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MEASUREMENT
Experiment No. 1
PROBLEM: A.
B.
APPARATUS:
To determine the least count of a metric rule, vernier caliper and micrometer caliper.
To compare the accuracy of a micrometer caliper with that of a vernier and a metric rule
in determining volume of solid and liquid, and also gauge number of copper wires.
metric rule, vernier caliper, micrometer caliper, block of wood, aluminum cup, copper
wires and platform balance.
PROCEDURES:
I. A. Examine the metric rule. Give the value of one smallest division. Express the relation between
interval and number of division within it to give the smallest division of a metric scale.
B. Examine the vernier caliper. For each of its scales determine the length S of the smaller main
scale division, the length V of each vernier division and the number n of divisions on the vernier
scale. Give the smallest value that can be read directly from a vernier scale (often termed as least
count) Express in equation form.
C. Examine the micrometer caliper. Determine and record the value of the smallest division of the
linear scale (L), the number of revolutions of the sleeve required to advance the screw and division
on the linear scale (n), the pitch (p) of the screw, the number of divisions on the circular scale (C).
Give the least count and express in equation form.
II. A. Measure all the dimensions of block of wood with the use of metric rule and vernier caliper. Take
at least three readings of each diameter. Using the average dimensions compute the volume of the
object and compare results.
Dimension
Metric Rule
Vernier Caliper
% Diff.
Vol.
1
2
3
Ave
1
2
3
Ave.
Length
Width
Height
Volume
B. Measure the internal diameter and depth of the measuring cup. Calculate the volume. Weigh the
empty cup. Fill it with water and weigh again. The volume by weighing is taken from the
relationship, 1 cc of water weighs 1 gram.
Measuring
1
2
Ave
Weighing
1
2
Ave. % Diff. Vol.
Diameter
Empty cup
Radius
Cup w/ water
Height
Wt. of water
Volume
Volume
C. Measure the diameter of the copper wires with the use of vernier caliper, micrometer caliper and
metric rule. Consult table on properties of copper wire for the gauge number of the wires.
Gauge Number
Diameter in mm (Expt’l)
Diameter from
table
Micrometer
Vernier
Rule
EXERCISES:
1. A micrometer caliper has a zero error each that when the jaws are closed, the zero marked on the sleeve
turns 0.05 mm past the zero on the main scale in other words, the zero mark on the sleeve coincides
with the 0.05 mm mark on the main scale. If the reading of the instrument in certain in measurement is
7.82, what is the correct measurement?
2.
3.
Determine the significant figure the approximate percentage error in each of the following:
Observed value:
108;
46.2;
339; .000011120
Standard value:
105;
49.5;
336; .000011180
Tell what reading is indicated on each of the following instruments:
1.
11
12
13
100
2.
50
0
B
A
C
0
5
3.
10
5
B
C
A
4.
3
4
B
A
C
5.
0
1
2
0
3
10
6.
40
50
30
0
10
7.
5
25 div. = 1 in.
1 pitch = 1 rev.
0
10
8.
5
0
10
10 div = 1 in.
1 pitch = 1 rev.
VECTORS: GRAPHICS AND ANALYTICAL METHODS
Experiment No. 2
PROBLEM: To determine the resultant of any number of forces.
To establish the relation between resultant and equilibrant.
APPARATUS:
Masses, pulley, protractor, metric rule, string
PROCEDURE:
A. Two Forces:
1. By experiment:
Suspend equal weights on strings passing over pulleys as in fig. 1. Record the force F1, F2 and
F3. Measure the angle between the forces. What is the relation of F3 and the resultant of F1 and
F2?
2. By parallelogram
In your graphing paper, adopt a
convenient scale and draw F1 and F2
with L1. Measure accurately the
F1
F2
angle with a protractor and the length
of F1 and F2 with your metric rule.
With F1 and F2 drawn to scale as
adjacent sides, construct a parallelogram.
F3
Draw diagonal line from the common point
and measure its length. How do you compare
this with F3?
3. By Polygon:
Draw F1 to scale. Measure L1 from the head of F1 and draw F2. Connect the tail of F1 and the
head of F2. Compare this F3.
4. By Cosine Law
Using the head to tail principle make a vector diagram representing F1 and F2 acting at L1.
Compute R using R 2  F12  I22  2F1 F2 cos  . Compare the result with those obtained using
methods 1, 2, and 3. (parallelogram method can also be used)
5. By component method
Draw F1 and F2 along x and y coordinates. Determine x component of F1 and F2 and find its
given. Do the same for 7 component. Using pythagorean theorem compute for R. How do you
compare the value to the above solutions.
Trial
F1
F2
L1
F3  R Expt.
R
RA R cos R comp
1. Equal
2. Unequal
B. Three Forces
Using the same set up find the resultant of F1, F2 & F3 using polygon and component method.
What is the expected result since the body is at rest.
Trial
F1
F2
F3
L1
L2
L3
R
R comps R comp
1. Equal
2. Unequal
Questions:
1. What is the effect on the resultant of increasing the angle between the two forces.
2. Why is it more difficult to push a floor map than to pull it.
3. Three football players participating simultaneously in a tackle exert the following forces on the ball
carrier. 80 g N, 100 g 20o N of E 120 g 35o W of N. What are the magnitude and direction of a single
force that would be needed to keep the point at rest.
INITIAL VELOCITY OF PROJECTED BODY
Experiment No. 3
PROBLEM: A.
To calculate the initial velocity of projected body using
v=
R
2 Sv
g
where: V = initial velocity of projected body
R = range
Sv = vertical distance
g = gravitational acceleration, and
v =x
2k
mT
where: X = displacement of spring
K = spring constant or force constant (absolute unit)
mT= total mass of bullet, spring, rod & nut
B. To determine: a) the angle of elevation that gives the greatest range b) two possible angles that have the
same range, c) the initial velocity using the angle of projection and the range.
APPARATUS:
Improvised ballistic launcher, protractor, ball bearings, meterstick and platform balance.
PROCEDURE:
A. Horizontal Projection
1. Determine the mass of the bullets, spring, rod and nut in grams (mT).
2. Put the ballistic launcher on the table and adjust the nut in the rod to 1.5 cm displacement and compress
the spring inside the barrel by pulling the rod and letting the nut anchored at the stopper. See to it that
the end of the barrel is in line with the edge of the table so that it will be easy to measure the height of
projection.
3. Put the bullet inside the barrel and see to it that it touches the spring.
4. Launch the bullet by pressing the trigger to release the nut that is anchored at the stopper.
5. Measure the range of each projectile and tabulate results.
6. Repeat the procedure using 2.0 cm as the displacement and using the same masses of bullets as in the
first experiment.
7. Measure the height of projection from the floor to the muzzle of the barrel.
8. Compute the initial velocity for each bullet using the formula:
v =x
9.
2k
mT
Compare the result in No. 8 with the value of initial velocity derive from the height and range of
projectile.
v=
R
t
Height
Displacement (x)
1
1.
2.
3.
2
Range
3
Average
t
v = R/T
v  x 2k / mT
B. Projection at an angle
Using the same projectile and the same displacement of 1.5 cm, incline the ballistic launcher to an
angle of 15 degrees attaching this time the launcher to the protractor. Then launch the projectile and
measure the range.
Repeat procedure (1) using 30, 40, 55, and 70 degrees angle of elevation. Record and tabulate data.
Compare the initial velocity of the bullet at 1.5 cm displacement with the computed velocity using the
range and angle of projection V = Rg/sin2
Angle of Projection
1
2
Range
3
Average
v
Rg
sin 2
QUESTIONS AND PROBLEM:
1. In broad jumping does it matter how high you jump? What factors determine the span of the jump?
2. Why are the sights on a rifle adjusted when the distance to the target is changed?
3. A baseball is batted with a speed of 120 ft/sec at an angle of 37o with the ground. Find how long the
ball is in the air, how high the ball goes, how far from the plate it is caught, and the components of the
velocity of the ball 4 sec after it is hit.
FRICTION
Experiment No. 4
PROBLEM: A. To compare starting friction with sliding friction.
B. To determine the coefficient of friction of different materials.
C. To determine the factors that affect coefficient of friction.
APPARATUS: Block of wood, rubber, glass, oil, water, spring balance and set of masses.
PROCEDURE:
A. Horizontal Plane 1. Measure and record the weight of the block of wood. Place the wooden block on a smooth level
plane with the larger surface in contact with the board. With a cord, attach the hook of the spring
balance to the screw eye in the front end of the block. Place a 500-g mass on the block and
measure the minimum force necessary just to start the block in motion (Fs). Be sure to keep the
string parallel to the board. Record also the pull that keeps the box sliding slowly and steadily
(Fk). Do this several times and use the average.
2. Repeat same procedure with block on its side so that contacting surface will be smaller area.
3. Replaced 500-g mass with 1000-g mass and record necessary data.
4. Using procedure 1 record necessary data when rubber sole is tack on block of wood.
5. Lay the glass plate on the table and measure frictional force between rubber soled block and glass
plate with 500-g load on block. Repeat with film of water on the glass and then with a thin film of
oil. For this step use only the block that has been designated for use with the lubricants. Clean the
glass plate and the block carefully after each test.
6. Get the weight of Hall's carriage and place 2-kg mass on the car. Determine Fs and Fk.
Condition of Experiment
Fs
Fk
N
s
k
Wood on wood with block flat
Wood on wood with block on edge
Wood on wood with additional load
Rubber on wood
Rubber on glass
Wood in water
Wood in oil
Carriage on wood
B.
Inclined Plane
1. Place the wooden block on the friction board and elevate one end of the board so that the plane has
an angle of about 30o. With a 500-g load on the block determine the force parallel to the plane
necessary to just start the block moving up the plane. Calculate the normal force and coefficient
of static friction. Make a sketch of the set up. Compare this value with that computed from the
data of procedure 1.
2. Place the block of wood and load on one end of the board. Increase the angle slowly until the
block just begins to slide. The angle which the plane makes with the horizontal, is called the angle
of repose. Make several trials to get the average angle of repose. Determine the tangent of the
angle to get the coefficient of static friction. Measure the vertical height of the plane and the
corresponding horizontal distance. Compare the value of the ratio h/b to that of tan Θ. Compare
this value with procedure 1.
Trial

h
b
QUESTIONS AND PROBLEMS:
1. In this experiment why is it necessary that the body move with uniform velocity?
2. a) How does the coefficient of friction depend upon the normal force between the surface in contact?
b) How does it depend upon the area of the surfaces in contact?
3. How does the coefficient of static friction compare with the coefficient of kinetic friction for the same
surfaces, areas, and normal forces?
4. Reduce the relation that exists between the coefficient of friction and the limiting angle of reposes of an
object on an inclined plane?
5. Calculate the force needed to pull a mass of 20 kilograms at a uniform slow speed up a plane inclined
at angle of 30o with the horizontal, if the coefficient of kinetic friction is 0.20.
THE PENDULUM
Experiment No. 5
OBJECTIVE:
1. To determine the factors that affect the rate of vibration of a pendulum.
2. To use a pendulum to determine the local value of the acceleration of gravity.
APPARATUS:
Wooden bob; metal bob; pendulum clamp; meter stick; strong thread; stop watch.
INTRODUCTION: A simple pendulum consists of a small dense weight or bob suspended by a
from A to B and back to A again, it makes a complete vibration, or cycle. The time required for
a cycle is the period of the pendulum. The number of cycles a pendulum makes per second is
its frequency. The displacement of the pendulum is its varying distance from C. The arc Ac,
representing the maximum displacement of the bob from C is the amplitude of vibration. The
length of a simple pendulum is measured from the center of suspension to the center of gravity
of the pendulum bob.
The formula for the frequency of vibration of a pendulum is
T = 2π
L
g
where T is the time in seconds of a complete vibration, L is the length of the pendulum, and g is
the acceleration of gravity. In this experiment, pendulum data will be used to calculate the local
value of g.
PROCEDURE:
1. Effect of material. Fasten one end of a strong thread a little more than 1 m long to the wooden
pendulum bob. Clamp the other end of the thread securely in the pendulum clamp so that the pendulum
is exactly 1.00 m long. It may be necessary to let the pendulum hang over the side of the lab table in
order to get enough length. Pull the bob to one side about 0.10 m, and release it to start it swinging.
Count the number of cycles in 10.0 sec. To do this, have one partner release the bob as the other
partner, who holds the watch, gives the "Go" signal. Count the return sweep of the first cycle as "1".
The return sweep of the second cycle is counted as "2", and so on. Continue counting until the partner
holding the watch says "Stop" at the end of 10.0 sec. Repeat the experiment two more times and record
the average. Calculate the frequency of the pendulum and its period (the reciprocal of the frequency).
Repeat the experiment, using a metal bob instead of
the wooden one and record all data.
2. Effect of amplitude. Use the metal bob with the
pendulum 1.00 m long. Pull the bob 0.05 m and
count the number of cycles in 10.0 sec. Calculate
the frequency and period of the pendulum aside 0.10 m
before starting. Make a third trial, pulling the
pendulum aside 0.30 m before releasing it. Record
your results in the data table.
3. Effect of length. Using the metal bob, record
the number of cycles a pendulum 1.000 m long makes
in 10.0 sec. Calculate the period of this pendulum.
Then count the number of cycles a pendulum 0.640 m
long makes in 10.0 sec. Again calculate the period.
Repeat, using a pendulum 0.250 m long.
4. Value of g. Solve of using the pendulum formula.
Use the data of this experiment to find g,
using the precision justified by the data. Compare
n
your findings with the accepted value of g for
your locality, as provided by your instructor.
Compute your % of error in each case.
DATA:
Trial Material
(name)
Amplitude
(m)
Length
(m)
Frequency
(sec-1)
Period
(sec)
(m/sec2)
QUESTIONS:
1. How is the period of a pendulum affected by very large amplitudes? Verify your answer by
experimentation.
2. How does the mass of the string affect the period of the pendulum? How does the clamp affect the
period?
3. How would the period of an iron pendulum be affected by a magnet held under it? Verify this by
experimentation. How is this effect similar to the effect of gravity? How is it different?
4. How could a pendulum be used as an altitude indicator? What are its draw backs when used for this
purpose?
5. Would a simple pendulum work in an orbiting spacecraft?
UNIFORM CIRCULAR MOTION
Experiment No. 6
OBJECTIVE:
1. To study uniform circular motion and to compare the calculated value with observed value of
centripetal force.
2. To measure the relationship among centripetal force, mass and velocity.
APPARATUS:
Ball pen barrel or glass tube 15 cm long and at least 1 cm in outside diameter, paper
clip, rubber stopper, set of masses, meterstick, stopwatch, revolution counter, nylon fishline.
THEORY:
When a body is in uniform circular motion, the magnitude of its velocity remains the same all
throughout the circular path, but the direction of its velocity changes from time to time, i.e., its velocity is
constantly changing. Consequently, this results to an acceleration that is always directed toward the center
of the circular path, called the centripetal acceleration (ac). The value of this acceleration is given by:
2
v
ac =
R
1
where:
v = speed of the rotating body or magnitude of its velocity
R = radius of the circular path in which the body is moving.
Consider a body moving constant speed around one complete circular path of radius R during the time
interval T (period) and its speed is given by:
total distance covered
circumference of the circle
v = ----------------------------- = --------------------------------time interval
period
V=
(2)
2( π )R
T
Period of a rotating body in circular path is defined as the time required for completing one whole
revolution; frequency is defined as the number of revolutions per unit time. So, frequency is also defined as
the reciprocal of period.
f = T-1
or
v = 2( π )Rf
3
According to Newton's second law of motion, for a body to have an acceleration, there must be a net
force acting on it. In the above case, the net force acting on In the body is called the centripetal force (Fc)
which is directed toward the center of the circular path. The value of this force is given by:
2
Fc = mac = mv 2 /R = 4(π ) f 2 mR
4
Without this centripetal force, circular motion would be impossible.
PROCEDURE:
Cut a 1.5 m length of fishline and fasten one end of it securely to the rubber stopper. Fire polish the
ends of the glass tube if they are not smooth. Cover the glass tube with masking tape to prevent breakage
during the experiment. Feed the fishline through the glass tube. Fasten a 50-g mass to the free end of the
fishline. Adjust the line so that there is about 1.0 m of line between the top of the tube and the stopper.
Fasten a paper clip to the fishline just below the bottom of the tube.
Support the 50 g mass with one hand and hold the glass tube in the other. Whirl the rubber stopper by
revolving the tube. Slowly release the 50-g mass and adjust the speed of revolution so that the paper clip
stays just below the bottom of the tube. Make several trial runs before recording any data.
When you have learned how to keep the rotational velocity and position of the paper clip constant, have
a fellow student measure the speed of revolution by measuring the time required for 30 or 40 revolutions and
calculating the time of a single revolution from this data. Record the centripetal force (weight of the 50-g
mass) and velocity (calculated from the radius and period of revolution).
Repeat the procedure, but increase the centripetal force by adding 20 g to the 50-g mass. Record the
resulting data. Run a third trial, using a still larger centripetal force.
GRAPH:
Plot a graph of the data, using F as abscissa and v as ordinate. Plot a second graph of the same data,
using F as abscissa and v2 as ordinate.
If time permits, run a series of trials in which (1) the radius is kept constant, but the mass of the
whirling object changes and (2) the mass of the whirling object is kept constant, but the radius changes.
Record the appropriate data and plot graphs to show the relationships.
DATA:
Trial
m
F
r
Period
v
v2
(kg)
(m)
(sec)
(m/sec) (m/sec)2
Fo
Fe
QUESTIONS:
1. How do your graphs verify the centripetal force formula? Explain the shapes of the two curves.
2. Explain two ways in which the effect of a change in radius in this experiment can be compensated for.
Verify by experiment.
3. At what point in the swing of a pendulum does the string exert the greatest centripetal force on the bob?
Why?
4. Describe the motion of the stopper if the string is cut. Explain.
5. A man with long arms and one with short arms are swinging identical pails of water in vertical circles.
Which man must swing his pail faster in order to keep the water from falling out? Why?
SIMPLE MACHINE
Experiment No. 7
PROBLEM: A.
To determine the actual mechanical advantage and ideal mechanical advantage of
inclined plane and system of pulleys.
B. To study the principle of work as applied to simple machine.
C. To determine the efficiency of these simple machines.
APPARATUS:
Inclined plane, wooden block, pulley, wheel and axle, iron stand with clamp, set of
masses, spring balance, meterstick, string, vernier caliper and balance.
PROCEDURE:
A. Inclined Plane 1. Incline the board at an angle of about 30o. Measure the length and height of the plane.
2. Weigh the wooden block using a platform balance and place it on the plane. Add a load of 100-g
on it and attach a string on the block. Using a spring balance pull the load slowly and uniformly
up the inclined. The motion can be kept uniform by holding the balance sidewise while the little
finger slides lightly on the plane. It is well to make several trials and record the average of these
readings.
3. Increase the load placed on the block at intervals of 100-g until you can complete five trials.
4. Repeat using an angle of inclination of 45o.
5. Plot a graph of the efficiency of the inclined plane using the values of Fw as abscissa and efficiency
as ordinate.
Mechanical Advantage Principles of work
Trial
Fw
Fs
h
1
Eff.
AMA
IMA
Input
Output
B.
Wheel and Axle.
1. Wind one string several times around the axle, and the other strings several times around the
wheel in the reverse direction. Hang a 500 gram mass on the string coming from the axle. This is
the load to be lifted. Attach the spring balance to the string coming from the wheel and pull the
string with a small constant speed. Record the average reading of the spring balance as Fe.
Transfer the load to the string would on the second axle and determine the force necessary to move
the load upward with a small uniform speed. Record the force.
Trial
2.
C.
Fw
Fe
Diameter
Wheel
Axle 1
Sr
Sa
IMA
AMA
Eff.
Measure the diameter of the wheel up to the surface on which the string is round. Similarly,
measure the diameter of the two axles. Record the values.
System of Pulleys1. Arrange a single fixed pulley. Attach a 500-g load in one end of the string and pass the other end
over the pulley. Attach the hook of the spring balance on the other end. Since the balance is
upside down it is necessary to obtain the zero reading of the balance when no force is applied to
the ring. This zero reading must be subtracted from subsequent readings when the balance is used
upside down.
2. Raise the load by pulling down slowly and uniformly on the ring of the balance. When the weight
is being raised, friction makes the effort (Eup) and hence makes the effect (Edown) loss. The
average Eup and Edown give the effort without friction. This procedure of eliminating friction must
be used through the entire experiment.
3.
4.
5.
6.
With a meterstick, measure the distance (Se) that the effort (E) must move to raise the weight.
Measure also the distance (Sw) moved by the weight.
Arrange a movable pulley. Repeat the observations taken with the single fixed pulley. Since the
balance is now used in its normal position, it is not necessary to make the zero correction. Record
the readings as observed. It should be noted that in addition to raising W, it is necessary to lift the
pulley. Record therefore, the sum of W plus the weight of the pulley as the total weight lifted.
Repeat with the following combinations of pulley; a) single fixed and single movable; b) double
fixed and single movable; c) double fixed and double movable; d) triple fixed and triple movable;
e) triple fixed and quadruple movable.
Plot a graph of efficiencies of the pulley system using the number of strands supporting the load as
abscissa and efficiency as ordinate.
Trial
Fw
Fe
Sw
S
Mechanical
Advantage
AMA
IMA
No. of
string
supporting
load
Principle of the
work
Input Output
Eff.
QUESTIONS AND PROBLEMS:
1. Can you use a machine to gain both force and speed at the same time? Explain why.
2. What arrangement of pulleys does a farmer generally use in transforming hay from a wagon to a barn.
3. Give five examples of machine using the principle of wheel and axle.
4. A pulley combination which supports a load of 320 kg is 80% efficient. If a force of 80 kg is needed to
raise the loads how were the ropes arrange, and what is the actual and ideal mechanical advantage of
the simple machine. Sketch the arrangement.
5. An 80-kg crate rest on a 3.2 m long plane, which is inclined so that one end is 0.80 m higher than the
other. A force of 290 N applied parallel to the plane is required to move the crate up the entire length
of the plane at constant speed.
a) How much work is done on the system in moving the crate to the top of the plane,
b) How much total energy is added to the system?
c) What is the efficiency?
d) How much P.E. does the crate gain,
e) How much internal energy is produced?
FIRST CLASS LEVER AND THE TORQUE PRINCIPLE
Experiment No. 8
PROBLEM:
A. To determine where the weight of a lever acts
B. To verify the torque principle
C. To identify the effect of center of gravity on a lever system
APPARATUS & MATERIALS: Knife edge fulcrum, meterstick, string platform balance, set of weights,
unknown weight
PROCEDURE:
1. Slip the meterstick through the knife edge (If knife edge is not available, the stick may be
supported by means of a string). Adjust the fulcrum so that the meterstick will balance in a
horizontal position. It is important that you observe carefully the reading of this point of balance,
as all distance must be measured from it. Mark the center of gravity of your lever.
2. Suspend a 100-g mass, 40 cm from the fulcrum; then find the point at which a 200-g mass hung on
the other side of the fulcrum will exactly produce equilibrium. Draw a simple sketch recording
both force and their distances from the fulcrum and calculate the torques. Compare the clockwise
torque and counterclockwise torque.
3. Hang two masses, a 100-g mass and a 50-g mass at different points on the same side of F near the
left end of the meterstick. Now balance the lever with a single 200-g mass hung on the right side
of F. Draw a simple sketch showing the observe data and calculate the torque and torque error.
4. Hang an unknown mass at some point near the left end of the meterstick. Balance the lever with a
200-g mass. By applying torque principle, calculate the unknown mass. Weigh the unknown
mass on the platform balance and compare with your calculated value make a single sketch to
show data obtained.
5. Center of gravity is defined as the point where all the weight of an object may be considered to be
concentrated. The center of gravity of the meterstick is the point F, where it was found to balance.
The entire weight of the meterstick may therefore be considered as acting at this point. Slip the
knife edge or adjust the loop to a point about 25 cm from the end of the stick. Balance the stick
with a 200-g mass placed between the new position of the knife edge or loop and the end of the
stick. By applying the torque principle calculate the mass of the meterstick. Convert the CGS
units to MKS and using the same principle calculate the weight of the meterstick. Compare this
result with that obtained by direct weighing and by direct conversion make a simple sketch to
show data.
6. Support the meterstick at the 20-cm mark. At the left end, hang a mass of 1.0-kg mass. At the
0.01-m mark hang a 0.500-kg mass; at the 0.80 m mark a 00.200-kg mass. Find where a mass of
0.100-kg mass must be hung to produce rotational equilibrium. Using the mass of the meterstick
obtained in procedure 4, compute the distance of 100-g mass and compare it with the actual
distance. Draw a single sketch recording both the force and their distances from the fulcrum.
QUESTIONS AND PROBLEMS:
1. Why isn't the center of gravity of the meterstick necessarily at exactly the 0.50-m mark?
2. How can the weight of the meterstick be cancelled out in the experiment.
3. Are the results affected if the meterstick comes to rest in a position other than the horizontal.
Explain and verify experimentally.
4. A bigger boy should sit nearer the fulcrum of a seesaw than a small boy. Explain.
5.
Two vehicles are crossing a bridge 60 ft long. A
passenger car weighing 3 x 103 lb is 10 ft from one end. A truck weighing 9 x 103 lb is 20 ft from the same
end. If the bridge is symmetrical with respect to the center and weighs 50 tons, what are the forces on the
two supports at the ends of the bridge?
MASS DENSITY OF SUBSTANCE
EXPERIMENT No. 9
PROBLEM: To determine the density of some solids and liquids by direct measurement of mass and
volume.
APPARATUS: Platform balance, block of wood, cylindrical object, spherical object, graduates cylinder,
irregular solids, thread, thermometer, pycnometer, burette, beaker, burst clamps with
stand, vernier caliper, alcohol and water.
PROCEDURE:
1. Regular solids - measure the dimensions of the regular solids with vernier caliper. Take several
readings at different positions and estimate all readings to the closet possible fraction. Record the
shape and composition of the solid and compute the volume.
Place the platform balance in a level surface. See that all the riders are at zero. Adjust the
screw until the pans are in equilibrium or until the pointers at zero. Place the object on the left pan and
balance it with weight on the right pan. Adjust the rider by moving it to the right. Add the reading on
the scale to the weights on the right pan. The sum is the mass of the object.
Materials Length
2.
Height Diameter
Mass
Volume
Density
Expt’l
Density
Accept.
Error
Irregular solids - find the mass of each irregular solid to the nearest tenth of a gram using the platform
balance. Tie a piece of thread about 30 cm long to the solid. Fill a graduated cylinder about two-fifths
full of water and read the heights of the water level as exactly as possible. Lower the irregular solids
into the water in the cylinder. Because matter has the property of impenetrability, the solid displace a
volume of water equal to its own volume. Take a second reading of the water level. Calculate its mass
density. Knowing its density identify the irregular solids used by comparing its value from a handbook.
Specimen
3.
Width
Mass
Initial
Reading
Final
Volume Density Density
Reading
(Expt’l.) Accepted
Name
of
Subs
%
error
Liquid - Determine the mass of pycnometer (including cover). Clamp a burette in a vertical position
and fill it with water to a height of about two centimeters above the zero mark. Then open stop cock to
draw enough water into the beaker to bring the water level below the zero mark into the graduated
portion of the burette. This method of filing and adjusting the liquid level in the burette should expel in
the burette all the air from the tip of the burette. (If not all the air has been expelled from the burette
tip; it will be necessary to let more water runs through the tip to expel the air. Then water should be
added to the burette, so that it contains at least 40 ml.)
Record the initial reading of the burette to the nearest tenth of a milliliter if the masses are
determined with a platform balance with a sensitivity of 0.1 g. Slowly draw off about 40 ml of water
into the psychometer. Record the final burette reading to the same precision as you did the initial
reading. Find the mass of both pycnometer and water. By subtraction, find the mass of the volume of
water used. Refill the burette, the repeat the experiment using 45 ml of water for the second trial. For
each trial, calculate the mass in grams of one cubic centimeter of water. Take the temperature of the
water and lock up in Appendix to find the accepted mass of one cubic centimeter of water at the
observed temperature.
4.
Drain the burette with water and rinse it several times with small portion of alcohol. Then fill the
burette with alcohol. Repeat the experiment with two alcohol samples of appropriate volume, and
determine its mass density. Consult a handbook to find the accepted value of the mass density of
alcohol at the observed temperature.
Liquid Used
Water
1
Alcohol
2
1
2
Burette, Reading Initial
Burette, Reading Final
Volume
Mass of psychometer
Mass of pychometer
Liquid
Mass Density of liquid (Expt’l)
Temperature
Mass Density of Liquid Accepted
% of error
QUESTIONS AND PROBLEMS:
1. Suppose that, by mistake, the object to the weighed were placed on the right hand pan of the balance,
and then weighed by placing weights on the left-hand pan and adjusting the rider. Would the weight
thus obtained be too large or too small? Explain.
2. In reading, the level of water inside a graduated cylinder should we not give an allowance for the
curvature of the water surface. What do you call this curvature and what causes it.
3. How could the volume of a cork be determined by water displacement?
4. A Romblon marble slab weighing 1280 pounds is 8 ft long and 6 ft wide. How thick is the slab?
Density of marble is 160 pounds per cubic foot.
5. Three fifths of the surface of the earth is covered by oceans with an average depth of 3 km. If the
diameter of the earth is 13,000 Km and the density of salt water is 103 kg/m3, what is the mass of the
ocean?
6. A cylindrical log with a length and diameter of 9 m and 75 cm, respectively, is allowed to float
vertically on the water having a density of 1 gm/cc. Determine the volume of water displaced and the
remaining height of the log that is not submerged in water if its mass is 3650 kg. Calculate also the
force required in order to keep the log just at water level
SPEED OF SOUND
Experiment No. ___10___
OBJECTIVE:
1. To determine the best resonant length of a closed tube for sounds of known frequency.
2. To determine the speed of sound from the wavelengths and frequencies of several sounds.
THEORY: Resonance, or sympathetic vibration, occurs when the natural vibration rates
of
two
objects are the same. The air column in a closed glass tube produces its
best resonance when it is
approximately one-fourth as long as the wavelength of the sound which it reinforces. For example, a tube
one meter long produces resonance
with a sound wave which is about four meters long. A small
correction in wavelength
must be made for the internal diameter of tube. The wavelength of the sound
may be calculated from the resonant length of the tube by the formula λ = 4(1 + 0.4d), where λ is the
wavelength, 1 is the length of the closed tube, and d is the diameter of the tube.
In this experiment the best resonant length of a closed tube will be determined. From this length and
the diameter of the tube, the wavelength of the sound will be calculated. The speed of sound will then be
calculated from the formula v = fλ, where v is the speed of sound, f is the frequency, and λ is the
wavelength.
APPARATUS:
Tuning forks of known frequency, glass tube, 2.5 cm to 4.0 cm in diameter and at least
40 cm long, tall cylinder, thermometer, meter stick, tuning fork hammer, large rubber stopper.
PROCEDURE:
Hold the tube vertically in a cylinder nearly full of water, as shown in the figure. Make a tuning fork vibrate
by holding it by the shank and striking it with the tuning fork hammer or striking it with a large rubber
stopper.
Do not strike the tuning fork on the table top or other hard surface. As you hold the vibrating tuning
fork over the end of the tube, move the glass tube slowly up or down in the water of the graduate cylinder to
locate the position of the loudest sound called the resonance. Then hold the glass tube firmly while another
student measures the length of the tube from its top to the water surface inside the tube. This length should
be recorded to the nearest thousandth of a meter. Carefully measure the internal diameter of the tube to the
nearest thousandths of a meter also. Use the thermometer to determine the temperature of the air inside the
tube in degrees Celsius. A second and third trial should be taken using forks of different frequencies.
For each fork compute the wavelength of the sound produced from the resonant length of the tube.
Also calculate the wavelength from the mark frequency of the fork and the speed of sound at the temperature
inside the tube. Find the differences between these values. Compute the accepted value for the speed of
sound using the to relation V = 331.45 m/s + toC (.61) m/s/oC.
Data:
Trial
Length
Diameter Waveof
the of tube length
tube (m) (m)
(m)
Frequency
(sec-1)
TemSpeed of Sound
perature ExperiAccepo
( C)
mental
ted
(m/sec)
(m/sec)
% error
QUESTIONS:
1.
Through what fraction of a vibration has the prong of a tuning fork moved while the sound wave
traveled down to the water surface and was reflected back up to the fork again?
2.
If a longer glass tube were available, would it be possible to find another position where resonance is
produced? Explain.
3.
How could you modify this experiment to determine whether the water vapor inside the tube affects the
results?
4.
How does the amplitude of vibration affect the data? Verify your answer by experimentation.
5.
How could you modify the experiment to find the resonant length of an open pipe?