EXPERIMENTAL REPORT department of general physics

- Step 1: Use Vernier caliper measure the height, external and internal diameter of metal hollow cylinder 5 trials- Step 2: Write all the measurement results in data sheet.. Steel ball:

111Equation Chapter 1 Section 1 HANOI UNIVERSITY

OR SCIENCE AND TECHNOLOGY

SCHOOL OF ENGINEERING PHYSICS

- -  

EXPERIMENTAL REPORT

Department of General Physics

Instructor: Prof Dr Dang Duc Dung

Name:

ID:

Group: 4Class: 708605

Hanoi, 2022

Experimental Report 1 MEASUREMENT OF BASIC LENGTH

Verification of the instructors

- To know how to use Vernier Caliper and Micrometer

- Understanding how to read a Vernier Caliper and a Micrometer

1 Vernier Caliper:

 To read result with a Vernier caliper, we need to use this equation:

D = n.a + m.∆ (mm)

- n be the number of divisions on the main rule

- m be the number of divisions on the Vernier scale

- a is the value of a division on main rule

- ∆ is the Vernier precision ∆ = 1/N

2 Micrometer:

 To read result with a micrometer, following equations:

D = n.a + m.∆ (mm) (1)

or D = n.a + m.∆ +0,5 (mm) (2)

- ∆ is the Vernier precision and also corresponding to the value of division on thimble

 If the distance between thimble and line on top half of main rule is closer than bottom half then we use (1)

 If the distance between thimble and line on bottom half is closer than top then we use (2)

3 Calculate the volume and density of the metal hollow cylinder and the volume of the steel ball:

 To calculate volume of metal hollow cylinder we use the following equation:

- V is the volume of metal hollow cylinder

- D is external diameter of metal hollow cylinder

- d is internal diameter of metal hollow cylinder

- h is the height of metal hollow cylinder

 To calculate density of metal hollow cylinder we use the following equation:

- is the density of metal hollow cylinder

- M is the mass of metal hollow cylinder

- V is the volume of metal hollow cylinder

 To calculate the volume of steel ball we use the following equation:

- Vb is the volume of steel ball

- Db is the diameter of steel ball

1 Metal hollow cylinder:

4

- Step 1: Use Vernier caliper measure the height, external and internal diameter of metal hollow cylinder (5 trials)

- Step 2: Write all the measurement results in data sheet

2 Steel ball:

- Step 1: Use the micrometer measure the diameter of steel ball (5 trials)

- Step 2: Write all the measurement results in data sheet

1 Metal hollow cylinder:

∆d = = 0.02

=43.36D

∆D = = 0.01

 ∆V = b Vb

= 520.20 = 1.74(mm ) 3

= 0,002(m )3

Hence: V = ( 0,52 0,002) (m ) 3

Experimental Report 2 VERIFICATION OF CONSERVATION OF MOMENTUM AND KINETIC

ENERGY USING AIR TRACK

Verification of the instructors

- Understanding more about conservation of momentum and kinetic energy

- Improving experimental skills

1 Momentum and conservation of momentum:

- The momentum of a particle is a vector quantity equal to the product of the particle’s mass m and velocity

- Newton’s second law says that the net force on a particle is equal to the rate

of change of the particle’s momentum

2 Elastic and inelastic collision

2.1 Elastic collision

- In any collision in which external forces can be neglected, momentum

is conserved and the total momentum before equals the total

III EXPERIMENTAL PROCEDURE

1 Preparation

- Set up the equipment so that the glide 2 will be stationary in the center of the track between the gates () and the glide 1 is placed in one end of the track

- Make several trial runs of the collision before doing any

measurements

2 Elastic collision

- Step 1: Gently push the glide 1, from one end to make it moving to

the right (direction of the arrow) toward the steel spring fixed onto the air track Quickly record the moving time displayed on the first digital timer The glide 1 will collide with the glide 2 in the middle Two glides bounce apart and go through the photogates, recording both the time displayed on the second timer and the total time on the first timer The moving time of the glide 1 after collision () is determined by subtract from the total time

- Step 2: Repeat the measurement procedure for more 9 times and

record all the measurement results in a data sheet

3 Inelastic collision

- Step 1: Attach a piece of clay on one end of glide 2 facing to glide 1

to make them stick together after collision

- Step 2: Perform measurement procedure and record the moving time

of two glides before and after collision

- Step3: Repeat the measurement procedure for more 9 times and

record all the measurement results in a data sheet

IV Experimental result

The percent change in kinetic energy

To conclusion, the kinetic energy after an elastic collision is insignificantly less than that one occurring before

The percent change in kinetic energy

To conclusion, the kinetic energy after a completely inelastic collision is

significantly less than that one occurring before

Experimental Report 3 MOMENT OF INERTIA OF THE SYMMETRIC RIGID BODIES

Verification of the instructors

- Calculating the moment of the inertia in the symmetric rigid bodies

- Gaining knowledge about the moment of the inertia in the symmetric rigid bodies

- The moment of inertia of the body about the axis of rotation is determined

by

- For a long bar

- For a thin disk or solid cylinder

- For a hollow cylinder having very thin wall:

- For a solid sphere:

- The parallel-axis theorem relates the moment of inertia Icm about an axis through the center of mass to the moment of inertia I about a parallel axis

through some other point

- The torque acting on angle is

- Theorem of angular momentum of a rigid body in rotary motion

- The oscillation is corresponds to a period

1 Measurement of the rod:

- Step 1: A mask is stuck on the rod to ensure the rod through the photogate

- Step 2: Press the button “Start” to turn on the counter

- Step 3: Push the rod to rotate with an angle of 180 then let it to oscillate freely (5 trials)

- Step 4: Press the button “Reset” to turn the display of the counter being 0

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2 Measurement of the solid disk:

- Step 1: Using the suitable screws to moment the solid disk

- Step 2: Perform the measurement procedure similar to that of the rod – Record result period T (5 trials)

- Step 3: Press the button “Reset”

3 Measurement of the hollow cylinder:

- Step 1: Using the suitable screws to moment the hollow cylinder

- Step 2: Perform the measurement procedure similar to the rod of the disk Record result period T (5 trials)

- Step 3: Press the button “Reset”

4 Measurement of the solid sphere:

- Step 1: Mount the solid sphere on the rotation axle of the spiral spring

- Step 2: Push the sphere to rotate with an angle of 270, then let it to oscillate freely Record the vibration period of the sphere (5 trials)

- Step 3: Uninstall the solid sphere and switch off the counter to finish the measurements

IV Experimental result

1 Measurement of the rod:

2 Measurement of the solid disk:

The different between theoretical and experimental number:

2 Solid disk:

2.1 Moment of inertia obtained by experiment

Hence,

2.2 Moment of inertia calculated by the theoretical formula

The different between theoretical and experimental number:

3 Hollow cylinder:

3.1 Moment of inertia obtained by experiment

+) Moment of inertia of the support disk

+) Moment of inertia of the coupled object (support disk + hollow cylinder)

=> Moment of inertia of the hollow cylinder

3.2 Moment of inertia calculated by the theoretical formula

The different between theoretical and experimental number:

4 Solid sphere:

18

4.1 Moment of inertia obtained by experiment

Hence,

4.2 Moment of inertia calculated by the theoretical formula

The different between theoretical and experimental number:

Experimental Report 4 DETERMINATION OF GRAVITATIONAL ACCELERATION USING SIMPLE PENDULUM OSCILLATION WITH PC INTERFACE

Verification of the instructors

- Understanding more about the harmonic oscillation

- Verifying the value of gravity acceleration

- Improving experimental skills

- When pendulum mass m is deviated to a small angle γ, a retracting force acts on it to the initial balanced position

- If one ensures that the amplitudes remain sufficiently small while

experimenting, the movement can be described by

- This is a harmonic oscillation having the amplitude γ0 and the oscillation period : 

- If one rotates the oscillation plane around the angle θ with respect to the vertical plane The oscillation period 

- Based on equation , , we would see how the gravitation acceleration  depends on its length and the inclined angle

1 Preparation:

- Set up the experiment such that the oscillating plane runs vertically

- The electric connection of the movement sensor for the COBRA interface

- Start the MEASURE software written for COBRA interface

2 Investigation for various pendulum lengths

- Step1: Choose an arbitrary pendulum length (400mm)

- Step 2: Move the 1-g weight holder

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- Step 3: Set the pendulum in motion (small oscillation amplitude) and click

on the “Start measurement” icon

- Step 4: After approximately 5 oscillations click on the “Stop measurement” icon, a graph appears on the screen

- Step 5: Determine the period base on the graph Record the measurement result in a data sheet

- Step 6: Repeat the measurement 5 times to get the average value of

the oscillation period

- Step 7: Repeat the measurement with different pendulum lengths (600mm and 700mm)

3 Pendulum with inclined oscillation plan

- Step 1: Rebuild the experiment set up this oscillation plane is initially

vertical

- Step 2: Measurement with these following angles

- Step 3: Perform the measurement 5 times for each case of angles to get

the average value of oscillation period

IV Experimental result

1 Pendulum with vertical oscillation plane:

L=40 0m: Trial 1

L=40 0m: Trial 2

L=40 0m: Trial 3

22

L=45 0m: Trial 1

L=450m: Trial 2

L=500m: Trial 1

L=500m: Trial 2

L=500m: Trial 3

24

2 Pendulum with inclined oscillation plane:

: Trial 1

: Trial 2

Trial 3

26

: Trial 1

: Trial 2

: Trial 1

: Trial 2

: Trial 3

28

: Trial 1

: Trial 2

: Trial 1

: Trial 2

: Trial 3

30

: Trial 1

: Trial 2

1 Determination of the oscillation period of a thread pendulum as a function

of the pendulum length:

Pendulum with vertical oscillation plane:

2 Determination of the gravitational acceleration as a function of the

inclination of the pendulum force:

Pendulum with inclined oscillation plane:

2.1

Hence:

2.2

32

2.6

Hence:

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Experiment Report 5 DETERMINATION OF MOMENT OF INERTIA BASED ON TORSIONAL

VIBRATION

Verification of the instructors

- Verifying the linear relationship between τ and φ z

- Understanding about the moment of inertia, torsion modulus

- If a body is regarded as a continuum, and if r0 and r denote the position vector of a point p in the un-deformed and deformed states of the body, then for small displacement vectors:

The deformation tensor is

- The stress tensor

- The relationship between where E is elastic modulus

- The equation of vibration as follows:

- The period of this vibration is:

- The linear relationship between τ and φ allows to determine Dτ and z

consequently the moment of inertia of the long rod

- Step 1: Assemble the steel rod on the torsion apparatus

- Step 2: Use the spring balance of the force to turn the disk being deflected

an angle

- Step 4: Pull out to turn the disk being deflected an angle , then let it ϕ

vibration and use the stopwatch to determine the vibration period

2.2 Determination of the torsion modulus D as the slope m of the above graph and its uncertainty

Using the above graph, we can see that:

Experimental Report 6 DETERMINATION OF SOUND WAVELENGTH AND VELOCITY

USING STANDING WAVE PHENOMENON

Verification of the instructors

- To understand the physical phenomenon of standing wave

- To determine the sound wavelength and propagation velocity

- A standing wave, also known as a stationary wave, is a wave that remains in

a constant position This phenomenon can arise in a stationary medium as a result of interference between two waves traveling in opposite directions The effect is a nodes and anti-nodes

- In this experiment, two waves with the same frequency, wavelength and amplitude traveling in opposite directions will interfere and produce

standing wave or stationary wave

- The sound wavelength λ (in meters) is related with the frequency f as the follows:

- The amplitude of the resultant wave at M is

- The positions of nodes where the amplitude equals to zero are correspondingto

- The positions of antinodes where the amplitude is maximum are

corresponding to

- The distance between two conjugative nodes or antinodes is

- The distance L between its open-end and point N is determined as

- The sound resonance is detected by a microphone The signal is shown by the ampere-meter of current amplifier Then, the phenomenon can be

recorded by observing the maximum deviation of ampere-meter’s hand corresponding to due to the position of piston

- Step1: Switch the frequency knob on the surface of base-box to the position

of 500 Hz

- Step 2: Turn slowly the crank to move up the piston and simultaneously observe the movement of ampere-meter’s hand until it gets the maximum deviation

- Step 3: Record the position L of the piston corresponding to the maximum 1

deviation of ampere-meter’s hand in table 1 of the report sheet

- Step 4: Continue to move up the piston and observe the movement of

microampere-meter’s hand until it gets the position of maximum deviation once again

- Step 5: Again, record the second position of the piston L (in millimeters) in2

table 1

- Step 6: Repeat the experimental steps of 2 to 5 for more four times

- Step 7: Perform again all the measurement procedures (from step 1 to step 6)corresponding to the frequencies of 600 Hz and 700 Hz The measurement results are recorded in table 2 and 3, respectively

1 Measurement result:

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2.3 Theoretical velocity of sound wave and experimental values:

Theoretically, the velocity of sound wave at a temperature T can be calculated as follows: