Aim: how To determine the Young`s modulus of the given material using a single cantilever.
Apparatus: Meter scale (steel), slotted weight 7x50gms, travelling microscope, half meter scale, etc.
Formula:
Y=( 4mgl^3)/(bxd^3 ) N/m2
where, Y is the Young`s modulus of the given material (N/m2).
g is the acceleration due to gravity (9.8 m/s2)
l is the length of cantilever (m)
b is the breadth of the beam (m)
d is the thickness of the beam (m)
m is the applied mass at the open end (kg)
x is the is the depression at the open end of the cantilever (m)
Procedure:
A meter scale (Steel) employed in this experiment to serve the purpose of a single cantilever. The experimental is made as shown in the fig. one scale pan is suspended at free end of the scale. The length of cantilever (l) is noted from the fixed end till the end of open end using meter scale. A pin is fixed exactly at the edge end of the scale by using wax, such that, it stands with its tip pointing vertically upwards.
A travelling microscope (TM) is brought in front of the scale and its microscope is focused such that its horizontal cross-wire is just in level with the image of the tip of the pin. The reading on the vertical scale is noted, which corresponds to the zero load state of the scale in the Tabular column. A load of 50 gm is placed in each of the pans due to which the beam bends, and the pin gets displaced. The microscope is again focused to the image of the pin tip, and the corresponding reading is noted.
The load in each of the pans is increased in steps of 50 gm, and the corresponding readings of TM are noted for each step under the heading load increasing (A), till the accumulated load becomes 250gm. The load in each of the pans is then decreased in same steps, till zero load state is reached, and the corresponding readings are entered in the column load decreasing (B). The mean value of depression x= (A+B)/2 is evaluated. A graph is drawn taking mass m along the X-axis and depression x along Y-axis as
shown in graph. From the straight line graph the slope (x/m) is determined. From which the Young’s modulus (Y) of the given material is calculated using the formula.