, breadth and thickness of the material bar using sliders on the right side of the simulator .
3. Fix the distance between knife edges and weight hangers using sliders.
4. Focussing the microscope using focussing knob and adjusting the tip of the pin coincides with the point of intersection of the cross wires using left and top knobs on microscope respectively.
5. Readings are noted using the microscope reading for 0g. Zoomed part of microscope scale is available by clicking the centre part of the apparatus in the simulator.
6. Total reading of microsope is MSR+VSR*LC. MSR is the value of main scale reading of the microsope which is coinciding exacle with the zero of vernier scale.
7. One of the division in the vernier scale coincides exactly with the main scale is the value of VSR. LC is the least count.
8. Weights are added one by one say 50g, then pin moves downwards while viewing through microscope. Again adjust the pin such that it coincides exactly with the cross wire.
9. Note the microsope reading and repeat 7 and 8 by increasing the weights.
10. The readings are tabulated and Y is determined using equation (3).

Observations and Calculations of Uniform Bending

Value of 1 m.s.d = 1/20
Number of divisions on the vernier, n = 50
Least count of microscope = 1 m.s.d/n = 1/1000 = 0.001 cm

Thickness of the material bar “d” = ……………………….. mm
Breadth of the material bar “b” = ……………………………cm
Mean value of pl2/e = ………………………….m
Load applied for elevation“e” = ………………………… m
Young’s modulus of the material bar ,= …………………………Nm-2

Example: For uniform bending for wood, p=0.5m, m= 0.02kg, g=9.8ms-2, pl2/e = 2.165 m2, b=2.956 x 10-2m,d=50693 x 10-3m.
Y = 1.1 x 1010 Nm-2

Result

1.Young’s modulus of the given material using uniform bending method= …………………………. Nm-2.