THE PHYSICS 11
LAB BOOK
Book 1: Labs 1 – 19
by
S. L. Morris
J. C. Fu
R. F. Whiting
Los Angeles Harbor College
© 2004
TABLE OF CONTENTS
MECHANICS AND PROPERTIES OF MATTER
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
11.
12.
13.
14.
15.
Measurement ............................................................................................................ 1
Vector Addition .......................................................................................................... 8
Topographic Mapping ................................................................................................ 13
Scientific Method – Simple Pendulum ....................................................................... 15
Acceleration Due to Gravity – Free Fall ..................................................................... 18
Simple Machines – Pulleys ........................................................................................ 21
Simple Machines – Lever, Wheel & Axle, Inclined Plane .......................................... 25
Newton's Second Law of Motion ............................................................................... 29
The Coefficient of Friction ......................................................................................... 33
Centripetal Force – Thistle Tube Method .................................................................. 36
Hooke's Law and Simple Harmonic Motion ............................................................... 40
The Ballistic Pendulum .............................................................................................. 43
Moments and Center of Mass ................................................................................... 47
Archimedes' Principle ................................................................................................ 53
Boyle's Law – Elasticity of Gases ............................................................................... 56
HEAT
16.
17.
18.
19.
Heat of Fusion of Ice ................................................................................................. 59
Heat of Vaporization of Water ................................................................................... 62
Specific Heat of Metals .............................................................................................. 65
The Coefficient of Linear Expansion ......................................................................... 70
Experiment 1
MEASUREMENT
INTRODUCTION
This experiment will involve making various measurements of mass, length, and
time using simple laboratory measuring equipment. The system of units we will be using is
called the metric system or the Systeme International, hereafter referred to as "SI".
The SI unit of length is the meter. We will be using the meter stick, the vernier
caliper, the micrometer, the tape measure and the wire gauge to measure this quantity.
The Meter Stick: The physical size of an object is a fundamental property, and the height,
width and depth of an object is measured by its length along each dimension. Examine the
meter stick in front of you. The meter stick is slightly longer than a yardstick, and is divided
into 100 centimeters. Each centimeter is further divided into 10 millimeters, so there are
1000 millimeters in a meter. The millimeter can be abbreviated as mm, and the centimeter
can be abbreviated as cm. Every measurement of length must be followed by its unit.
Whenever a meter stick or metric ruler is used, the result should be expressed to
the nearest millimeter. For example, the length of one-third of a meter stick can be
expressed as 333 millimeters, 33.3 centimeters or 0.333 meters. The left-hand edge of a
meter stick is supposed to be at 0.000 meters, but its edge may be damaged or worn. The
correct way to get an accurate measurement is to place the object being measured near
the center of the ruler, read the position of the left edge of the object, read the position of
the right edge of the object, and subtract one number from the other. For example, if the
left edge is at 321 mm and the right edge is at 674 mm, the length of the object is 674 321 = 353 mm.
The Vernier Caliper – This device can measure to an accuracy of one-tenth of a millimeter,
and all measurements obtained with this device should be quoted to this degree of
accuracy. To use this device, the length to be measured is placed in the jaws of the caliper,
and the jaws are then closed by pushing on the wheel to the right of the movable window.
The measurement is found by reading the ruler visible inside the window of the movable
jaw.
This reading is a two-step process:
First, look just below the window of the movable jaw. You should see eleven vernier
lines, and for this step you use only the leftmost of these eleven vernier lines. That leftmost
line points in between two ruler lines directly above it, seen inside the window. Write down
the value of the ruler line on the left. The measurement will begin with this value.
Second, which of the eleven vernier lines has a ruler line directly above it? These
vernier lines are numbered 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 and 10. This number is placed after
the value found in the first step. The vernier number 10 is never used.
For example, suppose the vernier caliper has been set as shown:
-1-
window
2
1
ruler
vernier
Performing the first step, the leftmost vernier line (thick arrow) points between the
ruler lines 1.1 cm and 1.2 cm. The ruler line on the left is 1.1 cm, so you would write down
the value ‘1.1 cm’. Performing the second step, the vernier line 3 (thin arrow) has a line
directly above it, and so a 3 is placed after the previous value. The answer is 1.13 cm.
As a second example, suppose the vernier caliper has been set as shown:
3
4
Performing the first step, the leftmost vernier line points between the ruler lines 2.5
cm and 2.6 cm. The ruler line on the left is 2.5 cm, so you would write down 2.5 cm.
Performing the second step, the vernier line 8 has a line directly above it, and so an 8 is
placed after the previous value. The answer is 2.58 cm.
The Micrometer - This device can measure to an accuracy of one-hundredth of a
millimeter, and all measurements obtained with this device should be quoted to this degree
of accuracy. To use this device, the length to be measured is placed in the jaws of the
micrometer, and the barrel is rotated until the jaws have closed. Warning! A large amount
of force should not be applied when rotating the barrel, as this will strip the screw inside the
barrel and ruin the micrometer. Close the jaws so that they are ‘finger-tight’. That means
that when your fingers rotate the barrel with only light pressure applied, your fingers slide
along the barrel and it does not rotate any more. Some of the micrometers have a small
friction barrel on the right-hand side of the barrel, which will prevent the barrel from rotating
when too much force is used. If your micrometer has a friction barrel, use it to close the
jaws.
This reading is a two-step process:
-2-
First, look at the ruler between the jaws and the barrel. The left edge of the barrel
cuts across the ruler, which is measured in millimeters, and shows millimeter lines (on top)
and half-millimeter lines (on bottom). Write down the value of the ruler line that is visible to
the left of the edge of the barrel.
Second, which of the barrel lines is closest to the horizontal line on the ruler? The
two-digit number of that barrel line (from .00 mm to .49 mm) is added to the value found in
the first step. If this is confusing, open the jaws slightly until the barrel value is .00 mm,
and the measurement is obvious. Then, slowly close the jaws until the barrel has returned
to its former position. The correct value will be slightly smaller than the value obtained
when the jaws were slightly open.
For example, suppose the micrometer has been set as shown:
0
5
30
barrel
horizontal line
25
ruler
Performing the first step, the ruler line 7.00 is the line that is visible to the left of the
barrel, so you would write down the value ‘7.00 mm’. Performing the second step, 26 is the
barrel line closest to the horizontal line, and so 0.26 mm is added to the previous value.
7.00 + 0.26 = 7.26, so the answer is 7.26 mm.
As a second example, suppose the micrometer has been set as shown:
0
5
40
Performing the first step, the ruler line 6.50 is the line that is visible to the left of the
barrel, so you would write down the value ‘6.50 mm’. Performing the second step, 40 is the
barrel line closest to the horizontal line, and so 0.40 mm is added to the previous value.
6.50 + 0.40 = 6.90, so the answer is 6.90 mm. Notice that the answer contains a ‘0’ in the
last place, to signify that the length has been measured to this level of accuracy.
-3-
EQUIPMENT & MATERIALS
Wire and nail samples
Vernier caliper
Micrometer
Stop clock
Meter stick
Rock specimen
Tape measure
Wooden block
Wooden sphere
Glass marble
Balance
Metronome
Wire gauge
EXPERIMENTAL PROCEDURE
A. LENGTH
1. METER STICK:
Measure the dimensions of the top of your student table to an
accuracy of the nearest millimeter. Enter all measurements in
the laboratory report at the end of this experiment.
Area = length X width.
2. VERNIER CALIPER: Measure the sides of a wooden block, to an accuracy of a tenth
of a millimeter. Measure the diameter of a wooden sphere.
3. MICROMETER:
Measure the diameter of a glass marble, to an accuracy of a
hundredth of a millimeter.
4. TAPE MEASURE:
Measure the length and width of the classroom floor in feet and
inches, using the 50 ft. tape measure. Convert to decimal feet
(3 ft. 4 in.  3.33 ft., for example). Then convert your
measurements into the SI system of units; 1 foot = 0.3048
meters. Calculate the area of the floor (length times width) in ft 2
and m2. Notice that in the Imperial (English) system you have
to convert to decimal feet before multiplying. In the metric
system, calculations are easier.
5. WIRE GAUGE:
Find the diameter of a small wire or nail by sliding it along the
rim of the gauge (measured in inches). Multiply this by 25.4 to
convert to millimeters, and check the result using the
micrometer.
B. MASS
1. BALANCE:
The SI unit of mass is the kilogram. In our lab, the balance is
used to measure this quantity. Slide the two scale weights to
their zero positions on the left-hand side, then calibrate by
rotating the weight on the screw until the needle at the top of
the scale is zeroed. The balance works by placing the mass to
be measured on the left-hand pan, then sliding the two scale
weights to the right until the needle is zeroed again. The mass
of the object is the sum of the two scale weights, to an accuracy
of one-tenth of a gram.
Determine the mass of three items on the balance such as a
block, a sphere and a rock.
-4-
C. TIME
1. METRONOME:
The SI unit of time is the second. The stop clock we use owes
its accuracy to the precise 60 Hz line voltage oscillations that
the power company provides. Set the metronome at a reading
of 120 by placing the top of the sliding weight just below ‘120’
on the metronome face. Use the stop clock to measure the
amount of time the metronome takes to count out 100 beats, to
a tenth of a second accuracy. Divide by 100 to get a measured
time for 1 beat, to a thousandth of a second accuracy. The
nominal time for 1 beat is determined from the ‘named’ value
given as 120 beats per minute. This is the given value used in
determining the percent difference. The percent difference is
given by:
% difference =
measured value - given value
given value
X 100%
The given value in a calculation of percent difference may be a
value that has been determined by very precise experiments, or
it may be a value expected from theoretical considerations.
2. PULSE:
Time 20 beats of your pulse, to a tenth of a second accuracy.
Repeat this four times to give a total of 5 measurements.
Calculate the average value of your pulse rate by adding up
your five measurements, then dividing that number by 5.
The deviation of each measurement is the measurement minus
the average. Some of those deviations will be positive numbers
and some will be negative. When you square each deviation,
the result must be either zero or a positive number.
Calculate the standard deviation. This is the typical scatter of a
single measurement around the average.
-5-
LABORATORY REPORT: MEASUREMENT
(Be sure to record the units for each measurement.)
METER STICK
VERNIER CALIPER
Table Top
Wooden Block
Length
Length
Width
Width
Area
Height
Volume
MICROMETER
VERNIER CALIPER
Glass Marble
Wooden Sphere
Trial No.
Diameter
Trial
1
1
2
2
Average
Average
TAPE MEASURE
Classroom Floor
Length
(in feet and inches)
Length
(in decimal feet)
Width
(in feet and inches)
Width
(in decimal feet)
Length
(in meters)
Area
(in square feet)
Width
(in meters)
Area
(in square meters)
-6-
Diameter
WIRE GAUGE AND MICROMETER
Wire Gauge
Micrometer
Range
Diameter
Trial No.
Smaller than:
1
Larger than:
2
Average
Average
BALANCE
Diameter
METRONOME
Object
Mass
Measured time for 100 beats
Block
Measured time for 1 beat
Sphere
Nominal time for 1 beat
Rock
Percent difference
PULSE
Trial No.
Time for 20 beats
(s)
Deviation from average, di
(s)
Deviation from average
Squared, (di)2
(s2)
i=1
i=2
i=3
i=4
i=5
Average
 = Standard Deviation =
(d1)2  (d2 )2  (d3 )2  (d4 )2  (d5 )2
= ____________________
5 1
-7-
Experiment 2
VECTOR ADDITION
INTRODUCTION
A vector is defined as a mathematical representation of a quantity that possesses
both magnitude and direction. A scalar quantity has only magnitude. In this experiment we
will add a number of forces using a force table and then compare the sum with that
obtained by vector addition.
EQUIPMENT & MATERIALS
3 clamp-on pulleys 
Circular (bubble) level
1 sheet of blank paper
3 Mass hangers, 50 g
Slotted masses
Force table
Ruler
Protractor
EXPERIMENTAL PROCEDURE
1. Place the circular level on top of the force table, and adjust the feet until the force table
top is horizontal. Arrange three pulleys with strings on the force table as shown in
Figure 1. Two of these will be forces A and B and the third, or equilibrant, will be
force C. The magnitude of the equilibrant will be chosen to balance the forces A and B,
creating a total force of zero.
y
B
C
x
A
Fig. 1. Force Table, Top View
2. Use masses (slotted masses plus the mass of each hanger) of 200 grams each to
create the forces A and B. Place A and B with a small angle of about 40o between
them (that is, at +20o and –20o), and balance them with a suitable amount of mass at C.
Record the magnitudes and angles for A, B, and C in the laboratory report. The system
is balanced when the central pin may be pulled up and the ring released without
changing its centered position.
3. Repeat step 2, this time with a larger angle of 60o between them.
4. Repeat step 2 again, using an angle of 90o between them.
-8-
5. Repeat step 2 again, using an angle of 140o between them.
6. Draw a labeled free-body diagram to scale on the sheets at the end of this lab for each
of the cases in steps 2 - 5. Let 200 grams on the force table be represented by 5.0 cm,
so the magnitude of each force can be converted to a length; multiply the number of
grams by 0.025 to get the length in centimeters. Using the parallelogram method, add
the vectors A and B on the same sheet to find their resultant vector. Draw the
equilibrant (Force C) along the negative x-axis. Compare the resultant so obtained with
the magnitude and direction of the equilibrant. Are the equilibrant and the resultant
exactly opposite and equal to each other?
Shown in Figure 2 is an example of how parallelogram addition works:
We wish to add vectors A and B. We move them so that their tails touch. (Note that
one can move a vector so long as the direction is not changed.) Make a parallelogram
out of A and B so joined. The diagonal of the parallelogram is called the resultant.
+
A
B
Equilibrant

Resultant
A
B
B
A
C
Fig. 2 Parallelogram Method of Vector Addition
7. Place 3 unequal forces at unequal angles in equilibrium on the force table. Draw to
scale a force polygon on a blank sheet of paper, by placing the tail of arrow B on the
head of arrow A and the tail of arrow C on the head of arrow B, as shown in Figure
3. Show the amount by which the polygon does not close by a labeled arrow.
Measure its value and indicate this as the resultant error.
resultant
error
Fig. 3 Typical Force Polygon
-9-
LABORATORY REPORT: VECTOR ADDITION
Data Table for Step 2:
Force
Magnitude
(grams)*
A
200
B
200
Angle
C
Data Table for Steps 3 - 5:
Step
Force
Magnitude
(grams)
Angle
A
3
B
C
A
4
B
C
A
5
B
C
* It is understood that a kilogram is not a unit of force, but a unit of mass. To get the
downward gravitational force by the earth one should multiply each mass by 9.80 m/s 2.
But since the force is proportional to the mass, it is suggested that you record the mass
instead of the weight.
- 10 -
Step 2:
y
x
Step 3:
y
x
Step 4:
y
- 11 -
x
Step 5:
y
x
- 12 -
Experiment 3
TOPOGRAPHIC MAPPING
INTRODUCTION
In this experiment the instructor will give you an overview of how to read topographic
maps, which are maps that describe the physical features of part of the Earth’s surface.
EQUIPMENT & MATERIALS
Topographic map 
360o protractor

Ruler 
String & scissors
LABORATORY REPORT
Place the answers to the following questions on the back of the map.
1. Name the highest mountain and give its elevation.
2. Which town has the highest elevation?
3. Which mountain has the steepest slope?
4. What is the latitude and longitude (to the nearest tenth of a minute of arc):
(a) of the center of Norton?
(b) of the summit of Bald Peak?
(c) of the summit of White Mountain?
(d) of the mine? (Draw the mine’s line of latitude and line of longitude on the map.)
5. How far is Blue Lake from Norton?
6. Is Dixon or Rockville closer to Norton?
7. How long is the railroad tunnel (use the edge of a sheet of paper to transfer the
scale)?
8. How far is Rockville from Norton by highway? Place a length of string along the
highway, then straighten it and compare it to the scale.
9. How much farther is this than the straight-line distance (the U.S. average is l5 percent
longer)?
- 13 -
10. How long would it take to walk from Rockville to Norton?
11. What direction would you travel from Dixon to Rockville? Directions are measured
from true north (0o) through east (90o).
12. Is the trip from Dixon to Rockville uphill or downhill?
13. What is the true direction from White Mt. to Bald Peak?
14. What is the magnetic direction from Summit Mt. to Bald Peak?
15. Starting at the peak of White Mt., you fly horizontally 125 o true for 3 minutes at
120 mph, turn and fly 270o true for 4 minutes and then turn to 180o true for 1 minute
while rising 500 ft. Draw these horizontal motions on your map. What is your final
latitude, longitude and height above sea level?
- 14 -
Experiment 4
SCIENTIFIC METHOD
Simple Pendulum
INTRODUCTION
This experiment will use the scientific method to determine what factors enter into
the value of the period of a pendulum. The period of a pendulum is the time for one
complete swing to and fro, and is given theoretically by the following relation:
L
g
T  2
where T is the period, L is the length, g is the acceleration due to gravity = 9.80 m/s 2 and
 = 3.14159…
The factors to be investigated as possibly affecting or not affecting the period will
include: length of string, mass of the bob, size of the bob, composition of the bob, and
amplitude of the swing.
As much as possible in this experiment, each factor will be varied by itself; that is,
the other factors will be kept constant while the effect of the one under consideration is
studied. Keep the amplitudes of the swings just large enough so that the pendulum will
complete the 25 swings. Avoid amplitudes larger than 10 o from the vertical.
EQUIPMENT & MATERIALS
Support rod 
String, scissors
Balance
Table clamp 
Stop clock
Metal spheres
Metal cubes 
Protractor
Wooden spheres
Pendulum clamp
Meter stick
EXPERIMENTAL PROCEDURE
A. Effect of Length
1. Attach a string to a heavy metal sphere and suspend it from the pendulum support.
Start with a long length (75.0 cm measured from the edge of the support to the center
of the ball) and measure the time taken for 25 complete swings. Use a stop clock to
measure the time. The period will be the total time divided by 25.
2. Repeat step 1 three times, each time shortening the string from the previous time
(lengths of 50.0, 40.0 and 30.0 cm will be convenient). Does the length of the string
have any effect on the period?
B. Effect of Mass of Bob
- 15 -
1. Replace the bob with a wooden sphere of about the same size as the metal sphere,
but of less mass.
Again count the time for 25 swings.
In all cases, be sure that
L = 75.0 cm, measured from the edge of the support to the center of the sphere,
accurate to the nearest millimeter! Now that you have changed the mass of the
pendulum bob significantly, is the period the same or different from that for the steel
sphere?
C. Effect of Shape
1. Use the same length as in Part B, and replace the bob with a large metal cube. Time
25 swings. Does the shape make any difference?
D. Effect of Size
1. Use the same length as in Part B, and replace the bob with a small metal sphere of
about the same mass as the wooden sphere in Part B. Time 25 swings as before.
Any difference?
E. Effect of Amplitude
1. It is no longer necessary to keep the amplitude of the swings small. Use the original
metal sphere and the same length as in Part B, and time 25 swings with amplitudes of
30o and 45o from the vertical. Can you observe any change?
F. Theoretical and Experimental Determination of the Period
1. The time for a pendulum to swing from the left extreme to the right and back to the left
again is called the period, T. Determine experimentally the length of a pendulum
which will have a period of exactly 2.0 seconds for small amplitude oscillations, to the
nearest millimeter.
2. Calculate the theoretical length of a pendulum having a period of 2.0 seconds from
the formula, by squaring both sides to get T 2 = 42L/g, and solving for L to get
L = T2g/42. Compare this with the value you obtained in the previous step by
computing the percent difference.
% difference =
measured value - given value
given value
- 16 -
X 100%
LABORATORY REPORT: SCIENTIFIC METHOD: PENDULUM
Data Table 1: Effect of Length
Pendulum
Length
(m)
Time for
25 Cycles
(s)
Data Table 2: Effect of Mass
Period
(s)
Trial No.
0.750
1
0.500
2
0.400
3
0.300
Average
Time for
25 Cycles
(s)
Period
(s)
Comments:
Data Table 3: Effect of Shape
Trial No.
Time for
25 Cycles
(s)
Data Table 4: Effect of Size
Period
(s)
Trial No.
1
1
2
2
3
3
Average
Average
Time for
25 Cycles
(s)
Period
(s)
Comments:
Data Table 5: Effect of Amplitude
Trial No.
Amplitude
1
Time for
25 Cycles
(s)
Period
(s)
Trial No.
Amplitude
30o
1
45o
2
30o
2
45o
3
30o
3
45o
Average
30o
Average
45o
Time for
25 Cycles
(s)
Comments:
Data for Part F:
Experimental length for T = 2.0 seconds _________________________
Theoretical length for T = 2.0 seconds ___________________________
Percent difference __________________________________________
- 17 -
Period
(s)
Experiment 5
ACCELERATION DUE TO GRAVITY
Free Fall
INTRODUCTION
When objects relatively close to the Earth's surface are allowed to fall freely, they
undergo uniformly-accelerated motion. In today's experiment, we will measure the
acceleration due to gravity which has the value of:
9.80
meters .
second2
The unit of meters per second squared means that the velocity is increasing by 9.80 m/s
each second.
A free fall apparatus will be used to make a paper strip record of the distance the
object falls as a function of time. This apparatus consists of a plastic and metal object that
falls freely between two vertical conducting wires with a tape strip of wax paper between
the object and one of the wires. The spark timer which is used with this apparatus is a fast
timing device which supplies a high voltage pulse at constant time intervals (for example,
1/60 s). The free fall apparatus has an electromagnet which holds the object until the timer
is activated.
The voltage supplied by the timer is great enough to jump between the conducting
wires only when the metal object is between them. When this occurs during fall, a series of
holes is burned in the wax paper. The holes on the tape are equal time intervals apart and
give the vertical distance of fall as a function of time.
In our analysis of the paper tape we will make use of the following kinematic
equation:
v average  v 
change in dis tance
change in time

Δd
Δt
or, in other words, the distance traveled in an interval divided by the time gives the average
velocity for that interval. However, since we are interested in instantaneous velocities at
certain instants of time, we can make use of the fact that the instantaneous velocity is
equal to the average velocity at the midpoint in time of the interval. So when successive
instantaneous velocities are plotted as a function of time, we should obtain a straight-line
graph, the slope of which is equal to the acceleration of gravity.
- 18 -
EQUIPMENT & MATERIALS
Free fall apparatus 
Spark timer, 1/60 sec.
Ruler
Meter stick
Masking tape Clear plastic triangle
Free fall tape
1 sheet of graph paper
EXPERIMENTAL PROCEDURE
1. The paper record tape will already be made for you, or your instructor will assist you in
making one. Use a piece of masking tape to secure your paper strip to the table.
Starting with the first well-defined hole, draw a straight line through it perpendicular to
the length of the tape. Do this for every other hole and number them 0, 1, 2, 3,
4, 5 etc., as shown in the diagram below.
0
1
2
3
4
5 etc.
2. Place the edge of the meter stick a few millimeters to the left of the zero hole, then
measure and record the position of each numbered hole. Putting the meter stick on
edge with the gradations in contact with the paper will help to avoid parallax errors.
Tape the meter stick to the table. Make your readings to the nearest millimeter and
record them in the data table.
3. Subtract each reading from the one immediately following it. This difference gives the
distance traveled during successive 1/30-second time intervals. Divide these
distances by the time interval (1/30 s) to obtain the average velocity for the interval
and record this in the data table. These averages are the instantaneous velocities at
the midpoint in time of the interval which is at the hole between the numbered holes.
4. Plot a graph with time on the horizontal axis and average velocity on the vertical axis.
Remember that each value of average velocity should be plotted so as to correspond
to the value of time at the middle of the interval for which the velocity was calculated.
Draw a single best straight line through the points (this means the same number of
points on both sides of the line and the total distance of the points to the line being the
same on both sides of the line). The slope of the graph obtained should be equal to
the acceleration of gravity. The y-intercept will give the velocity at the zero hole.
Record your value of acceleration in the laboratory report and calculate the percent
difference.
5. Remove masking tape from the table and the meter stick before leaving.
- 19 -
LABORATORY REPORT: ACCELERATION DUE TO GRAVITY
Data and Calculations Table:
Interval #
Position of Hole
On Left
(m)
Distance Traveled
In One Interval
(m)
Time at which
vaverage = v(t)
(s)
0–1
1/60
1–2
3/60
2–3
5/60
3–4
7/60
4–5
9/60
5–6
11/60
6–7
13/60
7–8
15/60
8–9
17/60
9 – 10
19/60
10 – 11
Value of Acceleration From Graph ___________________ m/s2
Percent difference ___________________
- 20 -
Average Velocity
In Interval
(m/s)
Experiment 6
SIMPLE MACHINES
Pulleys
INTRODUCTION
In this lab we will study a simple machine called the pulley. By making actual
measurements of input force, output force and appropriate distances, the ideal mechanical
advantage (IMA), the actual mechanical advantage (AMA), and the efficiency can be
determined for each case tested. All the simple machines that we will study are governed
by the physical law called the conservation of energy, that is, the energy put into the
system equals the energy you get out. For our system this can be expressed by the
following equation:
INPUT FORCE X DISPLACEMENT of INPUT = OUTPUT FORCE X DISPLACEMENT of OUTPUT
+ FRICTIONAL LOSS & ROTATIONAL LOSS
Some other definitions that you will need are:
IMA =
DISPLACEME NT OF INPUT FORCE
DISPLACEME NT OF OUTPUT FORCE
AMA =
OUTPUT FORCE
INPUT FORCE
EFFICIENCY =
AMA
IMA
X 100%
EQUIPMENT & MATERIALS
2 Single pulleys
2 Double tandem pulleys
2 Triple tandem pulleys
250 & 500-g spring balance
Pendulum clamp
String, scissors
Meter stick
Table clamp
- 21 -

Support rod
Hooked mass set
Ruler
Electronic balance
EXPERIMENTAL PROCEDURE
1. Calibrate your spring balance by holding it vertically without any mass attached, and
sliding the scale face until it reads zero. All measurements must be taken with the
spring balance held in this position, not sideways or upside-down.
2. Arrange the pulleys as indicated in the diagrams. Do one set-up at a time.
3. The ‘Output Force’ is the force that the pulley system lifts up, and is equal to the ‘Mass
of Brass Cylinder’ added to the ‘Mass of Movable Pulley’, if a pulley is being moved up
and down. Enter the masses in the table.
4. The ‘Input Force’ is the force that is exerted by you onto the pulley system, and is equal
to the ‘Spring Balance Reading’ added to the ‘Mass of Spring Balance’, if the spring
balance is adding its weight to the force you are exerting. Determine the ‘Spring
Balance Reading’ while the brass cylinder is moving slowly upwards at constant speed.
Be sure to make your loads progressively larger as you go from type I to type IV, in
order to obtain a large (and accurate) reading from the spring balance.
5. The ‘Displacement of Input Force’ is the distance the scale travels, measured against a
meter stick, and the ‘Displacement of Output Force’ is the distance the brass cylinder
travels upward. Measure both at the same time, to the nearest millimeter. It is
convenient if the ‘Displacement of Input Force’ is somewhere between 0.400 and 0.600
meters.
6. Compute the ideal and actual mechanical advantages, and the efficiency for each of
the eight cases.
Pulley Diagrams
I a. Single, Fixed
I b. Single, Movable
Input Force
Input Force
Output
Force
Output
Force
- 22 -
II a. Singles, Movable
II b. Singles, Movable
Input Force
Input Force
Output
Force
Output
Force
III a. Double Tandem, Movable
III b. Double Tandem, Movable
Input Force
Input Force
Output
Force
Output
Force
IV a. Triple Tandem, Movable
IV b. Triple Tandem, Movable
Input Force
Input Force
Output
Force
Output
Force
- 23 -
LABORATORY REPORT: SIMPLE MACHINES, PULLEYS
Data Table:
Pulley Type
Mass of
Movable
Pulley (grams)
Mass of Brass
Cylinder
(grams)
Output Force
(g-grams)*
Spring Balance
Reading
(grams)
Mass of Spring
Balance
(grams)
Ia
Ib
IIa
IIb
IIIa
IIIb
IVa
IVb
0.00
0.00
0.00
0.00
0.00
Input Force
(g-grams)*
Displacement of
Input Force
(cm)
Displacement of
Output Force
(cm)
AMA
IMA
Efficiency
* The proper unit here is the dyne, but since the acceleration due to gravity cancels out
in the calculation of the AMA, it is suggested that the acceleration due to gravity be left as
the letter unit g; as in g-grams.
- 24 -
Experiment 7
SIMPLE MACHINES
Lever, Wheel & Axle, Inclined Plane
INTRODUCTION
In this experiment we will study three types of simple machines; the lever, the
inclined plane, and the wheel and axle. By making actual measurements of output force,
input force and appropriate distances, the ideal mechanical advantage IMA, the actual
mechanical advantage AMA, and the efficiency of each case will be determined. Refer to
Experiment 6 for the definitions of these terms. Measure all distances to the nearest
millimeter.
EQUIPMENT & MATERIALS

 Table clamp
String & scissors
Meter stick
Knife-edge clamps
 Support rod
250-g spring balance
 Inclined plane Hooked mass set 
Knife-edge stand 
Hall's carriage
Double pan balance Clamp for wheel
Mass hanger, 50 g 
Transfer caliper
Slotted mass set
Wheel and axle
EXPERIMENTAL PROCEDURE
A. LEVER
Use a meter stick, knife-edge clamp and support stand to create a lever and fulcrum. Use
hooked masses for the output force (the load, designated by L) and a small spring balance
for the input force. For all three arrangements, place the fulcrum near the 50.0-cm mark so
the meter stick alone balances. With the fulcrum at this point, the weight of the meter stick
does not contribute to the readings. Be sure to zero the spring balance first.
1. Arrange the equipment as a first class lever. The
load can be suspended from a small loop of string.
Record the load, input force, and distances of each from
the fulcrum. For the first class lever only, the mass of
the spring balance must be added to the spring balance
reading to give the total input force. Choose an input
force lever arm (the distance from input force to fulcrum)
that is different from the load lever arm (distance from
load to fulcrum).
F
L
F
L
2. Arrange as a second class lever. Determine the input
force for a load of 500 grams using a spring balance.
3. Arrange as a third class lever. Determine the input
force for a load of 100 grams using a spring balance.
F
L
4. For all cases, calculate the actual and ideal mechanical advantage and the efficiency.
- 25 -
The AMA is the load divided by the input force. The IMA is the input force lever arm
divided by the load lever arm.
B. WHEEL AND AXLE
1. Set up the wheel and axle supported by the table clamp and support rod. Thread a
length of string through the back of the wheel and axle apparatus, into the hole closest to
the center. Tie a knot at the back end so the string cannot fall through the front, and tie a
loop at the front end to support the mass holder. Repeat for the hole on the outermost rim,
with a loop for another mass holder at the end. Arrange first as in case A, shown below,
with the load attached to the innermost string, wound around its circle.
2. The wheel radius is the distance from the center of rotation to the point where the input
force is applied. The axle radius is the distance from the center of rotation to the point
where the load is applied. Measure these by using the transfer caliper to find the
diameters accurately, then divide by 2. Use 550 grams for the load. Use other slotted
masses for the force and add them to the holder until the force is just enough to cause the
load to rise with a steady velocity, once the system is given a slight push.
3. Case B: Move the load to the middle position and repeat step 2.
4. Case C: Move the load to the outermost position and repeat step 2.
5. Calculate the AMA (load/input force), IMA (wheel radius/axle radius), and efficiency for
each case.
Force
Load
Case A
Force
Force
Load
Case B
Load
Case C
C. INCLINED PLANE
1. Use the Hall's carriage with the inclined plane set at 30 o. Determine the mass of the
carriage. The input force F is provided by the mass hanger and the slotted masses. The
displacement of the input force equals the distance the cart moves along the hypotenuse.
2. Place the cart at the bottom of the plane.
Add just enough mass to the hanger so that
the hanger descends at constant velocity.
The vertical distance is the distance any
point on the cart has moved vertically from
the beginning to the end of the trip.
Calculate the AMA, IMA and efficiency.
L
3. Make another trial as in step 2, using 400 grams in the cart.
- 26 -
F
LABORATORY REPORT: SIMPLE MACHINE – LEVER, Wheel & Axle, Inclined Plane
Data for Part A: Levers
Lever Type
Load
First Class
Second Class
Third Class
(g-grams)*
Input Force
(g-grams)
Input Force Lever Arm
(cm)
Load Lever Arm
(cm)
AMA
IMA
Efficiency
* For convenience, leave the acceleration due to gravity in symbol form, as in g-grams.
Data for Part B: Wheel and Axle
Case A
Load
(g-grams)
Input Force
(g-grams)
Wheel Radius
(cm)
Axle Radius
(cm)
Case B
AMA
IMA
Efficiency
- 27 -
Case C
Data for Part C: Inclined Plane
Trial
Angle of Incline
Mass Added to Cart
(g-grams)
Total Load, Cart + Mass
(g-grams)
Input Force
(g-grams)
Distance Cart Moves Along Hypotenuse
(cm)
Vertical Distance Cart Moves
(cm)
AMA
IMA
Efficiency
- 28 -
1
2
30o
30o
0
400
Experiment 8
NEWTON'S SECOND LAW OF MOTION
INTRODUCTION
This experiment will verify that acceleration is directly
proportional to force if mass is kept constant, and is inversely
proportional to mass if force is kept constant. In other
words, F = ma where F is the net force, m is the mass being
accelerated and a is the acceleration. The pulley system
shown to the right, with unequal masses on each side will be
used. Historically, this arrangement has been called the
Atwood's machine.
v
m2
v
m1 + mf
EQUIPMENT & MATERIALS
2 sets of slotted masses
2 one-kg mass hangers
Wheel & axle clamp
Wheel & axle Thick string
Two-meter stick
Scissors
Support rod
Ruler
Stop clock
Table clamp
Foam pad
EXPERIMENTAL PROCEDURE
A. PRELIMINARY
Set up the wheel and axle at the top of the support rod clamped to your table, and loop
a piece of string approximately 1.9 meters long over the largest wheel, with a mass
hanger at each end. Choose one side to be the descending side, and place a foam
pad beneath it for the mass hanger to land on. To determine the correction for friction,
add small masses to the descending side until that side, once started with a small push,
descends with constant velocity. Be sure to determine this as accurately as possible, to
the nearest gram. This is the friction allowance m f ; leave this amount on the side of the
pulley that is descending at all times, for both parts B and C. Write down the mass of
the friction allowance mf, and the mass of the pulley mp (printed on the pulley), on the
data page.
Warning! Never crouch beneath the pulley; you could be injured if the string snaps. If a
mass falls onto the floor, kick it away from the pulley before picking it up.
B. DRIVING FORCE KEPT CONSTANT
1. Add 20 grams to the descending side, so m 1 = 1.020 kg and m2 = 1.000 kg. Measure
to the nearest millimeter the distance that the descending mass will fall (~1 meter), with
the string over the largest wheel of the pulley.
2. Time the fall of the descending side, to the nearest tenth of a second. Calculate the
- 29 -
average velocity, final velocity and experimental acceleration from:
vaverage =
Dis tance of fall
Time of fall
(Eq. 1)
vfinal = 2vaverage
(Eq. 2)
v f inal
Time of fall
(Eq. 3)
aexperimental =
3. Theoretically, F = ma, where F is the (small) amount of force creating the acceleration,
and m is the (large) amount of mass being accelerated. The force is the weight of the
excess mass (m1 – m2) on the descending side, and the magnitude of this force is
F = (m1 – m2)g, where g = 9.80 m/s/s. Calculate the force F.
4. The mass being accelerated is m1, m2, mf and the pulley as it rotates. Most of the
mass of the pulley is not along the rim, and does not experience the full amount of
acceleration. The pulley needs only one-third the force to accelerate its rim in rotational
motion, as it would need to accelerate by moving in a straight line. To take this into
account, only one-third of the pulley’s mass mp needs to be used in the calculation of
mass. Calculate m = m1 + m2 + mf + (1/3)mp to determine the effective mass being
accelerated.
5 F = ma can be rewritten as a = F/m. Calculate atheoretical from the values of F and m in
the data table. Find the percent difference between the theoretical and experimental
values of the acceleration.
6. Add 100 grams to each pulley, and repeat steps 2 – 5. Notice that the force (m1 – m2)g
remains constant, but the total mass that is being accelerated increases.
7. Repeat step 6 twice, to test F = ma for different amounts of mass.
C. MASS KEPT CONSTANT
1. Remove the added 100-gram masses, so the descending side has 1000 grams plus mf
plus the 20 grams that accelerate the system, and the ascending side has 1000 grams.
Add four 5-gram masses to the ascending side, so the descending side descends with
constant velocity.
2. Move two of the 5-gram masses from the ascending side to the descending side, so
m1 = 1.030 kg and m2 = 1.010 kg. Repeat steps 2 – 5 of part A.
4. Move another 5-gram mass from the ascending side to the descending side, and repeat
steps 2 – 5 of part A. Notice that the force that creates the acceleration is increasing,
but the total mass that is being accelerated remains constant. Repeat this one more
time, moving the last 5-gram mass from the ascending side to the descending side.
- 30 -
LABORATORY REPORT: NEWTON'S SECOND LAW
Data for Parts A and B: Driving force kept constant.
Friction allowance = mf = _____________ kg
Trial No.
1
m1
(kg)
m2
(kg)
Distance of Fall
(m)
Time of Fall
(s)
vaverage
(m/s)
aexperimental
(m/s2)
F = (m1 - m2)g
m = m1 + m2 + mf + (1/3) mp
atheoretical
2
(m/s)
vfinal
Pulley Mass = mp = _____________ kg
(N)
(kg)
(m/s2)
Percent difference
- 31 -
3
4
Data for Part C: Total mass kept constant.
Trial No.
1
m1
(kg)
m2
(kg)
Distance of Fall
(m)
Time of Fall
(s)
vaverage
(m/s)
vfinal
(m/s)
aexperimental
(m/s2)
F = (m1 - m2)g
m = m1 + m2 + mf + (1/3) mp
atheoretical
(N)
(kg)
(m/s2)
Percent difference
- 32 -
2
3
Experiment 9
THE COEFFICIENT OF FRICTION
INTRODUCTION
In this experiment, the force laws governing sliding friction between dry surfaces will
be investigated. We will use wood-on-wood surfaces. The force of kinetic friction f k is
parallel to the two surfaces in relative motion, and follows the relation
fk = kN
where N is the normal force (the force of contact perpendicular to the two surfaces) and k
is the coefficient of kinetic friction.
The forces acting between surfaces at rest with respect to each other are called
forces of static friction and follow the relation:
fs  sN
where s is called the coefficient of static friction.
The above two relations will be verified by measuring the frictional forces associated
with increasing values of normal force. A plot of frictional force vs. normal force should
yield a straight line, the slope of which is equal to the coefficient of kinetic friction.
EQUIPMENT & MATERIALS
Ruler
Right-angle clamp 
Support rod, short 
Spirit level
Clamp-on pulley
Plastic triangle
Friction board
Electronic balance
Small rod for friction board 
Mass hanger, 50 g

Slotted masses

1 sheet of graph paper
- 33 -
Friction block
String, scissors
Table clamp
Inclinometer
Meter stick
EXPERIMENTAL PROCEDURE
1. Place the board flat on the table. If the carpenter’s level shows that the board is not
horizontal, the board can be leveled by placing strips of paper towel beneath it. Attach
the clamp-on pulley to the end of the board and let the pulley extend over the end of the
table.
2. Use the electronic balance to determine the mass of the block, and attach the string to
the block. Lay the string over the pulley and attach the mass holder to the lower end of
the string.
3. Place just enough mass on the mass holder so that the block moves at a constant
speed, after it is given a slight push to get it started. The mass needed to move the
block is the mass on the mass holder plus the mass of the mass holder itself. You
should be able to determine this to the nearest gram.
4. Place some mass (~100 grams) on top of the block to increase the normal force, and
repeat step 3. As before, the block must not gain speed, but nevertheless continue
moving at a constant speed. The total weight on the board is the total mass on the
board (the mass of the block plus the mass added to the block) times the local
acceleration of gravity. That is, W = mg, with g = 9.80 m/s/s and m in kilograms
(1 kilogram = 1000 grams).
5. Repeat step 4 three more times, each time with a different mass on top of the block in
order to show the effect of changing the normal force.
6. Plot the force of friction (which equals the weight needed to move the block) on the
vertical axis vs. the normal force (which equals the total weight on the board) on the
horizontal axis. Label both axes, and give the graph a title that described what was
occurring to generate the data.
7. From the graph, determine the coefficient of kinetic friction as the slope of the straight
line that passes as close as possible to all the data points.
8. Remove the string and weights from the block and the pulley from the board. Place
the board at an angle to the horizontal by inserting the small rod through the long hole
drilled through the side of the board, and supporting this rod on the vertical support rod
clamped to your table. To determine the critical angle of friction, slightly loosen the
clamp holding the board to the vertical support and smoothly increase the tilt of the
board until the block slides down the board of its own accord, without giving it a slight
push to get it started. Tighten the clamp at this position and measure the angle from
the horizontal with the inclinometer. Repeat this step two more times and determine
the average angle. The tangent of the angle is the coefficient of static friction.
- 34 -
LABORATORY REPORT: COEFFICIENT OF FRICTION
Trial
Block Only
Mass Added on
Top of Block (kg)
0
Total Mass
on Board
(kg)
Total Weight
on Board
(N)
Block + Mass 1
Block + Mass 2
Block + Mass 3
Mass Needed to
Move Block (kg)
Weight Needed to
Move Block
(N)
Coefficient of kinetic friction from graph: k = _______________
Data for Coefficient of Static Friction:
Trial 1 ____________ degrees
Trial 2 ____________ degrees
Trial 3 ____________ degrees
Average ____________ degrees
Coefficient of Static Friction = s = _________________
- 35 -
Block + Mass 4
Experiment 10
CENTRIPETAL FORCE
Thistle Tube Method
INTRODUCTION
In this experiment we will study the motion of an object traveling on a circular path,
in order to verify the equation for centripetal force. A small object of known mass, m, will
be forced to move in uniform circular motion. The centripetal force will be determined
directly and then calculated from measurements of the radius and the speed. The
following relation will be verified:
2
Fc = mv
(Eq. 1)
r
where m is the mass of the revolving object, v is the speed of the revolving object, and r is
the radius of the orbit of the revolving object .
EQUIPMENT & MATERIALS
Thistle tube

50-g & 100-g hooked masses
Stop clock
String & scissors
Rubber stopper, No. 5
Red marker pen
Balance
Meter stick
EXPERIMENTAL PROCEDURE
r
1. Measure the mass m of the
stopper. Tie it securely to a
string that is about 2 meters
long, and thread the other end
of the string through the top of
the thistle tube. Tie this loose
end to the 0.050-kg hooked
mass, which will function as the
hanging mass M. It is the weight
Mg of this mass that creates the
force of tension in the string,
which then functions as the
centripetal force.
Revolving mass, m
Thistle Tube
Mark
Hanging mass, M
(Actual Centripetal Force = Mg)
2. While the string is held taut, adjust the position of the thistle tube so that the distance
- 36 -
from the center of the revolving mass to the center of the wider opening of the thistle
tube is r = 0.500 meters, as shown in the diagram on the previous page. Be sure to
measure this to the nearest millimeter. Use a red marker pen to place a mark on the
string at the base of the thistle tube.
3. One student can now swing the revolving mass in a horizontal circle above the
student’s head. Maintain a steady swing, keeping the mark as close to the bottom
edge of the thistle tube as possible. Hold onto the thistle tube, but not the string,
while the mass is revolving.
4. Another student, using the stop clock, can measure the total time for 25 revolutions
for a radial distance of r = 0.500 meters. The time for one revolution is the total time
divided by 25.
5. The speed is given by the formula:
v=
circumfere nce
= 2r
t
time for one revolution
where r is the radius of revolution and t is the time for one revolution.
6. Repeat the experiment for r = 0.750 m and r = 1.000 m.
7. Repeat the experiment with M = 0.100 kg and the same lengths as above.
LABORATORY REPORT: CENTRIPETAL FORCE
- 37 -
Data & Calculations Table 1:
Trial
1
Mass of Stopper, m
(kg)
Radius
(m)
Time for 25 Revolutions
(s)
Time for 1 Revolution
(s)
Speed
(m/s)
A. Centripetal Force from Eq.1
Hanging Mass, M
B. Centripetal Force from Fc = Mg*
(N)
(kg)
(N)
Percent difference between
centripetal forces A and B, above
*Use g = 9.80 m/s2
Data & Calculations Table 2:
- 38 -
2
3
Trial
1
Mass of Stopper, m
(kg)
Radius
(m)
Time for 25 Revolutions
(s)
Time for 1 Revolution
(s)
Speed
(m/s)
A. Centripetal Force from Eq.1
Hanging Mass, M
B. Centripetal Force from Fc = Mg*
(N)
(kg)
(N)
Percent difference between
centripetal forces A and B, above
*Use g = 9.80 m/s2
- 39 -
2
3
Experiment 11
HOOKE’S LAW AND
SIMPLE HARMONIC MOTION
INTRODUCTION
The purpose of this experiment is to show that, to a good approximation, a spring’s
behavior can be described by Hooke's law:
Force = - kx.
In this equation, ‘Force’ is the restoring force that the spring exerts upwards, trying to
restore the spring to its original position, and x is the displacement of the lower end of the
spring downwards from its original position. The factor k is the spring stiffness constant,
which is often called Hooke’s constant or the spring constant. Since the force that we will
supply is in the same direction as the displacement, we can rewrite the equation as:
F = kx
where F = mg is the downward force applied to the spring, due to the weight of the mass m
attached to the bottom of the spring. A graph of applied force vs. displacement which
yields a straight line will verify that the spring obeys Hooke's law.
A spring oscillates with simple harmonic motion (motion that is sinusoidal with
respect to time) if an attached mass is given a displacement and then released. The
relationship between the period of oscillation and Hooke's constant is given by:
T2 = 42M/k, or
T = 2 M 
k
where T is the period of oscillation (time for one complete cycle) and M is the oscillating
mass. A graph of the square of the period vs. the oscillating mass M which yields a
straight line, will verify that the spring oscillates with simple harmonic motion.
EQUIPMENT & MATERIAL
Large brass spring
Pendulum clamp
Electronic balance
2 sheets of graph paper
Clear plastic straightedge
Table clamp
Hooked mass set
EXPERIMENTAL PROCEDURE
- 40 -
Support rod
Meter stick
Stop clock
1. Attach a pendulum clamp to the support rod and hang the spring. Attach small
increments of mass (50 grams or so) and measure the displacement of the bottom of
the spring from its original position. Take the spring to no more than about three times
its original length. If the spring is stretched longer than this, you might exceed the
elastic limit of the spring and permanently alter its shape. The applied force is the
weight of the attached mass, mg, where g = 9.80 m/s 2.
2. Make a plot of applied force (on the vertical axis) vs. displacement (on the horizontal
axis). Find the spring constant from the slope of the straight line on the graph that
passes as closely as possible through the data points.
3. Re-attach one of the masses used before, then pull it down several centimeters and
release. Keep the motion of the spring only in the vertical direction by pulling straight
down. Measure the time for 25 complete oscillations. One oscillation occurs as the
mass moves from its lowest point to its highest point and back to its lowest point again.
Compute the observed period of oscillation, from the time for 25 cycles.
4. Repeat step 3 for three other masses.
5. The attached mass is not the only mass that is oscillating. The bottom of the spring is
fully oscillating as well, with the rest of the spring oscillating to a lesser extent. To take
this into account, the equation for the square of the period uses the oscillating mass,
which equals the attached mass plus one-third the mass of the spring:
M = oscillating mass = attached mass + 1/3 (mass of spring)
Calculate the theoretical period, from your values of M and k.
6. Plot the square of the observed period vs. the oscillating mass. Explain any deviation
from a straight line.
LABORATORY REPORT: HOOKE'S LAW
- 41 -
Data Table 1: Hooke's Law Data
Trial
Attached Mass
(kg)
Applied Force
(N)
Displacement
(m)
1
2
3
4
5
6
7
Spring stiffness constant from graph: k = _________________ N/m
Data Table 2: Simple Harmonic Motion Data
Mass of spring = _________________ kg
Trial
Attached
Mass
(kg)
Oscillating
Mass
(kg)
Time for 25
Cycles
(s)
1
2
3
4
Experiment 12
- 42 -
Observed
Period
(s)
Theoretical
Period
(s)
THE BALLISTIC PENDULUM
INTRODUCTION
In this experiment, the speed of a projectile will be measured in two different ways;
through the use of conservation laws, and through the equations of projectile motion.
The Laws of Conservation of Momentum and Conservation of Energy
A ball of mass m is fired at an unknown speed v, and collides with a pendulum of
mass M. After the collision, the pendulum swings in an arc and comes to rest at a vertical
height h above the starting position.
Momentum is mass times velocity. According to the law of conservation of
momentum, the total momentum of the ball and (motionless) pendulum before the collision
must equal the momentum of the ball and pendulum immediately after the collision:
mv + M0 = mV + MV.
(Eq. 1)
Solving for v gives
v=
mM
V .
m
(Eq. 2)
So, the initial velocity v of the ball can be determined if the velocity V of the ball and
pendulum immediately after the collision can be determined.
The law of conservation of energy states that the kinetic energy of the ball and
pendulum immediately after the collision must equal the gravitational potential energy of
the ball and pendulum when they have risen to the top to the arc:
½(m + M)V2 = (m + M)gh.
(Eq. 3)
This can be solved to get
V=
2gh ,
(Eq. 4)
and this value of V can be substituted into Eq. 2 to get the initial velocity v of the ball.
The Equations of Projectile Motion
A ball of mass m is fired horizontally at an unknown speed v, and lands on the floor
- 43 -
a time t later, having fallen through a vertical distance y and a horizontal distance x. The
equation of projectile motion y = ½gt2 can be solved for the time of flight:
2y
g
t=
.
(Eq. 5)
The equation of projectile motion x = vt can then be solved for the initial velocity of the ball:
v= x.
(Eq. 6)
t
EQUIPMENT & MATERIALS
Ballistic pendulum 
Plumb bob

Masking tape
Plain and carbon paper

One-meter stick
Ruler

Two-meter stick
2 pieces of cardboard
Spirit level
4-inch “C” clamp
Electronic balance
EXPERIMENTAL PROCEDURE
A. Initial Velocity from Conservation Equations:
1. Use the spirit level to level the apparatus. Determine the mass m of the ball; the mass
M of the pendulum is indicated on the pendulum.
2. Place the ball on the end of the gun rod. Compress the spring by pushing on the ball
until the gun is cocked. The pendulum should hang freely and motionless.
3. Pull the trigger, firing the ball into the pendulum and onto the rack. Warning! Do not
fire the gun if anyone is in front of it. Repeat 6 times, each time recording the notch on
the rack in which the pawl rests. The pawl is the little catch that stops the pendulum at
its maximum height.
4. Take the average of these six positions and place the pawl at this position. The center
of mass of the pendulum is indicated by the tip of the pointed projection on the side of
the pendulum. Determine the height h of the center of mass above the initial freelyhanging position, to the nearest millimeter.
5. Calculate the velocities V and v.
6. As a check, calculate the initial momentum and final momentum; according to the law of
conservation of momentum, they should be approximately equal. Calculate the initial
kinetic energy and the final gravitational potential energy; they should be approximately
equal as well. If m is in kilograms and v is in meters/second, the unit of momentum is
kgm/s and the unit of energy is Joules.
B. Initial Velocity from Projectile Motion Equations:
1. Level the ballistic pendulum apparatus and clamp it lightly to the table.
- 44 -
2. Hold the pendulum out of the way by placing it on the top of the rack, so the ball misses
it completely. Place a large piece of cardboard against the wall, so that after striking
the floor the ball will hit the cardboard, not the wall.
3. Place another large piece of cardboard on the floor in the approximate location of
impact (about two meters away) and tape it securely to the floor. You may need to
rearrange the tables to create enough room. Do a single test firing to locate the area of
impact and tape a piece of plain and carbon paper at this location in order to record the
exact point of impact.
4. Perform six firings and take the average of the locations as the point of impact.
Measure the vertical distance y and horizontal distance x the ball has traveled to this
average location, to the nearest millimeter.
5. Calculate the time of flight t, and the initial velocity v.
6. Determine the percent difference between the initial velocity obtained in these two
different ways.
LABORATORY REPORT: THE BALLISTIC PENDULUM
Data Table 1:
- 45 -
Mass of Ball: m = ______________
Mass of Pendulum: M = ______________
Six pawl positions: _______________
_______________
_______________
_______________
_______________
_______________
Average pawl position: _______________
h = _______________
V = _______________
v = _______________
Momentum before collision: mv = ________________
Momentum after collision: mV + MV = ________________
Kinetic energy after collision: ½(m + M)V2 = ________________
Potential energy at average pawl position: (m + M)gh = _______________
Data Table 2:
y = _______________
x = _______________
t = _______________
v = _______________
Percent difference = ________________
Experiment 13
- 46 -
MOMENTS AND CENTER OF MASS
INTRODUCTION
For a body to be in static equilibrium, the vector sum of the forces F acting on it
must be zero and in addition, the algebraic sum of the clockwise and counterclockwise
torques  must be zero. These conditions can be stated mathematically as follows:





F = 0
 = 0
The first condition is concerned with translational equilibrium and the second
condition is concerned with rotational equilibrium. The first condition ensures that the body
is not moving (static case) or else is moving with constant velocity. The second condition
ensures that there are no unbalanced torques acting on the body (static case), or else the
body is rotating with constant angular velocity. The magnitude of the torque is equal to the
product of the lever arm and the component of force perpendicular to the lever arm.
The principle of moments (torques) will be used in this experiment to find the center
of mass of two non-homogeneous bars. One is a meter stick modified by weighting one
end, and the other is a bar which can be placed at a random angle.
Also, we will use the principle of moments to find analytically the forces of
compression and tension in a model crane boom. This result will be compared with
experimental measurements.
EQUIPMENT & MATERIALS

Knife-edge clamp
Knife-edge support stand
3 right-angle rod clamps Spring balance, 500 grams
Weighted meter stick
Non-concurrent forces apparatus
Hooked mass set
Long support rod 


Double pan balance Short support rod
Protractor
Heavy meter stick with hole at end
String
Scissors
2 table clamps
3 rod pulleys
EXPERIMENTAL PROCEDURE
A. Center of Mass of a Weighted Meter Stick
1. Determine the mass of the special meter stick which has a metal bar of unknown mass
attached to one end. Consider this weighted meter stick as a single object for the
purpose of finding its center of mass.
2. Attach a knife-edge clamp to the midpoint of the special meter stick, set it on the knifeedge support stand, and hang three different standard masses from small loops of
string positioned at random locations along the stick as shown in Figure 1. Adjust the
positions of the masses until the system is balanced. Measure all distances from the
fulcrum, with d as a negative number if the position is to the left of the fulcrum, and as a
- 47 -
positive number if the position is to the right of the fulcrum.
Fulcrum at Midpoint
m1
m2
m3
Fig. 1
3. Solve the torque equation for dstick, the distance of the stick’s center of mass from the
fulcrum. Show your calculations. Use this number to find the position of the center of
mass as a reading on the ruler.
4. Repeat for three other masses at different positions. The two values so obtained for
the center of mass should be within a few millimeters of each other. As a further check,
remove all extra masses and slide the stick through the clamp until it balances on the
knife-edge support, to locate the center of mass directly.
B. Center of Mass of Bar Located at Random Angle
1. Determine the mass of the bar.
2. Using three rod pulleys and right angle clamps, suspend the bar, with masses attached,
at an angle between the supports, as shown in Figure 2. Measure all angles from the
protractors attached to the bar. The angle  for the bar is read from the protractor
hanging freely downward. The distance d is measured from the lower end of the bar, to
the point where the force is applied on the bar by the string.
m2
Rod Pulley
m1
Bar with Protractors
Vertical Support
m3
Fig. 2
3. Find the location of the center of mass by solving the torque equation for d bar. As a
check, balance the bar on the edge of a meter stick to find the center of mass.
- 48 -
C. Model Crane Boom
1. Measure the mass of the meter stick with a hole at one end, then balance it on the edge
of another stick to determine the location of the center of mass, d stick.
2. Set up the apparatus as shown in Fig. 3 using the hooks and ledge of the chalkboard,
and the meter stick with a hole at the upper end and its zero point at the lower end.
Three small loops of string at the upper end can be used to attach m 1 and the spring
balances.
3. To find the compression on the meter stick, pull on spring balance #2 oriented parallel
to the meter stick until the meter stick is just ready to pull away horizontally from the
chalk ledge. The length d1 is also measured from the zero point of the ruler to the point
where the forces are applied to the stick. Record d 1, ,  and the readings of both
spring balances.
4. Calculate the tension T1, the theoretical reading of spring balance #1, from the torque
equation. When the meter stick just starts to pull away horizontally from the chalk
ledge, there is no horizontal force on the bottom of the meter stick. Use the force
equation and your theoretical reading of T 1 to calculate T2. Compare with the
experimental values by computing the percent difference.
Fig. 3
LABORATORY REPORT: MOMENTS AND CENTER OF MASS
Data For Part A:
- 49 -
Data Table 1: Center of Mass of Weighted Meter Stick
Mass of weighted meter stick: mstick ________________ kg
Trial
Mass 1
(kg)
Distance 1
(m)
Mass 2
(kg)
Distance 2
(m)
Mass 3
(kg)
1
2
Torque equation: d1m1 + d2m2 + d3m3 + dstickmstick = 0.
Trial 1:
dstick ________________ m
Position of center of mass ________________ m
Trial 2:
dstick ________________ m
Position of center of mass ________________ m
Center of mass from balancing on knife-edge ________________ m
Calculations:
Data For Part B:
- 50 -
Distance 3
(m)
Data Table 2:
Object
Angle 
(degrees)
Mass
(kg)
Sin 

2
3
Bar
Torque equation: d1m1sin1 + d2m2sin2  d3m3sin3  dbarmbarsinbar = 0
dbar ________________ m
dbar from balancing on a meter stick ________________ m
Calculations:
Data For Part C:
Data Table 3: Model Crane Boom
- 51 -
d
(meters)
mstick
(grams)
dstick
(meters)
m1
(grams)
d1
(meters)
Angle 
(degrees)
Angle 
(degrees)
Reading of Spring Balance #1
(grams)
Reading of Spring Balance #2
(grams)
Theoretical Reading
of Spring Balance #1
(grams)
Theoretical Reading
of Spring Balance #2
(grams)
% difference for
Spring Balance #1
% difference for
Spring Balance #2
Torque equation: mstickdsticksin + m1d1sin – T1d1sin = 0
Force equation: T2sin – T1sin( + ) = 0
Calculations:
Experiment 14
- 52 -
ARCHIMEDES' PRINCIPLE
INTRODUCTION
Archimedes' principle states that an object, partially or totally immersed in a fluid, is
buoyed up by a force which is equal to the weight of the fluid which is displaced by the
object. This experiment will make use of the principle of Archimedes in two ways: first, to
verify that the principle is valid by determining densities of various solids with known
densities; second, to use the principle to determine densities of various "unknown" solids
and liquids.
EQUIPMENT & MATERIALS
Balance
Support rod, short
Hydrometer

Scissors
Beaker, 600 ml
Vernier caliper
Rock specimen
Lab jack
Unknown fluid
Table clamp
Wooden sphere
Cylinders (Fe, Al, Cu)
Waterproof string
Graduated cylinder, 250 ml
Paper clip
EXPERIMENTAL PROCEDURE
Part A: Density of a Regularly-Shaped Object:
1. Place the balance on top of the support rod, clamped to your table. Turn the balance
so the left side of the balance is over the table. Unbend a paper clip, and attach it to
the bottom of the vertical shaft of the left balance pan, underneath the base. Set the
balance to read zero, and rotate the calibration mass until the needle is zeroed.
2. Tie an aluminum cylinder with waterproof string to the paper clip. Determine the mass
of the cylinder. Immerse the cylinder into a beaker of tap water and observe the
apparent mass on the balance. All measurements of mass should be to the nearest
tenth of a gram.
3. The density of water is 1.000 g/cm 3. Compute the density of the cylinder using
Archimedes' principle, which is given by the following equation:

object = fluid 
mass of object in air
.
mass of object in air – apparent mass of object in fluid
Compare your measured value with the accepted value by computing the percent
difference. As an alternate check, compute the density directly using the mass of the
object and the volume calculated from the dimensions of the object. In this case, the
volume of a solid cylinder of diameter d and length l is d2l/4, and the density is given
- 53 -
by the following equation:




object =
mass of object .
volume of object
4. Repeat steps 2 and 3 for the other two cylinders.
Part B: Density of an Object that Floats in Water:
1. Determine the mass M of an object such as a wooden sphere that can float on water.
Use one of the cylinders as a sinker. Tie the sinker to the wooden sphere.
2. Observe the apparent mass, M with the wooden sphere out of the water and the
sinker in the water (be certain the sinker isn't touching the bottom). Then observe the
apparent mass, M with both submerged and suspended. From these data, compute
the density using the following equation:
 object = fluid  apparent
mass of wood
.
mass, sinker in water, wood out – apparent mass, sinker and wood in water
That is,
 object = fluid 
M
M  M
Part C: Density of an Irregularly-shaped Object:
1. Find the density of a rock using Archimedes' principle, as performed in Part A.
Part D: Density of a Fluid:
1. Observe the apparent mass of the aluminum cylinder in the unknown fluid poured into
the beaker. Use this value, the mass of the aluminum cylinder in air and the accepted
value of its density to calculate the density of the unknown fluid fluid from
Archimedes’ Principle (the equation in step 3 of Part A).
2. Pour the unknown fluid from the beaker into the cylinder. Use a hydrometer to find
the density of the unknown fluid directly, making sure that the hydrometer does not
touch bottom. Read the scale that starts at 1.000. When finished, remove the paper
clip from the bottom of the scale, return the unknown fluid to its container, and
thoroughly wash and dry all glassware.
LABORATORY REPORT: ARCHIMEDES' PRINCIPLE
Data & Calculations Table for Part A:
- 54 -
Cylinder
Mass in air
(g)
Apparent mass in
water
(g)
Density by
Archimedes’ Principle
(g/cm 3)
Accepted value of
density
(g/cm 3)
Aluminum
Copper
Steel
2.7
8.9
7.8
% difference
Diameter
(cm)
Length
(cm)
Density = mass
volume
(g/cm3)
Data for Part B:
M = _________________ ,
M = _________________ , M = __________________
Density of wooden sphere __________________
Data for Part C:
Mass of rock in air __________________
Apparent mass of rock in water __________________
Density of rock __________________
Data for Part D:
Mass of cylinder in air __________________
Apparent mass of cylinder in the fluid __________________
Density of fluid __________________
Density from hydrometer__________________
Experiment 15
BOYLE'S LAW
- 55 -
Elasticity of Gases
INTRODUCTION
The purpose of this experiment is to observe the relationship between the pressure
and the volume of a gas (air), when the amount of gas and the temperature of the gas are
kept constant. The relationship between these two quantities is known as Boyle's law:
PV = c ,
where P is the total pressure in Newtons per meter squared, V is the volume in meters
cubed; and c is a constant for a particular quantity of gas at a fixed temperature.
Furthermore, the gas constant, R, can be calculated using the ideal gas law:
PV = nRT,
where n is the number of moles and R is the gas constant in Joules / moleKelvin.
The method that will be used to verify Boyle's law is to directly vary the pressure on
a column of gas enclosed by a cylinder and piston, and then read the resulting volume.
EQUIPMENT & MATERIALS
Boyle's law apparatus
Clear plastic triangle
1 sheet of graph paper
Thermometer, 0–100oC
0.5, 1 and 2-kg masses
Buret clamp
Ring stand
EXPERIMENTAL PROCEDURE
1. Set up the apparatus as shown
in Figure 1, using the buret
clamp and ring stand to hold the
cylinder securely. Tighten the
clamp enough to hold the
cylinder in position, without
squeezing it. Be careful at all
times to keep the masses from
falling on your feet.
Fig. 1.
2. Push the wooden block onto the piston and wet the piston with water in order to
lubricate it. Place a string in the cylinder and insert the piston. Set the piston at the
35.0-cm3 mark and pull the string out; this will be your initial volume of gas at
atmospheric pressure. The total pressure in the Boyle’s law equation is the applied
pressure plus the atmospheric pressure. Use the value of 101,000 N/m 2 for the
- 56 -
atmospheric pressure.
3. Start adding masses in 0.5-kg increments from 0.5 kg to 3.5 kg, reading the volume to
the nearest tenth of a cm3 after each addition. To assure that the piston is not bound by
friction, twist it gently and lift it slightly above the rest position each time. Then release
and read the scale where the piston comes to rest. Repeat but twist and compress the
piston slightly below the rest position, then release and read the scale. The average of
the two readings is the volume.
4. Pressure is defined as force per unit area, and the cross-sectional area of the cylinder
is 0.000452 m2.
Mass (in kg)  9.80 (in m / s 2 )
Force
Applied pressure =
=
Area
0.000452 (in m 2 )
P = Total pressure = Applied pressure + 101,000 N/m 2
5. Calculate c = PV for each set of P-V values and enter these in your data table.
Calculate an average value of c and enter this in your data table.
6. Plot total pressure P in Newtons/meter2 on the vertical axis vs. the reciprocal of the
volume 1/V in meters-3 on the horizontal axis of a sheet of graph paper, and draw the
best straight line through the points. A straight-line graph will demonstrate the validity
of Boyle's law. Choose the scale of each axis carefully, so the data spreads out over
most of the graph. Each axis should be labeled by the quantity it represents, with its
units in brackets. The graph should be given a label that describes the physical
arrangement that generated the data.
7. In the ideal gas law PV = nRT, “n” is the number of moles of gas, indicating how much
gas is present (n times 6.02 X 1023 is the number of particles of gas). In a warm room,
gas expands and the number of moles in 35.0 cm 3 decreases. Measure the room
temperature in oC. The ideal gas law uses temperature measured in Kelvin degrees,
which is the Celsius temperature plus 273.15. Calculate T.
8. The number of moles in a 35.0-cm3 cylinder at one atmosphere of pressure is
n = 0.42640 . Calculate the number of moles of air used in your experiment.
T
9. You can now use the ideal gas law to calculate a value for the gas constant, from
R = c/nT, where c is your average value of the constant c. Calculate your value of R
and compute its percent difference from the given value of 8.315 J/molK accepted by
the scientific community.
LABORATORY REPORT: BOYLE'S LAW
Data and Calculations Table:
- 57 -
Applied
mass
(kg)
Applied
Pressure
(N/m2)
Total
Pressure
(N/m2)
Volume
Constant c
(m3)
(Nm)
1
Volume
(m-3)
0.000
0.00
1.01 X 105
3.50 X 10-5
0.500
1.000
1.500
2.000
2.500
3.000
3.500
Average value of the constant c = ____________ Nm
Room temperature = ____________ oC
T = room temperature + 273.15 K = ____________ K
n = ____________ moles
R = ____________ J/molK
% difference ____________
Experiment 16
- 58 -
3.54
2.85 X 104
HEAT OF FUSION OF ICE
INTRODUCTION
When one gram of ice at standard pressure undergoes the phase change from ice
to water, it absorbs a certain amount of heat energy needed for the creation of the more
random molecular arrangement in water (crystals vs. a liquid), and this amount of heat is
known as the latent heat of fusion L f. The word latent means “hidden”. The usage stems
from the fact that during a phase change the temperature of the substance doesn’t change
as the substance is absorbing heat.
In this experiment the latent heat of fusion of ice will be determined by using the
method of mixtures and applying the conservation of energy, that is, the heat lost is equal
to the heat gained.
An ice cube placed into a measured amount of warmed water is melted, cooling the
water in the process. By observing the various temperatures before mixing, T i, and after
mixing, Tf, the heat of fusion may be calculated as follows:
HEAT LOST (in calories):
by water = (mass of water in grams)(1 cal/gramoC)(Ti - Tf)
by calorimeter = (mass of calorimeter in grams)(0.22 cal/gramoC)(Ti - Tf)
HEAT GAINED (in calories):
by melting ice cube due to phase change = (mass of ice cube in grams) L f
by ice cube after melting = (mass of ice cube in grams)(1 cal/gramoC))(Tf - 0oC)
So, from the law of conservation of energy,
Heat gained by melting ice = heat lost by water + heat lost by calorimeter
 heat gained by ice cube after melting
HEAT OF FUSION (in calories/gram):
Lf =
heat absorbed due to phase change of melting ice
mass of ice
EQUIPMENT & MATERIALS
Double wall calorimeter
Balance
Counter weight masses
Dewar flask
Electric steam generator
Ice cubes (in ice water)
Thermometer
Glycerin
Forceps
600 ml Beaker
EXPERIMENTAL PROCEDURE
1. In a beaker, mix some of the hot water from the steam generator with cold tap water
- 59 -
until a temperature of about 40oC is reached.
2. Determine the mass of the inner cup plus stirrer of the calorimeter (without the fiber
collar).
3. Fill the inner calorimeter cup about two-thirds full of the warmed water from step 1 and
then determine the mass of the cup, stirrer and water combination. The difference
between the mass measured in step 2 and step 3 is the mass of the water.
4. Replace the fiber collar on the inner cup and carefully place inner cup and water into
the outer jacket. Cover with the plastic disk, place the thermometer through the central
hole and place the stirrer through the hole beside it. Record the initial temperature, T i.
Place the ice cube into the water after wiping it with a paper towel.
5. Stir the mixture carefully, being careful not to break the thermometer. When the ice
cube has just melted, record the final temperature, T f.
6. Determine the mass of the cup, stirrer and contents. The difference between this mass
and that of step 3 is the mass of the ice cube.
7. Add the heat lost by the water and by the calorimeter, and subtract the heat gained by
the ice cube after it has melted. The result must be the heat gained by the ice cube as
it was melting. Divide this by the mass of the ice to get the heat of fusion of the ice.
8. Repeat this procedure two more times and average three suitable values.
accepted value for the heat of fusion of ice is 79.6 cal/gram.
9. Before leaving, thoroughly dry your equipment with paper towels.
LABORATORY REPORT: HEAT OF FUSION OF ICE
Data & Calculations Table:
- 60 -
The
Trial
1
Mass of inner cup and
stirrer of calorimeter
(g)
Mass of inner cup,
stirrer and water
(g)
Mass of water
(g)
Initial temperature
of water, Ti
(oC)
Final temperature
of contents, Tf
(oC)
Mass of inner cup,
stirrer and contents
(g)
Mass of ice cube
(g)
by water
2
(cal)
HEAT
LOST:
by calorimeter (cal)
HEAT
GAINED:
HEAT OF
FUSION:
by ice cube
after melting
(cal)
by melting
ice
(cal)
Lf
(cal/gram)
(cal/gram)
Average value, heat of fusion _____________________ cal/gram
% difference _____________________
Experiment 17
- 61 -
3
HEAT OF VAPORIZATION OF WATER
INTRODUCTION
When a substance undergoes a phase change from a liquid to a gas, the heat
energy goes into doing work against intermolecular forces. This heat energy is called
latent (hidden) since no temperature change is seen during the process. The accepted
value of the latent heat of vaporization of water is 540 cal/gram.
In this experiment we will use the calorimetry method of mixtures, or heat gained is
equal to heat lost, to obtain a value for this latent heat. From conservation of energy, and
assuming negligible heat loss or gain to the surroundings, we can write an equation for our
system:
HEAT GAINED: BY THE COOL WATER + CALORIMETER CUP AND STIRRER
= HEAT LOST:
BY CONDENSING STEAM + HOT CONDENSED WATER,
or symbolically: Qcool water + Qcup and stirrer= Qcondensing steam + Qhot water
so: Qcondensing steam = Qcool water + Qcup and stirrer - Qhot water
where
Qcool water = mwcw (Tf - Ti)
Qcup and stirrer = mcsccs (Tf - Ti) and
Qhot water = mscw (100oC - Tf) .
The m's and c's are masses and specific heats respectively, T f is the final temperature, and
Ti is the initial temperature of the cup contents and stirrer. The subscripts s, v, w, and cs
stand for steam, vaporization, water, and cup/stirrer, respectively. The specific heat of
water is cw = 1.00 cal/gramoC, and the specific heat of the aluminum cup and stirrer is
ccs = 0.22 cal/gramoC.
The latent heat of vaporization, Lv, is the amount of heat released by one gram of
steam at 100oC as it condenses to become one gram of liquid water at 100oC.
EQUIPMENT & MATERIALS
Double wall calorimeter
Electric steam generator
Counter weight masses
Double pan balance
Thermometer
Water trap assembly
600 ml Beaker
Dewar flask
Ice

EXPERIMENTAL PROCEDURE
- 62 -
Glycerin
Balance
Pinch clamp
1. Set up the steam generator, water trap and calorimeter as indicated in Figure 1. Do not
insert the steam line (the glass tube) into the calorimeter as yet. Fill the boiler half-full
with water and begin to heat it. The water trap is used to prevent condensed water
from entering the calorimeter.
Fig. 1.
2. Determine the mass of the inner cup plus stirrer of the calorimeter (without the fiber
collar).
3. Fill the inner cup of the calorimeter about two-thirds full of water. Cool the water to
about 15oC below ambient temperature with ice. Weigh and record the mass of the
inner calorimeter cup, stirrer and cooled water. Gently stir and make sure that all the
ice has melted and record the initial temperature Ti. Immediately do the next step.
4. The water in the boiler should be boiling freely by now. Place the fiber collar and inner
cup inside the calorimeter, and cap it with the thermometer in the center, touching the
water. Introduce the steam tube into the calorimeter water by lifting up and carefully
lowering the steam generator and water trap together, then stir continually. Open the
pinch clamp occasionally to drain any water that collects in the water trap into your sink.
When the temperature is about 15oC above ambient temperature, turn off the boiler
and wait for the steam to stop entering the water trap. Remove the steam tube, gently
stir and record the final temperature Tf.
5. Reweigh the inner cup, stirrer, water and condensed steam in order to determine the
mass of the condensed steam.
6. Calculate Qcool water, Qcup and stirrer, Qhot water and Qcondensing steam.
7. In the previous step, you calculated Qcondensing steam. Because this equals msLv, you
can divide Qcondensing steam by ms to get the latent heat of vaporization, L v.
8. Repeat this experiment twice to get an average value of L v. Compare this average
value to the accepted value of 540 cal/gram by computing the percent difference.
9. Before leaving, thoroughly dry your equipment with paper towels.
LABORATORY REPORT: HEAT OF VAPORIZATION OF WATER
- 63 -
Data & Calculations Table:
Trial
1
Mass of inner cup and
stirrer of calorimeter, mcs
(g)
Mass of inner cup,
stirrer and water
(g)
Mass of water, mw
(g)
Initial temperature
of water, Ti
(oC)
Final temperature
of contents, Tf
(oC)
Mass of inner cup,
stirrer and contents
(g)
Mass of steam, ms
(g)
by cool water
(cal)
2
(cal)
HEAT
GAINED:
by cup & stirrer (cal)
HEAT
LOST:
by hot water
(cal)
by condensing
steam
(cal)
Latent heat
of vaporization
(cal/gram)
Average value, heat of vaporization _____________________ cal/gram
% difference _____________________
Experiment 18
- 64 -
3
SPECIFIC HEAT OF METALS
INTRODUCTION
In this experiment the specific heat of two metals (copper and lead) will be
determined by the method of mixtures; heat lost is equal to heat gained. The increase in
temperature of chilled water and the decrease in temperature of the heated metal will be
used to calculate the specific heat of the metal.
EQUIPMENT & MATERIALS
Electric steam generator 
Copper shot

Double wall calorimeter
Two 100 oC thermometers
Copper cylinder
Ice cubes
Specimen holder
Vernier caliper
600 ml beaker
Bunsen burner
Balance
Mallet
Lead shot
Flint striker
Forceps
EXPERIMENTAL PROCEDURE
Part A: Specific Heats of Copper and Lead.
1. Fill the steam generator three-quarters full of water and start heating it.
2. Determine the mass of the empty specimen holder, to the nearest tenth of a gram,
and record this on the data sheet. Fill the specimen holder one-third full of copper
shot, determine this mass, and calculate the mass of the shot alone.
3. Bury the bottom of the thermometer in the copper shot inside the specimen holder,
and suspend the specimen holder in the heating water.
4. Weigh the inner cup and stirrer of the calorimeter (without the fiber collar). Pour into
the cup enough chilled water (10oC below room temperature) to make it one-third
full. If the water is not cool enough, add some ice and wait for the ice to melt. Then
weigh the inner cup, stirrer and water, and calculate the mass of the water alone.
Place the cup, stirrer and fiber collar into the outer cup. Cover with the lid. Place
the thermometer into the calorimeter through the central hole in the lid to record the
initial temperature of the water and the aluminum. Try to measure the temperatures
in this lab to the nearest tenth of a degree.
5. When the shot is heated to a temperature greater than 90oC, record the
temperature, then carefully remove the shot and cup from the steam generator.
Carefully pour the shot (no splashing, and do not break the thermometer) into the
inner calorimeter cup, and replace the lid.
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6. Stir the contents of the cup.
thermometer.
Record the highest temperature reached on the
7. When you are finished with the shot, spread it out on a paper towel to dry, then
return it to its container.
8. Repeat the entire procedure using the lead shot.
9. The heat gained by the water in calories is Q = m X c X T:
heat gained = (mass of water) X (specific heat of water) X (temperature change).
The specific heat of water is 1.00 cal/goC.
The heat gained by the aluminum calorimeter in calories is:
(mass of calorimeter) X (specific heat of aluminum) X (temperature change).
The specific heat of aluminum is 0.22 cal/goC.
The calorimeter (inner cup and stirrer) went through the same temperature change
as the water.
The heat lost by the shot must equal the heat gained by the cool water and the
calorimeter, according to the law of the conservation of energy.
The specific heat of the shot is:
c
(heat lost )
Q
.

m  T (mass of shot ) x (temperatur e change of shot )
10. Compare your experimental values of the specific heat with the accepted value by
computing the percent difference. The specific heat of lead is 0.031 cal/goC and
0.093 cal/goC for copper.
Part B: Estimating The Temperature of a Bunsen Burner Flame.
1. Determine the mass of your copper cylinder.
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As in the previous part of the
experiment, add chilled water to the inner cup of the calorimeter so that it is about
one-third full. Determine the mass of this chilled water.
2. Put the inner cup into the calorimeter and insert a thermometer through the lid.
3. Connect the Bunsen burner base to the methane tap above your sink, turn the gas
flow on, and light the top of the burner by creating sparks with the flint striker. If
necessary, strike the tap with the mallet to dislodge obstructions to the gas flow.
Adjust the air flow at the bottom of the burner to get a hot flame. Warning! Keep
the flame away from all flammable objects.
4. Hold a copper cylinder with forceps directly in the hottest part of a bunsen burner
flame for about 2 minutes. Record the temperature of the chilled water. Quickly
transfer the cylinder to the inner calorimeter cup, then turn off the gas flow to the
Bunsen burner.
5. Record the highest final temperature reached, while stirring the water with the stirrer.
6. Determine the initial temperature of the copper cylinder, using the accepted value of
Q
the specific heat of copper, T =
and Tinitial = Tfinal + T. The initial
mc
temperature should approximately equal the temperature of the flame.
7. Dry all equipment thoroughly before handing in your lab work. Be sure that your gas
taps are turned all the way off.
LABORATORY REPORT: SPECIFIC HEAT OF METALS
Data and Calculations Table for Part A:
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Composition of shot
Copper
Mass of empty specimen holder
(g)
Mass of specimen holder and shot
(g)
Mass of shot
(g)
Mass of inner cup & stirrer of calorimeter
(g)
Mass of inner cup, stirrer and water
(g)
Mass of water
(g)
Initial temperature of water in calorimeter
(oC)
Initial temperature of shot
(oC)
Final temperature of contents
(oC)
by cool water
(cal)
by calorimeter
(cal)
by shot
(cal)
HEAT GAINED:
HEAT LOST:
Specific heat of shot
(cal/goC)
Percent difference
Data and Calculations Table for Part B
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Lead
Composition of cylinder
Copper
Mass of cylinder
(g)
Mass of inner cup & stirrer of calorimeter
(g)
Mass of inner cup, stirrer and water
(g)
Mass of water
(g)
Initial temperature of water in calorimeter
(oC)
Final temperature of contents
(oC)
by cool water
(cal)
by calorimeter
(cal)
by cylinder
(cal)
HEAT GAINED:
HEAT LOST:
T
(oC)
Flame temperature
(oC)
Experiment 19
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THE COEFFICIENT OF LINEAR EXPANSION
INTRODUCTION
With rare exceptions, when materials are heated or cooled they undergo expansion
or contraction respectively. From the standpoint of materials science, this process must be
taken into account when designing structures that are subjected to temperature variations.
Otherwise, tensile or compressive stresses might develop which would destroy the
structure.
The coefficient of linear (one-dimensional) expansion is defined as the fractional
increase in length divided by the temperature change. The coefficient is found to be
almost constant over a large range of temperatures. If we call this coefficient alpha, the
definition can be stated mathematically as follows:
=
L / L
T
where L is the change in length, L is the original length, and T is the temperature change
in Celsius degrees.
In this experiment, we will determine the value of the coefficient of linear expansion
of several common metals. The length of the metal rod is measured at room temperature,
then steam is passed over the rod, causing it to expand. The amount of expansion is then
measured with a dial indicator. The coefficient of linear expansion can then be determined
using the data gathered.
EQUIPMENT & MATERIALS
Expansion apparatus
Thermometer
Rubber tubing
Electric steam generator
Glycerin
Metal rods (Cu, Al, Fe)
Meter Stick
Dial indicator
EXPERIMENTAL PROCEDURE
1. Measure the length of the rod carefully to the nearest millimeter and record this
length, L. Determine the ambient (room) temperature and record it on the data sheet.
2. Set up the apparatus as shown in Figure 1. The steam jacket for the rod has openings
for steam, water, thermometer, and rod ends. Dab the bottom of the thermometer with
glycerin if it does not slide smoothly through the stopper. Be careful not to shatter the
thermometer against the metal rod. Fill the steam generator two-thirds full with water
and start to heat it, but do not connect the steam line to the apparatus yet. Insert the
rod into the apparatus and make careful contact with the dial indicator by screwing in
the caliper so the dial indicator’s dial advances as the caliper is turned. You can
unscrew the clamp and rotate the black plastic outer dial, to zero the dial indicator.
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Steam inlet tube
Thermometer
Rod
Steam
Generator
Caliper
Dial Indicator
Steam outlet tube
To sink
Fig. 1. Linear Expansion Apparatus with Associated Equipment
3. When the steam generator is producing steam briskly, connect the steam tube to the
inlet on the apparatus. Warning! Do not get scalded or burned by the steam or the
steam generator.
4. After several minutes have passed, the temperature will be near 100 oC and the dial
indicator will have a constant reading. Record both values. L will equal the final
reading of the dial indicator minus the initial reading. Remove the black rubber top from
the steam generator to permit the apparatus to cool between experiments. Use paper
towels to insulate your hands while removing the top.
5. Compute the coefficient of linear expansion and record it on the data sheet. Compare
your values to the known values by computing the percent difference.
6. Repeat the above procedure for the other two rods.
7. Before leaving, thoroughly dry your equipment with paper towels.
Clamp
20
30
0.1 mm / div
40
10
1 mm / div
0.01 mm / div
0
8 7
90
1 2
50
6
9
0
5
1
4
2 3 60
0
80
70
10 mm / div
Fig. 2. Dial indicator
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LABORATORY REPORT: COEFFICIENT OF LINEAR EXPANSION
Ambient Temperature _________________ oC
Data and Calculations Table:
Type of Rod
Length of Rod at
ambient temperature
(m)
Initial reading of micrometer
(m)
Final reading of micrometer
(m)
Tmax
(oC)
T
(oC)
L
(m)

(oC-1)
Known
(oC-1)
Aluminum
Copper
Steel
0.000024
0.000017
0.000011
Percent difference
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