Young's modulus - Cantilever (Deflection method)

    The TANSCHE curriculum for first year B.Sc. Physics practical emphasizes experiments that enhance theoretical knowledge through practical experience. A key experiment in this curriculum is measuring Young's Modulus through cantilever by deflection method. This experiment allows students to assess the elasticity of a material by observing how a beam bends evenly when a load is applied.

    In this blog post, we will provide a step-by-step guide to help you carry out the experiment correctly. From setting up the equipment to interpreting the results, this guide offers a thorough approach for students to accurately determine the Young’s modulus of a material using the cantilever method.

Young's modulus - Cantilever

(Deflection method)

Aim:

To determine the Young's modulus of the material of the cantilever by measuring the depression at the loaded end using deflection method.

Apparatus required:

The cantilever, weight hanger and slotted weights, mirror, scale and telescope arrangement, screw gauge, vernier caliper etc.

Formula:

Young’s modulus,

Here,

E is the Young's modulus of the material of the bar N/m2

L is the length of the cantilever m

D is the distance between the mirror and the scale in the scale and telescope arrangement m

y is the depression corresponding to the load m

b is the breadth of the bar m

d is the thickness of the bar m

Procedure:

        The bar is positioned along the edge of a table and firmly clamped, allowing a portion of it to extend past the table. A weight hanger is hung from a point close to the free end, where a mirror is vertically fixed. A scale and telescope arrangement are set up about one meter away from the mirror. The horizontal cross-wire in the telescope is aligned with a specific division on the scale, and the reading is recorded.

Initially, with only the weight hanger, the horizontal cross wire, and the reading from the vertical scale is recorded. Weights are then added in increments of 50 grams until the maximum load is reached, with readings taken each time. After that, the weights are removed in 50-gram increments, and the microscope readings are noted again.

From these readings, the average elevation of the midpoint of the bar due to the load ‘m’ applied is determined. From these measurements (m/y) can be calculated.

This ratio can also be calculated by plotting a graph, with elevation ‘y’ along the x-axis and the mass ‘m’ along the y-axis. This leads to a straight line. The slope of this line will give (m/y).

The breadth (b) and the thickness (d) of the bar are measured with the help of vernier caliper and screw gauge respectively. The experiment can be repeated with different values of L.

Tabular Column 1: To find the shift (s) corresponding to the load (m)

Load ‘m’ gm	Telescope scale readings						Mean cm	Shift in the scale reading for 100 gm ‘s’ cm
	Loading cm			Unloading cm
w
w+50
w+100
w+150
w+200
w+250

Tabular Column 2: To find the breadth of the beam using Vernier calliper

            The procedure of using Vernier caliper and its table can be found here.

Tabular Column 3: To find the thickness of the beam using screw gauge

            The procedure of using Screw gauge and its table can be found here.

Result: 

Young's modulus of the material of the bar by the method of cantilever depression is found to be, E =______ N/m2