APAC1001
Physics Laboratory Manual
First semester 2021/22
Roy, Leong Chon Chio
royleong@um.edu.mo
Faculty of Science and Technology
UNIVERSITY OF MACAU
A. Newton’s Laws
Objective
To verify Newton’s Laws of a uniformly accelerated motion in a straight line with the
aid of the air track rail.
Equipment
Tripod base
2
Support rod, 400mm
1
Right angle clamp
1
Slotted weight, 1g
20
Slotted weight, 10g
10
Slotted weight, 50g
4
Weight holder
1
Silk thread
1
Rod, 130mm
1
Rod, 165mm
1
Forked light barrier
1
Precision pulley
1
Air track rail
1
Glider
1
Screen, 100mm long
1
Screen, 25mm long
1
Hook for air track
1
Connecting cords
6
Balance
1
Catapult release
1
Retention magnet with plug
1
Pressure tube, 1.5m
1
Air blower
1
Electronic counter
1
1
Theory
Newton’s equation of motion for a point mass m on which a force F is applied, is given
as
F  ma
where a is the acceleration of the particle. If the particle is started from the origin of
the reference frame at rest,
s
at2
2
and
v  at
In our experiment,
m2  m1a  m0g
where m0 is the mass of the body hanging on the hook, m2 is the mass of the glider, and
m1 is slotted weights adding on the glider.
Set-Up
The experimental set up is shown in Figure 1. The catapult mechanism and forked light
barrier must be wired up as illustrated in Figure 2.
Figure 1. Experimental set-up for determining the mathematical inter-relationship for uniformly
accelerated motion in a straight line
2
Figure 2. Wiring the light barrier
Procedure
1.
To determine the distance as a function of time.
The length of travel to be measured is determined by moving the forked light
barrier. To do this, the glider is set to the desired distance (taking a reading, say, at
the front of the glider) with the air blower switched off. The light barrier is now
moved along the track to a position such that the screen attached to the glider just
triggers the electronic counter (the bulb flashes). Make sure that the electronic
counter stops when the screen blocks the light barrier. Denote t1 as the measured
time. The measurements of t1 should be repeated for five times. We should measure
t1 for four different positions.
2.
To measure the speed of the gliders as a function of the time.
Push STOP-INVERT key so that the electronic timer stops when the back edge of
the screen leaves the light barrier. Denote t2 as the measured time. The
measurements of t2 should be repeated for five times. The average speed of glider
at that position is
v
s
t
where s (10 cm) is the width of the screen and t is the duration when the light
was blocked (  t  t 2  t 1 ). We should measure t2 for four different positions (same
angles as pt. 1), and then the average speed at different time can be calculated.
3.
To determine the acceleration as a function of the mass while the force is kept as
the same.
3
The acceleration is found from average speeds. Repeat pt.1 – 2 for four different
values of mass of glider. The mass of the glider is increased successively by adding
slot weights on the glider and the added mass on the both sides are the same.
4
B. Moment of Inertia
and Angular Acceleration
Objective
To determine the moment of inertia of a rotating disk from its angular acceleration.
Equipment
Tripod base
1
Barrel base
1
Bench clamp, small
2
Bearing rotary plate with angle scale
1
Retaining device with wire release
1
Mask for rotary plate
1
Wright holder for rim apparatus
1
Silk thread
1
Slotted weight, 1g
20
Slotted weight, 10g
10
Slotted weight, 50g
2
Spirit level
1
Connecting cords
6
Fork light barrier
1
Precision pulley
1
Handle, 145mm
1
Pressure hose, 1.5m
1
Air blower
1
Electronic counter
1
Theory
The relationship between the angular momentum L of a rigid body in the stationary
coordinate system with its origin at the center of gravity, and the torque  acting on it,
is
5

d
L
dt
The angular momentum is expressed by the angular velocity  and the inertia tensor I
from
L  I
In the present case,  has the direction of a principal inertia axis (z-axis), so that L has
only one component,
L z  Iz
where Iz is the z-component of the principal inertia tensor of the plate. For this case,
z  Iz
d

dt
The torque of force F which is perpendicular to radius r gives
 z  mgr
so that the equation of motion reads
mgr  I z
d
  Iz
dt
where  is the angular acceleration. From this, we obtain
Iz 
mgr

The moment of inertia Iz of a body with density (x,y,z) is


I z   x , y , z  x 2  y 2 dxdydz
Figure 1. Moment of a weight force on the rotary plate
6
For a flat disc of radius r and mass m, we have
Iz 
mr2
2
In our experiment, the diameter and the mass of the disk are
2r = 0.350 m
m = 0.829 kg
respectively, so that
Iz = 12.69  10-3 kgm2
Set-Up
The experimental set up is shown in Figure 2. By means of a spirit level, and with the
blower switched on, the rotary bearing can be adjusted to be horizontal by turning three
screw feet on the tripod. The release starter must be adjusted that it is in contact with
the inserted sector mask before it starts. The measured angle can be adjusted by altering
the location of light barrier.
The precision pulley is clamped so that the thread is horizontally above the rotating
plate and the pulley.
The release starter and the light barrier are to be connected as shown in Figure 3. The
counter will start to count when we press the release starter. And, the counting will stop
when sector mask blocks (leaves) the light barrier. The normal stopping operation of
Figure 2. Experimental set-up for investigating uniformly accelerated rotary motion
7
Figure 3. Connection of the counter
the counter is triggered on while the sector mask blocks the light barrier. But if the setup
of STOP-INVERT buttons is changed, the stopping operation can also be triggered on
while the sector mask leaves the light barrier.
Procedure
1.
To determine the angular displacement as a function of time under constant
acceleration.
The angle is determined by moving the light barrier. Make sure that the electronic
counter stops when the sector mask blocks the light barrier. Denote t1 as the
measured time. The measurements of t1 should be repeated for five times at a
particular angle. We should measure t1 for four different angles.
2.
To measure the angular speed as a function of the time under constant acceleration.
Push STOP-INVERT key so that the electronic timer stops when the back edge of
the sector mask leaves the light barrier. Denote t2 as the measured time. The
measurements of t2 should be repeated for five times. The average speed at that
angle is
 t  

t
where ∆ (15) is the angle of sector mask and t is the duration when the light
was blocked (  t  t 2  t1 ). We should measure t2 for four different angles (same
angles as pt. 1), and then the angular speed at different time can be calculated.
3.
To measure the angular acceleration as a function of applied force.
8
The angular acceleration is found from angular speeds. Repeat pt.1 – 2 for four
different values of slotted weight.
9
C. Mathematical Pendulum
Objective
To determine the acceleration of free fall (g) by means of the mathematical pendulum.
Equipment
Tripod base
2
Support rod, 400mm
1
Support rod, 630mm
1
Right-angle clamp
2
Plate holder
1
Meter scale
1
Steel ball with eyelet
2
Fishing wire
1
Connecting cords
6
Rod, 130mm
1
Forked light barrier
1
Electronic counter
1
Caliper
1
Theory
The most direct method for finding the acceleration g of a free falling object is to
determine the time required for the object to fall a measured distance. From the time
and distance, the acceleration is easily computed. However, for any distance of fall
which is feasible to use in the laboratory, the time interval, if measured manually, is so
short that large probable errors are introduced.
A more precise value of g may be found by the method used in this experiment. Here g
is determined from the period of pendulum. It should be apparent that the time for one
cycle of a periodic motion may be accurately determined even though the period is
short, since a long time interval may be used by timing large number of cycles.
10
Figure 1. Motion of the pendulum
Consider an object of mass m which is mounted free to swing from a fixed axis in the
manner of a pendulum. When the object is swing through an angle  from its
equilibrium position a restoring torque  about the axis is established. This torque is
   mg l sin 
where l is the distance between the axis and the center of mass of the object. The minus
sign shows that the torque is in the opposite direction to the motion. If the object is
allowed to swing freely, the torque causes an angular acceleration
d2

mgl sin
 
2
l
l
dt
where l is the moment of inertia of the object about the axis.
If the angular displacement is small enough, we may approximate sin    (in radian)
and
T  2
l
g
After measuring the period T and the length l of the system, the acceleration of free
falling object can be calculated.
11
Set-Up
The set up is as in Figure 2.
Figure 2. Experimental set-up for determining the oscillation period of a mathematical pendulum
Procedure
In this experiment, it is important to obtain a precise value for the period T. You are
required to measure the period with two methods. (1) use timer manually; (2) use
electronic timer automatically. In both cases, it is important to avoid introducing large
errors.
1.
Adjust the length of the pendulum to a value between 90 – 100 cm.
2.
With the meter stick, determine the distance from the point of support to the bottom
of the bob.
3.
Measure the diameter of the bob with the vernier caliper. Calculate the length l.
4.
Start the pendulum swinging through an arc not exceeding 15 degree.
5.
Measure the period of swinging manually with timer.
i. Start the clock at the instant of a transit of the suspension, in a given direction.
Stop the clock at the end of 40 cycles of the motion. Repeat measurements for three
12
times and calculate the period of pendulum. Call this value "T1". Calculate
uncertainty in T1.
ii. Start the clock at the instant of a transit in a given direction, as above. About 5
minutes later, stop the clock when a cycle is completed. It is not necessary to count
the number of cycles. Since a whole number of cycles was timed. The result of
dividing this measured time interval (about 5 minutes) by T1 should be close to
actual number of cycles. If the result is not an integer but is within 0.3 of an integer,
it is reasonable to assume that the nearest integer represents the number of cycles.
Use this integer (correct number of cycles) and the measured time interval to
determine an improved value of the period, "T2". Calculate the uncertainty in T2.
Repeat this measurement for three times.
6.
Measure the period of the swinging automatically with electronic timer.
Connect the electronic timer with light barrier as Figure 3 and the lighter barrier is
placed as in Figure 2. The timer starts to count when the bob goes through the light
barrier first time and the timer stops counting when the bob goes through the light
barrier second time. Therefore, semi-period is to be recorded.
Record the semi-period in one direction for five times and the semi-period in
another direction for five times. Average them.
7. From the results of periods, calculate the acceleration of a free falling object for
different methods.
Figure 3. Connection of the counter
13
D. Thermal Expansion
Objective
To determine the linear expansion of copper and volume expansion of Glycerol.
Equipment
Barrel base
2
Support rod, square, 250 mm
2
Right angle clamp
2
Syringe, 1ml luer, 10 off
1
Cannula 0.660 mm
1
Measuring tube, 300 mm
2
Brass tube
1
Copper tube
1
Aluminium tube
1
Dilatometer with gauge
1
Thermostat, 65 C
1
Chemical thermometer
1
Glycerol, 250 ml
1
Distilled water, 3000 ml
1
Flask, flat bottom, 50 ml
2
Universal clamp
2
Rubber tubing, 7 mm
2
Pinchcock
2
Bath for thermostat, plastic
1
Balance
1
Theory
An increase in temperature T of solid always increases the vibrational amplitude of the
atoms in the crystal lattice of that solid. The average spacing between the atoms
increases, and therefore does the total volume V (at constant pressure).
14
Figure 1. Potential curve as a function of inter-atomic spacing r.

1  V 


V  T  p
is called the volume expansion coefficient. In case of one dimension, the coefficient of
linear expansion
l 
1  L 
 
L  T  p
where L is the total length of the body.
An increase in temperature of a liquid causes a greater thermal agitation of the
molecules in a liquid and therefore increases its volume.
Set-Up
The set-up for measurement of thermal expansion is shown in the Figure 2. Put the flat
flask in the distilled water and connect the dilatometer to the water circuit in the
thermostat. Two measurements: one for liquid and one for solid can be carried out at
once.
15
Figure 2. Experimental set-up for measuring thermal expansion
Procedure
1.
Measure the coefficients of the volume expansion of Glycerol and the linear
expansion of Copper at the same temperature run.
2.
In our set-up, the volume of flat flask is 70 ml when the liquid is at top level: zero
on the tube scale. The volume spanned by each 10 scales of the tube is 1.2 ml.
3.
Put the flat flask in the distilled water in the thermostat with a standard clamp.
4.
Connect the rubber tubing from the thermostat to the dilatometer. And keep the
rubber tubing as far away from the dilatometer as possible so that its body will not
be heated up.
5.
Tight the tube to be measured at one end by screwing up the screw on the top and
set the scale on the dial gauge to ‘0’ at the other end by turning the rim of the gauge.
6.
Measure the temperature of the distilled water in the thermostat. Then set a
temperature of the thermostat about ten degree higher than the measured one but
less than 65C.
7.
Wait for thermal equilibrium: the light on the thermostat will be on and off quite
often. And measure the volume increase of the liquid and the length increase of the
solid rod.
8.
Set the temperature ten more degree higher and do the measurements again.
16
E. The Vibration of Strings
Objective
To measure the frequency of vibration of a string as a function of tension and length of
the string.
Equipment
Barrel base
1
Bench clamp
3
Rod, 250mm
3
Right angle clamp
3
Sign holder
2
Rod with hook
1
Fishing line, 50cm
1
Meter scale
1
Spring balance
1
Striking hammer
1
Tension adjusting device
1
Distributor
2
Kanthal wire, 120cm
1
Connecting cord
2
Screened cable, BNC
3
Photocell
1
Slit diaphragm for photocell
1
Oscilloscope
1
LF amplifier
1
Counter/timer
1
Lamp holder
2
Lamp bulb
1
Connector, T-type
1
Adapter, socket-plug
1
Plug with push-on sleeve
1
17
Theory
When a piece of string between two fixed ends is vibrating with one loop, the frequency
given out is called fundamental note. This frequency is given by the formula
f 
1 F
2L 
(1)
where f = frequency
L = length of string
F = tension in the string
 = mass per unit length of the string
For a given length of string, L and  are constants. Thus, (1) can be written as
f  AF B
(2)
where A and B are constants.
Taking log on both sides of (2),
log f  B log F  log A
(3)
If the tension of the given string is held fixed, (1) becomes
f  CL D
(4)
where C and D are constants. We have
log f  D log L  log C
(5)
Set-Up
The experimental setup is shown in Fig.1.
The string is laid across two triangular slides and clamped between a fixed hook and a
spring balance, as shown in Fig.1. The spring balance is attached to string tensioner
with fishing line. The tension force should be no greater than 30 Newtons, otherwise
the string may break.
The string length can be set by moving the triangular sliders along the measuring scale.
If a piece of the string outside these sliders vibrates as well it can be stopped by gently
laying a finger on it (this must not, however, alter the string tension).
A gentle tap with the rubber hammer is sufficient to start the string vibrating. The
counter/timer is only started when the harmonics in the vibration have died away. This
can be done by observing waveform in the oscilloscope.
18
Figure 1. Experimental set-up for measuring the frequency of vibration of strings
Procedure
1.
Switch on the oscilloscope, LF amplifier and counter/timer and wait until a trace
appears in the oscilloscope.
2.
Set the LF amplifier gain to 102 and counter/timer knob to 101 KHz scale.
3.
Using the tensioner, set the tension in the string to about 10N.
4.
Make sure that the shadow of the string falls on the aperture slit of the photocell.
5.
Gently tap the string with the rubber hammer to produce vibrations.
6.
In order to obtain the fundamental frequency, counter/timer is started once the
harmonics in the vibrations have died away.
7.
Measure the frequency of vibration of string by varying tension at fixed length.
8.
Repeat the measurement of frequency by varying length of string at fixed tension.
19
F. Equation of State of Ideal Gases
Objective
To find the relationship between the state variables: pressure, temperature and volume
of an ideal gas.
Equipment
Gas laws apparatus
1
Plastic pot
1
Connecting tube, 150mm long
1
Rubber tubing, D = 7mm
2
Rubber tubing, D = 10mm
1
Pinchcock, width 15mm
1
Mercury tray
1
Mercury, pure, 1000g
1
Thermometer, -10C to 110C
1
Thermostat, 65C, 220V
1
Theory
For an ideal gas, the equation of state is
pV  nRT
where n is the number of moles of the gas and R is the universal gas constant.
The expansion coefficient , the pressure coefficient  and the compressibility  are
defined as follows,

1  V 


V0  T  p

1  p 
 
p 0  T  V

1
V0
 V 


 p  T
where the indices p, V, T mean the constancy of these variables and 0 means the
operating condition.
20
When the temperature of the gas has a small change T, we have
V  V0 1  T
p  p0 1 T
where V0 , p0 are original volume and pressure before the temperature changes.
Since
 V 
 V 
 dp
dV  
 dT  
 T  p
 p  T
so
 V 


 T  p 
 p 
 or p 0   
  


T



V
 V


 p  T
Set-Up
The experimental setup is shown in Figure 1. Distilled or deionized water is
recommended for the thermostat-controlled circulating liquid. The volume V of the
measuring tube is proportional to the length l read on the scale so that the physical
relationships involving l can be converted to V (cross area of the tube = 1.0210-4m2).
The pressure p of the enclosed air is composed of the external air pressure p0 and the
difference in height of the Mercury p:
p  p0  p
The external atmospheric pressure is measured with a barometer (in our experiment,
we assume that it is one atmosphere).
The rubber pin chained to the mercury reservoir is used for closing the reservoir when
the instrument is not in use for protecting against mercury vapor. However, when
measurements are being carried out the pin must be removed; otherwise another
“external” pressure is introduced.
21
Figure 1. Experimental set-up for studying the variables of state of a gas.
Procedure
1.
p-V measurement at room temperature.
Measure the temperature of the water in the thermostat. Don’t switch on the
thermostat. Take the rubber cock off the Mercury tube on the right and record the
pressures of the air inside the tube on the left and its corresponding volumes. Then,
move the tube on the right to other position and record the p and corresponding V
again. Totally, four sets data of p and V should be obtained. In our experiment, the
cross section area of the tube A is 1.0210-4m2.
2.
p-T and V-T measurements.
Turn on the thermostat to set different temperatures of the water. Wait for about 10
minutes so that the signal light is on and off quite often that means the water in the
thermostat and the air in the tube are almost in thermal equilibrium. At each set
temperature, measure the volume of the air while keep the pressure of the air at
22
particular value (decided yourself) and measure the pressure of the air while keep
the volume of the air at particular value (decided yourself). In order to keep the
constant pressure or constant volume, you should adjust the height of the Mercury
tube on the right.
23
G. Maxwellian Velocity Distribution
Objective
To measure the velocity distribution of model gas by spheres.
Equipment
Tripod base
2
Mat
1
Stop watch
1
Rheostat, 500 ohms
1
Kinetic gas theory apparatus
1
Receiver with recording chamber
1
Stroboscope
1
Test tubes, 16016mm
9
Test tube rack
1
Theory
Maxwell speed distribution law:
3
 M  2 2 M 2 2 RT
P   4
  e
 2RT 
where  is the molecular speed, T is the gas temperature, M is the molecular weight of
the gas, and R is the gas constant. P() is a distribution function, defined as follows:
The product P()d (which is a dimensionless quantity) is the fraction of molecules
whose speeds lie in the range  to +d. The integration of P()d over zero to infinity
is the probability of finding a particle whose speed is within the range from zero to
infinity. It should be unity (one). If we introduce the total velocity element d above 
is
3
M
N  M  2  2 RT  2 2
dN   4
 d
 e
V  2RT 
24
Set-Up
The set up of the experiment is as shown in Figure 2. The receiver with recording
chamber with two orifices is fitted to the chamber orifice to act as a filter as shown
Figure 1.
The particle density should be kept constant during the experiment. A preliminary run
should be carried out in order to determine the average number of spheres ejected per
minute.
The motor speed of 1300 rpm should be checked with the stroboscope and readjusted
if necessary. The speed of the motor is adjusted by means of a variable transformer. At
the beginning, the movable knob in the transformer should be set in the position so that
the output voltage of the transformer is zero. Otherwise there will be a chance of
damaging the motor!
In order to measure the speed of the motor, a light from the stroboscope is shined to a
vibrating plate in the apparatus. The vibrating frequency of the plate is the speed of the
motor. Adjust the knob on the stroboscope while look at the vibrating plate. When the
plate becomes stationary image under the shining light, the frequency readout is the
speed of the motor.
Figure 1. Filter chamber for direction selection.
25
Figure 2. Experimental set-up for measuring the velocity distribution of a model gas.
Procedure
1.
Put spheres into the apparatus. Increase the output voltage of the transformer
connected to the apparatus while shinning a light of the stroboscope to the vibrating
plate. Set the frequency of the stroboscope at about 1300 round per minute (rpm).
Stop increasing the output voltage once the image of the vibrating plate is
stationary.
2.
Run a preliminary test to find the number of spheres ejected per minute. After
obtain this number, put back this number of spheres into the mouth on the apparatus
and start the experiment. Make sure that the density of the balls is kept to be
constant during the experiment, so spheres should be put into the apparatus each
minute.
3.
Stop the experiment when one of the individual sectors is almost full. And count
the number of spheres in the individual sectors or measure the height of each sector.
4.
Plot the measured velocity distribution of sphere.
26
Guidelines for Physics Laboratory
THE FOLLOWING GUIDELINES WILL BE EXECUTED STRICTLY.
IN CLASS:
1.
Be on time.
If you late more than 15 minutes, you are not allowed to do the experiment. It means that you
cannot submit report for that experiment. If you are late less than 15 minutes, I will let you have
the experiment. But, some marks will be deducted.
If you are absent, you will miss the chance to have the experiment and cannot re-do. But, you may
ask for leave with reason, for example, a non-Yr2 student need to join a test at the same time. In this
case, you should inform me before; otherwise, you still are considered as absence and miss the
experiment.
In case of you are sick; you can inform me later because it cannot be expected. However, it will be good
habit if you call your group mate to let me know or send a message to me.
2.
Before start experiment.
I will ask you questions group by group before you can start experiment. The purpose is to let me know
whether you have prepared for the experiment. If I find you have not prepared, I will not let you start
until you can answer the questions. Please don’t touch any instrument before you are permitted.
As mentioned, I need to come to you group by group and so you may need to wait for me. I will let the
students, who do the time-consuming experiment, to start first. Please be patience.
3.
During experiment.
Please don’t hesitate to ask me questions for any problem during class. Please keep clean in the lab.
room.
4.
After finish experiment.
After finish experiment, please let me know. I will check whether you properly switch off the
instruments. Moreover, you need to give me a copy of your data sheet. The purpose is to let me have a
record. Moreover, you need to finish your experiment in class. You have to stop if time is over; even
you have not completed all measurements.
REPORT:
1.
Student should submit individual report for each experiment. You MUST give me your report
when I come to you for asking questions at the beginning of class. Late report will NOT be
accepted. Moreover, the lab. report has to be done by computer and well bound. If I find you copy
report from classmates, you will get zero mark.
2.
A lab. report should include the items are, i) Objective; ii) Procedure; iii) Data; iv) Analysis; v)
Conclusion.
a. Although “Objective” and “Procedure” can be found in the lab. manual, you still need to put
into your report for completeness. And, you can also make some necessary changes.
b. For the part of “Data”, it is usually arranged in the format of table.
c. Calculations and graphs should be put in “Analysis”. Moreover, discussion can be included in
this part.
d. Finally, you should conclude your experiment in “Conclusion” at the end of report.
27
Template of Table and Graph:
Trial 1
Trail 2
Trial 3
X (unit)
Y (unit)
Z (unit)
Table no. Table caption (for example, measurement of X, Y and Z)
Trial 4
Trial 5
12
y = 2.07x - 0.03
Y-axis label (unit)
10
2
R = 0.9968
8
6
4
2
0
0
1
2
3
4
5
6
X-axis label (unit)
Figure no. Figure caption (for example, Y vs. X)
Remarks:
1.
Proper table and figure captions should be decided yourself.
2.
Unit of data should be indicated clearly in table and figure.
3.
In the figure template, fitting line is put to trend the data points. The type of fitting curve depends
on the relation of variable X and Y. Here is just an example. And, equation of fitting curve and R2
value should be shown.
28