PHYSICS LABWORK for PH1016 (new version)

- Step 1: Count the number of division n on the main rule – T, lying to the left of the 0-mark on the vernier scale – T’ see example in Fig.. 2 - Step 2: Look along the division mark

Hanoi University of Science and Technology (HUST)

School of Engineering Physics (SEP)

PHYSICS LABWORK

For PH1016 (New version)

Edited by Dr.-Ing Trinh Quang Thong

Hanoi, 2019

Fig.1 Structure of an ordinary vernier caliper

When the jaws are closed, the vernier zero mark coincides with the zero mark on the scale

of the rule The vernier scale (T’) slides along the main rule (T) The main rule allows you to determine the integer part of measured value The sliding rule is provided with a small scale which is divided into equal divisions It allows you to determine the decimal part of measured result in combination with the caliper precision (Δ), which is calculated as follows:

N

1

=

Δ (1)

Where, N is the number of divisions on vernier scale (except the 0-mark), then, for N = 10

we have Δ = 0.1 mm, N = 20 we have Δ = 0.05 mm, and N = 50 we have Δ = 0.02 mm

1.2 How to use a vernier caliper

- Preparation to take the measurement, loosen the locking screw and move the slider to check

if the vernier scale works properly Before measuring, do make sure the caliper reads 0 when fully closed

1

- Close the jaws lightly on the item

which you want to measure If you are

measuring something round, be sure the

axis of the part is perpendicular to the

caliper In other words, make sure you

are measuring the full diameter

1.3 How to read a vernier caliper

In order to determine the

measurement result with a vernier

caliper, you can use the following

equation:

D = n a + m Δ (2)

Where, a is the value of a division on

main rule (in millimeter), i.e., a = 1

mm, Δ is the vernier precision and also

corresponding to the value of a division

on sliding rule that you can either find

it on the caliper body or determine it’s

value using the eq (1)

- Step 1: Count the number of division

(n) on the main rule – T, lying to the

left of the 0-mark on the vernier scale –

T’ (see example in Fig 2)

- Step 2: Look along the division mark

on vernier scale and the millimeter

marks on the adjacent main rule, until

you find the two that most nearly line

up Then, count the number of divisions

(m) on the vernier scale except the

0-mark (see example in Fig 2)

- Step 3: Put the obtained values of n

and m into eq (2) to calculate the

measured dimension as shown in Fig.2

Attention:

(a)

(b)

(c)

Fig.2 Method to read vernier caliper

The Vernier scale can be divided into three parts called first end part, middle part, and last end part as illustrated in Fig 2a, 2b, and 2c, respectively

+ If the 0-mark on vernier scale is just adjacently behind the division n on the main rule, the division m should be on the first end part of vernier scale (see example in Fig.2a)

+ If the 0-mark on vernier scale is in between the division n and n+1 on the main rule, the division m should be on the middle part of vernier scale (see example in Fig.2b)

+ If the 0-mark on vernier scale is just adjacently before the division n+1 on the main rule,

the division should be on the last end part of vernier scale (see example in Fig.2c) m

micrometer principle are shown in Fig.3 Each revolution of the rachet moves the spindle face 0.5mm towards the anvil face A longitudinal line on the frame (called referent one) divides the main rule into two parts: top and bottom half that is graduated with alternate 0.5 millimetre divisions Therefore, the main rule is also called “double one” The thimble has 50 graduations, each being 0.01 millimetre (one-hundredth of a millimetre) It means that the precision (Δ) of micrometer has the value of 0.01 Thus, the reading is given by the number

of millimetre divisions visible on the scale of the sleeve plus the particular division on the thimble which coincides with the axial line on the sleeve

Anvil face

Sleeve, main scale - T Thimble – T’ ScrewSpindle

rule

Referent line

Anvil face

Lock nut

Sleeve, main scale - T Thimble – T’ ScrewSpindle

Double rule

Referent line Thimble – T’

Thimble edge

Fig.3 Structure of an ordinary micrometer

2.2 How to use a micrometer

- Start by verifying zero with the jaws closed Turn the ratcheting knob on the end till it clicks If it isn't zero, adjust it

- Carefully open jaws using the thumb screw Place the measured object between the anvil and spindle face, then turn ratchet knob clockwise to the close the around the specimen till it clicks This means that the ratchet cannot be tightened any more and the measurement result can be read

2.3 How to read a micrometer

In order to determine the measurement result

with a micrometer, you can also use the following

equation:

D = n a + m Δ (3)

Where, a is the value of a division on sleeve

-double rule (in millimeter), i.e., a = 0.5 mm, Δ is

the micrometer’s precision and also corresponding

to the value of a division on thimble (usually Δ =

0.01 mm)

- Step 1: Count the number of division (n) on the

sleeve - T of both the top and down divisions of the

double rule lying to the left of the thimble edge

- Step 2: Look at the thimble divisions mark – T’

to find the one that coincides nearly a line with the

referent one Then, count the number of divisions

(m) on the thimble except the 0-mark

- Step 3: Put the obtained values of n and m into

eq (3) to calculate the measured dimension as the

examples shown in Fig.4

(a)

(b)

Fig 4 Method to read micrometer

3

.Attention:

The ratchet is only considered to spin

completely a revolution around the sleeve

when the 0-mark on the thimble passes the

referent line As an example shown in Fig.5, it

seems that you can read the value of n as 6,

however, due to the 0-mark on the thimble lies

above the referent line, then this parameter is

determined as 5 Fig.5 Ratchet does not spin completely a

revolution around the sleeve, yet

III EXPERIMENTAL PROCEEDURE

1 Use the Vernier caliper to measure the

external and internal diameter (D and d

respectively), and the height (h), of a

metal hollow cylinder (Fig.6) based on

the method of using and reading this rule

presented in part 1.2 and 1.3

Note: do 5 trials for each parameter

2 Use the micrometer to measure the

diameter (Db) of a small steel ball for 5

trials based on the method of using and

reading this device presented in part 2.2

and 2.3 Fig.6 Metal hollow cylinder for measurement

IV LAB REPORT

Your lab report should include the following issues:

1 A data table including the measurement results of the height (h), external and internal diameter (D and d, respectively) of metal hollow cylinder

2 A data table including the measurement results of the diameter (Db) of small steel ball

3 Calculate the volume and density of the metal hollow cylinder using the following equations:

6 Report the last result of those quantities in the form as: V = V ± ΔV

7 Note: Please read the instruction of “Significant Figures” on page 6 of the document

“Theory of Uncertainty” to know the way for reporting the last result

4

Experiment 2

MOMENTUM AND KINETIC IN ELASTIC AND INELASTIC COLLISIONS

Equipment:

1 Aluminum demonstration track;

2 Starter system for demonstration track;

3 End holder for demonstration track

4 Light barrier (photo-gate)

5 Cart having low friction sapphire bearings;

6 Digital timers with 4 channels;

7 Trigger

I THEORETICAL BACKGROUND

1 Momentum and conservation of momentum

Momentum is a physics quantity defined as product of the particle's mass and velocity T

is a vector quantity with the same direction as the particle's velocity

p   m v  (1)

Then we may demonstrate the Newton's second law as

dt

p F







 (2) The concept of momentum is particularly important in situations in which we have two or more interacting bodies For any system, the forces that the particles of the system exert on each other are called internal forces Forces exerted on any part of the system by some object outside it are called external forces For the system, the internal forces are cancelled due to the Newton’s third law Then, if the vector sum of the external forces is zero, the time rate of change of the total momentum is zero Hence, the total momentum of the system is constant:

const p

2 Elastic and inelastic collision

2.1 Elastic collision

If the forces between the bodies are much larger than any external forces, as is the case in most collisions, we can neglect the external forces entirely and treat the bodies as an isolated system The momentum of an individual object may change, but the total for the system does not Then momentum is conserved and the total momentum of the system has the same value

before and after the collision If the forces between the bodies are also conservative, so that

no mechanical energy is lost or gained in the collision, the total kinetic energy of the system

is the same after the collision as before Such a collision is called an elastic collision This case can be illustrated by an example in which two bodies undergoing a collision on a frictionless surface as shown in Fig.1

Fig 1 Before collision (a), elastic collision (b) and after collision (c)

Remember this rule:

- In any collision in which external forces can be neglected, momentum is conserved and the total momentum before equals the total momentum after that is

2 2 1 1 2 2 1

1 1 2 2 1 2 1 1

2

12

1'2

1'2

1

v m v

m v

m v

m    (5)Using the two laws of conservation (4) and (5), the velocities after the collision and can be calculated based on the initial velocities as follows

 

2 1

2 2 1 2 1 1

2'

m m

v m v m m v

1 1 2 1 2 2

2'

m m

v m v m m v

1 2 1 1

'

m m

v m m v





 (8)

2 1

1 1 2

2'

m m

v m v

1 2

1

'

v v

v v







 (10)

In the case of a completely elastic collision, the value of this coefficient of restitution is 1 and

in the case of an inelastic collision, its value is 0 Then, eqs (6) and (7) can be rewritten as

   

2 1

2 2 1

2 1 1

1'

m m

v m v

m m v

1 1 2

1 2 2

1'

m m

v m v

m m v

2.2 Inelastic collision

A collision in which the total kinetic energy after the collision is less than before the collision is called an inelastic collision An inelastic collision in which the colliding bodies stick together and move as one body after the collision is often called a completely inelastic collision The phenomenon is represented in Fig.2

Fig 2 Before collision (a), completely inelastic collision (b) and after collision (c)

Conservation of momentum gives the relationship:

2 1 1

1 v m m

m v





1

' (14) Let's verify that the total kinetic energy after this completely inelastic collision is less than before the collision The motion is purely along the x-axis, so the kinetic energies and K l K 2

before and after the collision, respectively, are:

2 1

1 v m 2

1

K  (15)

1 2

2 2

2 1

m m

m m

m 2

1 v' m m 2

1 K

1

1 1

m K

In this experiment, the collisions between two carts attached with “shutter plate (length ” as

100 mm) (Fig 3a) will be investigated One end of cart 1 is attached with a magnet with a plug facing the starter system and the other one is attached with a plug in the direction of motion The moving time before and after the collisions through the photogates will be measured by the time counter (Fig 3b) that enable to calculate the corresponding velocities

2.2 Elastic collision

- Step 1: Assemble cart 1 with a shutter plate and plug facing to the cart 2 Attach also “ ” a a

“shutter plate , a bow-shaped fork with rubber band facing to cart 1 and an additional mass ”

of 200 g on cart 2, as shown in Fig 3a In this case, the weight m 1 of cart 1 should be haft of

(a) (b)

Fig 3 Carts enclosed with shutter plates (a) and the timer counter (b)

- Step 4: After collision, cart 1 moves back through the photogate 1 and cart 2 moves with the

velocity v’ 2 through the photogate 2 (Fig 4c)

- Step 5: Record the time for cart 1 before collision as and after collision ast 1 t’ 1 displayed on the first and second window, respectively The time for cart 2 after collision as t’ 2 displayed

on the third window of time counter The measurement result can be demonstrated in data table 1

- Step 6: Repeat the measurement procedure from step 1 to 5 for more 9 times and record all

results in data table 1

- Step 7: Weight two carts to determine their masses by using an electronic balance Record

the mass of each cart

- Step 1: Put off the right plug of cart 1 and attach the other one with a needle facing to cart 2

take off the additional weight from cart 2 and place it on cart 1 For cart 2, replace the shaped fork plug with another one having plasticine and also put off the shutter plate In “ ”

bow-this case, the weight m 1 should be twice m 2

- Step 2: Place the cart 1 ( m 1) on the left of track closer to the starter system and the cart 2

(m ) also stationary between the photogates (Fig 5 a)

- Step 3: Push the trigger of the starter system that enables cart 1 to be released and accelerate

through the photogate 1 to cart 2 (Fig 5b)

- Step 4: After collision, cart 1 sticks with cart 2 then both carts move together with the same velocity through the photogate 2 (Fig 5 v’ c)

- Step 5 : Record the time for cart 1 before collision as t 1and time after collision for both carts

as t’1 = t’2 displayed on the first and third window, respectively The measurement result can

be demonstrated data table 2 in

- Step 6: Repeat the measurement procedure from step 1 to 5 for more 9 times and record all

results in data table 2

- Step 7: Weight two carts to determine their masses by using an electronic balance Record

the mass of each cart

(a)

( )b

(c)

Fig.5 Experimental procedure to investigate the inelastic collision

III LAB REPORT

Your lab report should include the following:

1 Two data sheets of time recorded before and after the collision (should be 10 trials) in both cases of elastic and inelastic collision

2 Calculations of the velocities and momentums of each measurement system before and after the collision in case of elastic and inelastic collision based on the eqs (1), (11 and ) (12)

3 Evaluation of the average total momentum before and after the collision in case of elastic and inelastic collision Make the conclusions of the obtained results

4 Evaluation of the percent changes in kinetic energy (KE) through the collision for the two sets of data specified above before and after the collision in case of elastic and inelastic collision (using eq 17) Make the conclusions of the obtained results

5 Evaluation of the uncertainties in the momentum and kinetic energy changes

Note: The collision is not completely elastic because there is still some residual friction when

the carts move That’s why the total momentum may decrease slightly by approximately 6 % and the kinetic energy may decrease up to 25 %

6 Note: Please read the instruction of “ Significant Figures” on page 6 of the document

“Theory of Uncertainty” to know the way for reporting the last result.

Experiment 3 MOMENT OF INERTIA OF THE SYMMETRIC RIGID BODIES

If the axis of rotation is chosen to be through the center of mass of the object, then the

moment of inertia about the center of mass axis is call Icm In case of the typical symmetric and

homogenous rigid bodies, Icm.is calculated as follows

- For a long bar: 2

of mass to the moment of inertia I about a parallel axis through some other point The theorem states that,

I = I cm + Md 2 (6)

This implies Icm is always less than I about any other axis

In this experiment, the moment of inertia of

a rigid body will be determined by using an

apparatus which consists of a spiral spring

(made of brass) The object whose moment of

inertia is to be measured can be mounted on

the axis of this torsion spring which tends to

restrict the rotary motion of the object and

provides a restoring torque If the object is

rotated by an angle φ, the torque acting on it

will be

τz = D z φ (7)

where D z is a elastic constant of spring

This torque will make the object oscillation

Using the theorem of angular momentum of a

rigide body in rotary motion

2 2

dt

d I dt

d I dt

τ= = = (8)

We get the typical equation of oscillation as

Fig 1 Experimental model to determine the

moment of inertia of the rigid body

10

2

2

=+ φ

φ

I

D dt

(9) The oscillation is corresponds to a period

z

D

I

T =2π (10) According to (10), for a known D z, the unknown moment of inertia of an object can be found

if the period T is measured

II EQUIPMENT

1 Rotation axle with spiral spring having the

elastic constant, D z = 0,044 Nm/Rad;

2 Light barrier (or photogate) with counter;

3 Rod with length of 620mm and mass of

7 Supported thin disk;

8 A set of screws for mounting the objects;

III EXPERIMENTAL PROCEDURE

3 1 Measurement of the rod

- Step 1: Equipment is setup corresponding

to Fig.3 A mask (width ~ 3 mm) is stuck on

the rod to ensure the rod went through the

photogate

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

the counter Then, you can see the light of

LED on the photogate

- Step 3: Push the rod to rotate with an angle

of 1800, then let it to oscillate freely The

time of a vibration period of the rod will be

measured In this case, the result you got is

averaged after several periods Make 5 trials

Fig 3 Experimental setup for measurement

of the rod

and record the measurement result of period T in a data sheet

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

next measurement

11