Procedure

Apparatus

Uniform bending apparatus with microscope, material bar, knife edges, weight hangers, and measuring scales.

Procedure for Simulation

1. Select the Environment from the Select Environment drop-down menu.
2. Select the Material of the bar from the Select Material menu.
3. Set the following parameters using the sliders:
   • Mass of the weight hanger
   • Breadth of the bar (b)
   • Thickness of the bar (d)
   • Distance between the weight hangers
   • Distance between the knife edges
4. Note the initial microscope reading before adding any load (0 g).
5. Add weights to the weight hangers one at a time and observe the downward bending of the bar.
6. After each load is applied, note the new microscope reading. Use the magnified microscope view, if required, to read the scale accurately.
7. Record the load and the corresponding microscope reading for each observation.
8. Repeat the observations for all the required loads.
9. Tabulate the recorded readings in the observation table.
10. Calculate the Young's Modulus (Y) of the selected material using Equation (3).
11. Click Result to verify the Young's Modulus of the selected material.
12. Click Reset to restore the simulator to its default settings and repeat the experiment with different materials or parameters.

Procedure for Real lab

Uniform Bending

The bar is placed symmetrically on two knife edges. Two weight hangers are suspended at equal distance from the knife edges. The distance l between knife edges and distance p of the weight hanger from knife edges are measured. A pin is fixed vertically at the midpoint of the bar with its pointed end upwards. The microscope is arranged in front of the pin and focused at the tip of the pin. The slotted weights are added one by one on both the weight hangers and removed one by one a number of times, so that the bar is brought into an elastic mood. With the some "dead load" W0 on each weight hanger, the microscope is adjusted so that the image of the tip of the pin coincides with the point of intersection of cross wires. The reading of the vernier scale and vernier of microscope are taken. Weights are added one by one and corresponding reading are taken. From these readings, the mean elevation (e) of the mid-point of the bar for a given mass is determined. The value of $$\frac{l^{2}}{e}$$ is calculated . The breadth of the bar (b) is measured by using vernier calipers and thickness of the bar (d) is measured by using screw gauge. Hence calculate the Young's modulus of the material bar.

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 $\frac{pl^{2}}{e}$ = ..........m Load applied for elevation…e = .............. m

Young's modulus of the material bar, $$Y=\frac{3mgpl^{2}}{2bd^{3}e}$$ = ........... $Nm^{-2}$

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

Young's modulus of the given material using uniform bending method= ........... $Nm^{-2}$