Young's modulus - Cantilever (Pin and microscope 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 with a Pin and Microscope. 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 technique.

Young's modulus - Cantilever

(Pin and microscope method)

Aim:

To determine the Young's modulus of the material of the cantilever by measuring the depression at the loaded end using a pin and microscope.

Apparatus required:

The cantilever, weight hanger and slotted weights, Pin and microscope, 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

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 pin is vertically fixed. A vernier microscope is focused on the tip of this pin.

Initially, with only the weight hanger, the horizontal cross wire is aligned with the pin's tip, and the reading from the vertical scale of the vernier microscope is recorded. Weights are then added in increments of 50 gm until the maximum load is reached, with readings taken each time. After that, the weights are removed in 50 gm 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 depression (y) corresponding to load (m)

Least count (LC) = 0.001 cm

Load ‘m’ gm	Microscope readings						Mean cm	Elevation corresponding to 100 gm ‘y’ cm
	Loading			Unloading
	MSR cm	VSR cm	TR cm	MSR cm	VSR cm	TR   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