Experiment No . 1 ( B.Sc. 2nd Semester Physics Project file )

Experiment No. 1  bsc.2^nd semester

1.     Determination and Verification of the Time Period of a Cantilever

Object

            To determine and verify the time period of oscillation of a cantilever beam whith a known mass attached at its free end.

Apparatus Required

1.      Cantilever beam (e.g a steel or aluminum ruler)

2.      Clamp and stand to fix the beam.

3.      Set of known masses.

4.      Stopwatch

5.      Measuring scale or ruler

6.      Vernier caliper or micro meter screw gauge.

7.      Balance (for measuring mass)

Theory

            When a mass is attached to the free end of a cantilever beam and displaced slightly it undergoes simple harmonic motion. The time period T of oscillation is given by –

                                                T = 2π √ML³/√3EI

For a rectangular cross – section .

                                                                        I = bd³/12

Where             b = width of the beam

                        .d = thickness (depth) of the beam.

Procedure

1.      Setup secure one end of the beam finely using the drop and stand ensuring it acts as a cantilever.

2.      Measurement measure the length L from the fixed end to the point where the mass will be attached.

3.      Cross – sectional dimensions use the vernier caliper or micrometer to measure the with b and thickness d of the beam.

4.      Mass attachment- attach a known mass M to the free end of the beam

5.      Oscillation – displace the mass slightly downward and release to allow oscillation.

6.      Timing – use the stopwatch to measure the time taken for a certain number of oscillation “(e.g. 20 oscillation) to minimize error.

7.      Repeat – repeat the timing for multiple trials to obtain an average value.

8.      Variation – repeat the experiment with different masses and or lengths to observe the effect on the time period.

Observation  

                       

S. No.	Mass M (Kg)	Length L (m)	Width b (m)	Thickness d (m)	Time for 20 oscillations (s)	Time period T (s)
1.	0.100	0.30	0.025	0.003	16.2	0.81
2.	0.150	0.30	0.025	0.003	19.0	0.95
3.	0.200	0.30	0.0025	0.003	21.5	1.06
4.	0.250	0.30	0.025	0.003	23.8	1.19
5.	0.300	0.30	0.025	0.003	26.0	1.30

 

Calculations

1.      Moment of Inertia I

I = bd³/12 = 0.025 x (0.003)³/12 = 5.625 x 10⁻ⁱ⁰ m⁴

2.      Theoretical time Period T-

                                                                                    T = 2π √ML³/√3EI

            Assuming –

a.      Young’s modulus for steel E = 2 x 10ᴵᴵ Pa

b.      Length L = 0.30 m

c.       Moment of inertia I = 5.625 x 10ᴵ⁰ m⁴

For Trial 1 (M = 0.100 kg)   

  3.     Percentage , calculate for other trials.

Percentage error

                                                            

Result -

            The experimental time periods closely match the theoretical predictions with minimum percentage error validating the theoretical madel for the cantilever’s oscillations.

Calculation

                        The experiment successfully demonstrates the relationship between the mass attached to a cantilever and its oscillation period . the close agreement between experimental and theoretical values conform the validty of the theoretical formula used.

Precautions

a.      Ensure the beams rigidly clamed to prevent unwanted movements.

b.      Measure dimensions accurately using appropriate instruments.

c.       Avoid large displacements to maintain simple harmonic motion conditions.

d.      Use consistent method for timing oscillations to reduce human error. 

Note.

(Please note: if a particular experiment is not visible, please search for it using the search box—for example, Experiment No. 2.)

कृपया ध्यान दीजिये जो एक्सपेरिमेंट न दिख रहा हो वो आप सर्च बॉक्स में सर्च कर लीजिये . जैसे , एक्साप्रिमेंट नंबर.2

Experiment No . 2 ( B.Sc. 2nd Semester Physics Project file )

 Experiment No. 2  bsc.2^nd semester

2. Determination of ultrasonic Velocity in Liquids using ultrasonic interferometer.

Object

            To determine the velocity of ultrasonic waves in various liquids using an ultrasonic interferometer

Apparatus Required

1.      Ultrasonic interferometer (comprising a high frequency generator , measuring cell with micrometer and quartz crystal)

2.      Sample liquids (e , g distilled water , glycerol , paraffin)

3.      Micrometer screw gauge

4.      Thermometer

5.      Measuring cylinder

6.      Ammeter

Theory

An ultrasonic interferometer is a device that measures the velocity of ultrasonic waves in liquids by creating standing waves within the medium. When ultrasonic waves are generated in the liquid , they interfere with reflected waves , forming standing wave patterns. The distance between successive maxima or minima in the standing wave pattern corresponds to half the wavelength (ʎ/2) of the ultrasonic waves. The velocity v of ultrasonic waves in the liquid in given by.

                        V = f x ʎ

Where

a.      .d = distance between two successive maxima or minima (m) combining the equations.

.v = 2x f x d

Procedure

1.      Set up the ultrasonic interferometer and ensure all connections are secure.

2.      Pour the sample liquid into the measuring cell of the interferometer.

3.      Insert the quartz crystal into the base socket and clamp it tightly.

4.      Switch on the high frequency generator to produce ultrasonic waves in the liquid.

5.      Adjust the micrometer to vary the distance between the reflector and the crystal.

6.      Observe the anode current on the ammeter. Note the micrometer readings corresponding to successive maxima (or minima) in the anode current.

7.      Record at least five such readings to calculate the average distance d between successive maxima or minima.

8.      Repeat the above steps for different sample liquids.

Observation and Calculations

            Assuming the frequency f of the ultrasonic waves is 2 MHz (i.e. 2 x 10⁶ Hz) , and the micrometer readings for successive maxima are as follows.

For Distilled Water

S . No .	Micrometer Reading (mm)	Difference d (mm)
1	1.000
2.	1.381	0.381
3.	1.762	0.381
4.	2.143	0.381
5.	2.524	0.381

                       

Average d = 0.381 mm = 0.381 x 10⁻³  m

ʎ = 2 x d = 2 x 0.381 x 10⁻³ = 0.762 x 10⁻³ m

            v = f x ʎ = 2 x 10⁶ x 0.762 x 10⁻³  = 1524 m/s

For Glycerol

S. No	Micrometer reading (mm)	Difference d (mm)
1.	1.000
2.	1.472	0.472
3.	1.944	0.472
4.	2.416	0.472
5.	2.888	0.472

 

Average d = 0.472 mm = 0.472 x 10⁻³ m

            ʎ = 2 x d = 2 x 0.472 x 10⁻³ = 0.944 x 10⁻³ m

            v = f x ʎ = 2 x 10⁶ x 0.944 x 10⁻³ = 1800 m/s

For Paraffin

S. No	Micrometer Reading (mm)	Difference d (mm)
1.	1.000
2.	1.708	0.708
3.	2.416	0.708
4.	3.124	0.708
5.	3.832	0.708

 

Average d = 0.708 mm = 0.708 x 10⁻³ m

            ʎ = 2 x d = 2 x 0.708 x 10⁻³ = 1.416 x 10⁻³ m

            v = f x ʎ = 2 x 10⁶ x 1.416 x 10⁻³ = 2832 m/s

Results

                        Liquid                                      Velocity v (m/s)

                        Distilled Water                        1524

                        Glycerol                                   1888   

                        Paraffin                                   2832

 Conclusion

            The experiment successfully determined the velocities of ultrasonic waves in different liquids using an ultrasonic interferometer.

Note.

(Please note: if a particular experiment is not visible, please search for it using the search box—for example, Experiment No. 2.)

कृपया ध्यान दीजिये जो एक्सपेरिमेंट न दिख रहा हो वो आप सर्च बॉक्स में सर्च कर लीजिये . जैसे , एक्साप्रिमेंट नंबर.2